but can you show that?
#help-10
brazen gorge
tulip sky
oh so its saying that attempting to show it is dumb?
i thought it was saying attempting to show that, is futile because even if it is shown it wouldn't prove the original inequality
brazen gorge
it says "unfortunately this is false", where this is the inequality 3abc >= whatever
brazen gorge
i thought it was saying attempting to show that, is futile because even if it is...
yeah it's weird
brazen gorge
it says "unfortunately __this__ is false", where __this__ is the inequality 3abc...
but that's what they are trying to say
so when you realize that the inequality is false, even proving that a^3 + b^3 + c^3 >= 3abc is not to much use either
fathom flicker
obtuse pebbleBOT
fathom flicker
Working on this problem. I thought to let X be a random variable that represents the amount of distinct prizes. So we can write X=x1+x2+…x5 where xi are random variables which take on 0 if we don’t have the ith prize and 1 if we do.
Then by linearity do expectation we’d have the expected value of X would be the expected value of x1 + …. + The expected value of x5
My issue is, I’m getting stuck computing the expected value of xi after n boxes
Could anyone help?
mortal kelp
Could anyone help?
so in your set up x1 is the event that you obtain the first prize
if you win the 1st prize with probability p, then you don't win with probability (1-p), and these are the only possible outcomes
to find expected value you take the sum of the probabilities of each outcome multiplied by their values
mortal kelp
yeah!
fathom flicker
But what about n=2 and onward? I was expecting somehting to come out in terms of the amount of boxes
That’s where I was getting stuck
If that makes sense
mortal kelp
now each prize you get from a cereal box is independent and uniformly random
and in order to find the probability you win prize 1, you can take 1- the probability you dont win prize 1
fathom flicker
The probability we don’t win prize 1 is (4/5)^(n) for n draws?
So the probability we do win it would be 1-(4/5)^(n) ?
fathom flicker
So then we have for the expected value, 1 * the probability we do win it (above) + 0 * the probability we don’t (doesn’t matter because 0)
So the expected value is exactly just the probability that we do win it
mortal kelp
yep!
mortal kelp
and as a good sanity check you also have that when n=1 this gives the 0.2 you would hope for
fathom flicker
Yeah
So then
Final answer would be
The expected value after n draws is
5(1-(4/5)^(n))
mortal kelp
fathom flicker
Awesome tysm
Now I have to do buffons needle problem
But I don’t think I need help with that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
junior zephyr
How does the median of a sequence differ from that of a random variable
obtuse pebbleBOT
How does the median of a sequence differ from that of a random variable
junior zephyr
Why is median of a r.v. only defined for probability distributions
Cant it be abstracted for other distributions
kind hawk
what kind of other distributions do you mean?
just intuitively, median means 50% is lower and 50% is higher. the probability aspect is very fundamental for that
obtuse pebbleBOT
@junior zephyr Has your question been resolved?
dusky totem
I am trying to solve this problem. I have to calculate the integral of a vector field over the curve C which is the intersection between the cylinder x^2+y^2=4 and z=x^2. I have tried applying Stokes theorem and calculated the curl and gotten [0, 0, 2]. However I don't know how to get the normal vector n-hat and dS. Do I have to find the gradient of z = x^2?
The solution says I should get n-het dS = [2x, 0, 1]dxdy
obtuse pebbleBOT
I am trying to solve this problem. I have to calculate the integral of a vector ...
dusky totem
obtuse pebbleBOT
@dusky totem Has your question been resolved?
dusky totem
<@&286206848099549185>
obtuse pebbleBOT
@dusky totem Has your question been resolved?
obtuse pebbleBOT
@dusky totem Has your question been resolved?
dusky totem
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tawdry elbow
Can anyone help me with this exercise, i need to do 1.26
obtuse pebbleBOT
Can anyone help me with this exercise, i need to do 1.26
tawdry elbow
Here's what i did up untul now
I didn't get the same answer as the book
?
<@&286206848099549185>
tawdry elbow
<@&286206848099549185>
obtuse pebbleBOT
@tawdry elbow Has your question been resolved?
tawdry elbow
<@&286206848099549185>
obtuse pebbleBOT
@tawdry elbow Has your question been resolved?
north anchor
help me with a graph
obtuse pebbleBOT
help me with a graph
north anchor
what is the adjacency matrix?
[ 0 2 1 1]
[2 0 2 1]
[1 2 0 1]
[1 1 1 0] I am alright?
obtuse pebbleBOT
@north anchor Has your question been resolved?
vivid nest
E + A =
obtuse pebbleBOT
@north anchor Has your question been resolved?
obtuse pebbleBOT
@north anchor Has your question been resolved?
supple monolith
obtuse pebbleBOT
river badger
Uh, what is S in that drawing?
It isn't very visible.
Could you maybe draw it more clearer?
river badger
Or whatever it's called in english
Just say whenever.
obtuse pebbleBOT
@supple monolith Has your question been resolved?
supple monolith
I solved it already I did some research
sand wren
obtuse pebbleBOT
sand wren
Idk why but the only thing I end up getting is A a subset of B
mortal kelp
getting that A is a subset of B is a good start
can you use the fact that $A\Delta B=B$ and $A\subseteq B$ to show that $A$ is empty?
warm shaleBOT
Willow
mortal kelp
yep!
sand wren
thanks!
mortal kelp
In particular that last step is only true because A is a subset of B
rugged locust
Hi, is there anyone who knows how to calculate limit of this function when x approaches ∞
obtuse pebbleBOT
Hi, is there anyone who knows how to calculate limit of this function when x app...
@rugged locust Has your question been resolved?
wispy wadi
your limit is the same as limit of sin²(x)/(x(2^x-1)) when x goes to 0
sin²(x) ~ x² around 0 and 2^x-1 ~ ln(2)x
low basalt
How do i find x
obtuse pebbleBOT
How do i find x
smoky vigil
just to verify, the equation is: $\log_{7}(x^{2})=(\log_{7}(x))^{2}$
warm shaleBOT
Moosey
smoky vigil
Right?
low basalt
Yes
smoky vigil
well, you can apply a log property, and do a subtitution to make it into a quadratic :)
minor gate
Like 2u = u^2? u=log7 x
smoky vigil
and you can factor this
then you sub back in for u and solve for the individual roots (one of them may be extraneous,maybe not, always good to check)
obtuse pebbleBOT
@cosmic veldt Has your question been resolved?
robust raven
read the stokes theorem
outer trench
I'm confused why this is not the correct parameterization for this ellipsoid
obtuse pebbleBOT
I'm confused why this is not the correct parameterization for this ellipsoid
@outer trench Has your question been resolved?
twilit gazelle
I need to determine the attributes of this relation (reflexivity, symetry, transivity)
obtuse pebbleBOT
I need to determine the attributes of this relation (reflexivity, symetry, trans...
twilit gazelle
I say, the relation is reflexive, therefore not asymetric. It is not symetric. It is antisymetric and transitive.
Am I correct ?
fossil crag
Can you show your proof for antisymmetry?
twilit gazelle
Yes, one sec..
fossil crag
And transitivity as well
twilit gazelle
fossil crag
Its not ? What would be a proof then ?
Well it's a number of logical steps that start from your hypotheses (here, "let x1 and x2 such that 6x1 >= 5x2 and...") and reach the conclusion you want ("x1=x2") that are all well justified
An example of valid proof :
"Suppose x² - 4 = 0.
Then (x-4)(x+4) = 0
Then x-4=0 or x+4 = 0
Then x=4 or x=-4"
In this example, the reasoning between every step is clear and well justified.
An example of invalid proof :
"Suppose f(x) = f(y).
Then x = y"
In this example, there is no logical reason or justification between lines, which makes the proof invalid
A consequence of not justifying every step is that you may reach false conclusions
In your case, you may have asserted something that isn't true...
twilit gazelle
Ok let me see...
Soooooo, for anti symetry, if I take 10 for m and 9 for n, then it is 6×10 is greater or equal to 5×9 AND 6×9 is greater or equal to 5×10, yet m =/= n
So it is not anti symetric
Let me check transivity again...
fossil crag
Soooooo, for anti symetry, if I take 10 for m and 9 for n, then it is 6×10 is gr...
Yep
twilit gazelle
This is how my prof solved anther exercise though.
Is that a proof ?
But it is transitive. I cannot kmagine how it is not
fossil crag
This is how my prof solved anther exercise though.
Damn your prof doesn't know how to prove stuff
Unless you already know that if z1 >= z2 and z1 <= z2 implies that z1=z2 then there's no real point
twilit gazelle
Ok, I am watching math sorcerer atm to learn a bit about proofs. Thanks fot your help
.close
obtuse pebbleBOT
fossil crag
But it is transitive. I cannot kmagine how it is not
Small warning on this tho
Try 5 6 7
twilit gazelle
Ok, I will
obtuse pebbleBOT
Available help channel!
worldly arrow
Does anyone know how to do this?
obtuse pebbleBOT
Does anyone know how to do this?
worldly arrow
I’m not sure how to explain it
junior bobcat
Does anyone know how to do this?
obtuse pebbleBOT
@worldly arrow Has your question been resolved?
ripe mango
obtuse pebbleBOT
ripe mango
i need help ;-;
shadow flame
what's the question?
latent walrus
polynomial
ripe mango
ye
shadow flame
is it asking to find the polynomial
latent walrus
what degree do you think said polynomial will be?
ripe mango
degree?
shadow flame
the highest power in the equation
latent walrus
highest power of x
ripe mango
-3?
latent walrus
why -?
latent walrus
whats that supposed to mean?
shadow flame
like for x^2 + 2x + 3 = 0, the degree would be 2
because 2 is the highest power of x in the given polynomial
ripe mango
idk if were on the same page
but like the teacher gave me an example
for another graph is it like the same thing yall are saying?
shadow flame
we're askign something different so i guess the teacher didnt teach about highest degree
shadow flame
ok so what you can start with is the "zeroes" of the function, meaning where the curve either passes through or touches the x-axis
at what x-values does it do so ?
latent walrus
you just wrote a non-zero y value
shadow flame
that's a point that will be used but it doesnt touch the x-axis
maybe it'd be easier if you think about it where y=0
ripe mango
is it possible if u guys just explain step by step
on how to get the answer
but like not involve me like answering
and ill jst like
shadow flame
i can try just ask questions to clarify or whatever when u need
ripe mango
kk
shadow flame
so to determine what the polynomial is, it's good to look at where the curve either touches or passes through the x-axis
on the graph you've given, it looks like it does that at x=-2 and x=0, right?
ripe mango
ye
shadow flame
ok so what that means is that when x=-2 or x=0, f(x)=0
so we can start setting up the polynomial to be a(x+2)^2(x-0)=y
and (x+2)^2 just means (x+2) squared
which we have because it only touches the x-axis so it's called a "double zero" and is squared
shadow flame
so we can start setting up the polynomial to be a(x+2)^2(x-0)=y
and this is how we set it up because you can see that if we put either -2 or 0 for x, the function will equal 0
the "a" is meant to be some constant (like a fraction or other number that doesnt have variables) that will may shift the function in some way
we can find what "a" is equal to by using some of the other points like (-1,2) that you mentioned earlier
shadow flame
so we can start setting up the polynomial to be a(x+2)^2(x-0)=y
if we plug those two numbers into x and y in the function i'm replying to, we'll get a(-1+2)^2(-1-0)=2
we can simplify into a(-3)^2(-1)=2
simplified: -9a = 2
so a = -2/9
shadow flame
so we can start setting up the polynomial to be a(x+2)^2(x-0)=y
we take this "a" value and plug it back into the function to (hopefully) get the right equation
ripe mango
oh
ripe mango
ok so what that means is that when x=-2 or x=0, f(x)=0
why is it like f(x) tho?
like when x=-2 or x=0
shadow flame
f(x) just means the "y-value" of the function at the point "x"
f(x)=y
so f(-2) is the "y-value" of the function at x=-2
ripe mango
ok ty i think i get it now
shadow flame
sorry if i couldn't explain well enough, good luck 🙏
past cloud
This is from a midterm in 2020. I also have the solution that someone did but I don't even know where to start.
obtuse pebbleBOT
This is from a midterm in 2020. I also have the solution that someone did but I ...
past cloud
Task 1. Write an example of the function f : R2 —>Y R2 that has no limit at the point (0, 1) and prove it in two ways: Straight from the definition of limit. Using Heine's characterization.
obtuse pebbleBOT
@past cloud Has your question been resolved?
timid silo
How would you verify if an identity is valid through desmos
obtuse pebbleBOT
How would you verify if an identity is valid through desmos
timid silo
or just simply if two things are equal
^ in terms of identities of course
was told it was possible but not sure how
daring rock
I mean it's not very rigorous but you can graph both expressions and see if they're the same graph
if you graph y = sin^2 x + cos^2 x
and y = 1
you'll see they're the same
for example
timid silo
if you graph y = sin^2 x + cos^2 x
and y = 1
you'll see they're the same
I'm getting this error message for some reason
below is the identity I have to have
above is what I'm at so far
empty cypress
well they surely arent, because they dont even have the same variables in them
timid silo
I just algebraically did a lot to it
upbeat plinth
line 2 isnt an equation
upbeat plinth
well yeah thats why it works
timid silo
upbeat plinth
what identity are you doing
timid silo
hm, guessing they're not equal then
timid silo
what identity are you doing
it's supposed to be $sin(x+y)sin(x-y)=cos^2y-cos^2x$
warm shaleBOT
mj
timid silo
just tracing back my steps because I'm getting stuck at a point, this seems to be it
or the thing I had before
empty cypress
,w sin(x+y)sin(x-y)=cos^2y-cos^2x
upbeat plinth
i plotted each side but replaced y with y_0, and set y_0 as a slider
warm shaleBOT
upbeat plinth
timid silo
desmos is neat
alright my simplification was correct in that case
just graphing and checking lol
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
steady scarab
after getting to this point how do i solve the inequality?
obtuse pebbleBOT
after getting to this point how do i solve the inequality?
soft patrol
steady scarab
what about the second solution
heavy depot
interval form
steady scarab
btw the key says the answer is -inf, -9) U (-1, inf)
oh wait
hold up i didn’t realize it was that simple
thanks
.close
slow prawn
obtuse pebbleBOT
slow prawn
Where do I even start with this
I need to find the derivative
I’m thinking of
Ln
Both sides
minor furnace
you can also try product rule
and you'll have to use chain at one point with the e term
teal turret
teal turret
you can also try product rule
Ln both sides is cleaner
minor furnace
you can just factor out the coefficient 1/2sqrt(pi)
and then differentiate x^2 e^-x^2
minor furnace
$\frac{1}{2\sqrt{\pi}}(x^2e^{-x^2})$
warm shaleBOT
Triaxyz
minor furnace
$\frac{d}{dx}(\frac{1}{2\sqrt{\pi}}(x^2e^{-x^2}))=\frac{1}{2\sqrt{\pi}}\frac{d}{dx}(x^2e^{-x^2})$
warm shaleBOT
Triaxyz
minor furnace
$=\frac{1}{2\sqrt{\pi}}[2xe^{-x^2} + x^{2}\frac{d}{dx}(e^{-x^2})]$
warm shaleBOT
Triaxyz
chrome relic
how to do this
i cant really see how to appraoch
i mean i did the basic stuffs such as equations sum of the roots to 2
taking their products to b , if there is atleast one complex roots then it must be in conjugate pairs
moreover there must be at least one complex roots or otherwise the sum of the roots would be 0 producing a contradiction and so
also using the given relation to get something
but nothing is working,
obtuse pebbleBOT
how to do this
i cant really see how to appraoch
i mean i did the basic stuffs...
bold siren
so i need a hand on how to work something out
obtuse pebbleBOT
so i need a hand on how to work something out
bold siren
and im unsure if im going the right way about it
what would be the way you should go about doing this?
calculate a first?
lyric crane
law of cosines then law of sines
well you could use law of cosines both times but law of sines is faster
bold siren
all good
lyric crane
yes, and then you solve for cos(A) then take inverse cos
lyric crane
which gets you this
lyric crane
so for that equasion it would need to be found yes?
yes
you need to square the lengths
to use the rule
runic void
obtuse pebbleBOT
runic void
Can you explain how we are able to determine the multiplicity of a root from the taylor form centered at the root?
I don't get what they are trying to explain
gotcha mb
.close
flat fossil
I don't even know where to begin with this story problem:
The top three prices for works of art sold at auction in 2013 totaled $306.6 million. These three works of art were a sculpture, a painting, and a photograph. The selling price of the painting was $50.4 million more than that of the photograph. Together, the painting and the photograph sold for $21.8 million more than the sculpture. What was the selling price of each work?
obtuse pebbleBOT
I don't even know where to begin with this story problem:
The top three prices ...
warm shaleBOT
Floopschrute
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
polar fossil
assign variables to the price of each thing
s for sculpture
p for painting
f for fotograph
obtuse pebbleBOT
@flat fossil Has your question been resolved?
oak marlin
obtuse pebbleBOT
oak marlin
I'm not sure how to approach (b).
I think M(R) is the set of 2x2 matrices with real elements but also not sure on that
kind hawk
well we dont know what notation your course uses. that said 2x2 real matrices would of course make sense cause intuitively thats also four copies of R put together
some of the important elements of rings are the 1, the units and the zero divisors. maybe try doing something with those
blissful bane
How do i factor $1+z + z^2 + z^3 + z^4 + z^5 + z^6$?
obtuse pebbleBOT
How do i factor $1+z + z^2 + z^3 + z^4 + z^5 + z^6$?
warm shaleBOT
Dubs
inland matrix
You're adding the terms that are in a GP
Are you familiar with the sum of terms in a GP formula?
blissful bane
yes, this will be $\frac{z^7-1}{z-1}$ ?
blissful bane
there are 7 terms in the sequence
inland matrix
Yes
inland matrix
Ye
warm shaleBOT
Dubs
inland matrix
Is that how you're supposed to factorise it?
Coz one of the terms is in the denominator
blissful bane
i'm supposed to deflation
idk if you are fimilar with the term, like write it as product of factors of zeros
inland matrix
Oh
inland matrix
Yeah
blissful bane
Is x^2 + 2x + 1 = (x+1)(x+1) counted as deflation?
(x+1)^2
inland matrix
But the denominator can't be 0 can it
blissful bane
i mean p(1) isn't zero right?
inland matrix
Nope
blissful bane
right, so ill only get 6 solutions
inland matrix
Hmm
blissful bane
so exactly 6 solutions
inland matrix
Yes
inland matrix
Yup
blissful bane
let me try it
inland matrix
Alright
blissful bane
the 7th roots of unity are going to be in polar i guess
inland matrix
They'll be of the form e^(2pi/n)
blissful bane
yes
blissful bane
$1=e^{(2 \pi +k)i}$
warm shaleBOT
Dubs
blissful bane
$1^{1/7} =e^{\frac{(2 \pi k)}{7}i}$
blissful bane
for each k ranging from 0 to 6 i get a root right?
warm shaleBOT
Dubs
blissful bane
roots are; 1, $e^{\frac{(2 \pi)}{7}i}, e^{\frac{(4 \pi)}{7}i}, e^{\frac{(6 \pi)}{7}i}, e^{\frac{(8 \pi)}{7}i}, e^{\frac{(10 \pi)}{7}i}, e^{\frac{(12 \pi)}{7}i}$
inland matrix
First and last are the same
blissful bane
right
warm shaleBOT
Dubs
blissful bane
so i can just multiply all of them and get the factored form?
inland matrix
so i can just multiply all of them and get the factored form?
And yes, i think you can
inland matrix
Coz the numerator is 0
blissful bane
And yes, i think you can
all of them defintely have multiplicity 1 right?
inland matrix
Coz the numerator is 0
Which makes the original expression 0
inland matrix
all of them defintely have multiplicity 1 right?
I'm not sure what that means
inland matrix
Np
blissful bane
have a great day
inland matrix
You too
obtuse pebbleBOT
@blissful bane Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
mint nebula
In a rectangle, a parallel is drawn to one of the sides, which divides it into two rectangles with areas of 12cm2 and 36cm2, respectively. Find the maximum perimeter of the original rectangle, knowing that one of the two rectangles is a square.
My answer was 20sqrt(3)
obtuse pebbleBOT
In a rectangle, a parallel is drawn to one of the sides, which divides it into t...
mint nebula
And i'm not sure if it's correct or not.
obtuse pebbleBOT
@mint nebula Has your question been resolved?
fathom flicker
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
short ore
In a rectangle, a parallel is drawn to one of the sides, which divides it into t...
Well there are 2 cases
Either the 12 part is the square
Or the 36 part
If 36 is the square
That means one side length of the rectangle is 6
And since the 12 rectangle also has a side length of 6 as it is a part of the same bigger rectangle
The other side length is 2 + 6
Which is 8
short ore
If 36 is the square
So the perimeter for this case is 12 + 16 = 28
Now if 12 is the square
Following the same logic one side length is the square root of 12 and the other is 4(sqrt(12))
So we double them and add together to get 10(sqrt(12))
Sqrt(12) = 2(sqrt(3))
short ore
So we double them and add together to get 10(sqrt(12))
So this is 20(sqrt(3))
short ore
So now all that’s left to determine is whether 28 or 20(sqrt(3)) is bigger
You can use a calc but I can already tell that your answer is right
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
celest musk
Please can somebody help D:
obtuse pebbleBOT
Please can somebody help D:
celest musk
Let f : A → B be a surjective map. Prove that there exists a subset C ⊂ A of its domain such that the restriction f|C of the map f to C is a bijection C → B
I can take a singleton subset in A
But how to extend it to all elements in A?
sweet lichen
I feel like Choice is needed here. Have you already encountered that?
celest musk
No never
But my professor is famous for testing us on things we haven't studied :/
So it might be the solution
sweet lichen
But my professor is famous for testing us on things we haven't studied :/
Ohh... assume for now that A and B are finite or even small, like maybe B = 3 and A is something larger (to make a surjective map possible). How would you construct C?
celest musk
Ohh... assume for now that A and B are finite or even small, like maybe B = 3 an...
Make C with three elements each mapped to each element of B
So it Is biijective
sweet lichen
Yes. C must have 3 elements. But we need to get the elements from A so that C ⊂ A is satisfied. It's good to draw this.
"Choice" is a hint, but another hint is that in the definition of surjective map ($\forall y \in B \exists x \in A: y = f(x)$), there can be many $x\in A$.
warm shaleBOT
poypoyan
celest musk
Yes. C must have 3 elements. But we need to get the elements from A so that C ⊂ ...
Like this?
sweet lichen
Yep, but you did not have the mapping f that is surjective. Draw an f first.
celest musk
Oh wait
sweet lichen
Also, is that really $C \subset A$, or $C \subseteq A$?
warm shaleBOT
poypoyan
celest musk
sweet lichen
No. As in for each point in A, draw a line to a point in B.
celest musk
Also, is that really $C \subset A$, or $C \subseteq A$?
Well the exercise says only $C \subset A$ and not necessarily $C \subseteq A$ (?)
warm shaleBOT
Tommy
sweet lichen
Well the exercise says only $C \subset A$ and not necessarily $C \subseteq A$ (...
Ok, maybe we have difference in notation, but can $C$ be equal to $A$ and still satisfy $C \subset A$?
warm shaleBOT
poypoyan
celest musk
celest musk
Ok, maybe we have difference in notation, but can $C$ be equal to $A$ and still ...
In my course if C is equal to A $C \subseteq A$ but not $C \subset A$
warm shaleBOT
Tommy
sweet lichen
In my course if C is equal to A $C \subseteq A$ but not $C \subset A$
Then if f is also injective, then we cannot find C because we are forced to set C = A, which does not satisfy $C \subset A$. Let's set this aside by letting f be not injective.
warm shaleBOT
poypoyan
sweet lichen
Good, notice the bottom point in B. There are 2 points in A pointing to it, then you chose a point among the 2, and put it in C.
sweet lichen
f is not injective in this chat for now. What I described in my last reply is the gist of "choice": you can choose because there exist a set of elements to choose from (in our case, this is guaranteed by the $\exists x \in A$ part of the definition of surjective map). I hope this helps, then you just write this construction of C "formally".
warm shaleBOT
poypoyan
celest musk
f is not injective in this chat for now. What I described in my last reply is th...
Thank you again 🙂
.close
long hedge
for 272
warm shaleBOT
putridplanet
long hedge
$\int \sqrt{1-u} U^{10} \frac{du}{-2t}$
warm shaleBOT
putridplanet
obtuse pebbleBOT
Available help channel!
dull void
can you explain me how to solve this derivaite
$\frac{2}{x} - \frac{1}{x^2}$
warm shaleBOT
odokawa
final thunder
use linearlity of deriative you can just find the derivatives of each term seprately
,, \red{\diff{}{x} \p{\df2x}} - \blue{\diff{}{x} \p{\df{1}{x^2}}}
warm shaleBOT
Pure
final thunder
and then using exponent rules you can write this as
,, \red{\diff{}{x} \p{2x^{-1}}} - \blue{\diff{}{x} \p{x^{-2}}}
warm shaleBOT
Pure
final thunder
after that you can just use normal power rule of derivative
dull void
hiii
final thunder
dull void
<a:HelloLuv:892943811041439794>
are you busy
final thunder
ill need to go in 5 mins
final thunder
v and u?
ruby path
You don't really need the product rule
ruby path
Only the regular power rule
dull void
what else i have to do
sage dagger
just differentiate them separately
dull void
just differentiate them separately
what does differentiate means
ruby path
Use $\dv{x} x^n = nx^{n - 1}$
warm shaleBOT
jan Nejon
sage dagger
what does differentiate means
to take the derivative
final thunder
**jan Nejon**
use this
you have
,, \red{\diff{}{x} \p{2x^{-1}}} - \blue{\diff{}{x} \p{x^{-2}}}
warm shaleBOT
Pure
final thunder
okay...
ruby path
We have failed you
sage dagger
sage dagger
jan
dull void
would understand yo u
sage dagger
its time to take away ur helpful role
dull void
.close
obtuse pebbleBOT
sage dagger
give me a negative helpful role too
obtuse pebbleBOT
Available help channel!
vernal pagoda
Hello
vernal pagoda
Can I get help with principal of mathematical induction
The problem is about an atm machine
A weird AM (Automated Teller Machine) is designed to cater to the new denomination of money bills in the (country), namely, the 300 bill This machine can only dispense bills in 300 and 500 denomination bills. The good thing about this machine is it does not run out of cash
You are to:
- Prove by the principle of mathematical nduction that any amount of money greater than or equal to P800 can be withdrawn from the machine in multiples of hundreds; that is, P900, P1300, P20 000, F25 300, etc
Show that the base case is true. This amount is P800
Show that another cates true for some value k. Show that the case after k which is k+ 1 is also true,
It's a bit difficult so I was hoping I could find help on this!
obtuse pebbleBOT
@vernal pagoda Has your question been resolved?
vernal pagoda
<@&286206848099549185>
tough hearth
yea
vernal pagoda
Hello!
vernal pagoda
Can I get help with principal of mathematical induction
.
obtuse pebbleBOT
@vernal pagoda Has your question been resolved?
vernal pagoda
<@&286206848099549185>
oak marlin
Show that it is true for 800. This is easy, because 800 = 500 + 300. Now, suppose the case for k is true. This means that k = 500a + 300b, for some non-negative integers a and b. Then you want to show that it is true for k + 100.
obtuse pebbleBOT
@vernal pagoda Has your question been resolved?
obtuse pebbleBOT
hallow reef
What are you confused by exactly?
Here’s what we know so far:
- There are n total slices.
- The slices are divided evenly, with a fourth given to Marc.
- Marc ate one less than everyone else.
Assuming that everyone else ate all the pizza they were given, you can write the expression with the variable n, a single division sign, and one subtraction.
mossy fjord
If you want to make it conceptually easier, you can replace n with an actual amount of slices.
hallow reef
No. Everyone got a fourth of the total “n” slices.
If the total slices were n=4, everyone would get one slice and Marc would eat none as you stated.
Try to write an expression so that plugging in n=4 would get you this solution!
No, remember that n is the total slices of the pizza, and that Marc gets a fourth of those slices.
Then and only then will he eat one less than he got.
👍
Remember to write (1/4) in parentheses or write n/4 so nobody thinks that n is in the denominator lol
fluid snow
Let $\overline a + \overline b = \overline{a + b}$ und $\overline a \cdot \overline b =\overline{ab}$. We need to prove that $(\mathbb Z/m\mathbb Z, +, \cdot)$ is a commutative ring with $1 = \overline 1$.
obtuse pebbleBOT
Let $\overline a + \overline b = \overline{a + b}$ und $\overline a \cdot \overl...
abstract beacon
yes
fluid snow
yes
Well, that's a bunch, lol
So addition under the overline is just common addition, right?
abstract beacon
yeag
fluid snow
So 4. is proven
abstract beacon
similarly with 1., 5., and 7.
fluid snow
similarly with 1., 5., and 7.
For the neutral element of +, we just say "pick overline 0", right?
abstract beacon
yeag
abstract beacon
well u can show that 0 is neutral
fluid snow
Ah
abstract beacon
i cant overline so im just gonna underline
fluid snow
true
abstract beacon
fairly easy to do 3. as well
abstract beacon
yep
abstract beacon
you remember it
fluid snow
We need to show $\overline a + \overline 0 = \overline 0 + \overline a = \overline a$.
Because of our definition of +
We have $\overline a + \overline 0 = \overline{a + 0} = \overline a$.
Q.E.D?
abstract beacon
yes
obtuse pebbleBOT
fluid snow
.reopen
obtuse pebbleBOT
✅
fluid snow
"outer +" is what youre given in the question
Ah, and the reason we don't "rewrite" the + in Z with that is that it takes into account the elements we have
Right?
For overline a + overline b, they're both in Z/mZ, so it'll use our defined addition
abstract beacon
yes
fluid snow
for a + b, they aren't in Z/mZ
So it doesn't have to do with our definition
Thanks
.close
obtuse pebbleBOT
abstract beacon
if you really want to be clear you couold distinguish them explicitly as $+{\bZ}$ and $+{\bZ/m\bZ}$
warm shaleBOT
fluid snow
.reopen
obtuse pebbleBOT
✅
fluid snow
if you really want to be clear you couold distinguish them explicitly as $+_{\bZ...
But it's already rigorous like this, right?
Since we define the mappings like that
abstract beacon
Yea its fine not to write all the subscripts, everyone still knows what u mean
unborn vigil
Hi. I have some math questions, where can I ask them?
obtuse pebbleBOT
Hi. I have some math questions, where can I ask them?
unborn vigil
<#903430332324405288>
what does it mean?
unborn vigil
Is it possible to predict the result of the shift register with linear feedback using mathematical operations?
obtuse pebbleBOT
@unborn vigil Has your question been resolved?
verbal niche
whats a better final answer?
obtuse pebbleBOT
whats a better final answer?
chrome narwhal
The top one usually, I know that some places are weird and always want a rational denominator though
It really doesn’t matter though
cyan kite
The top one usually, I know that some places are weird and always want a rationa...
what
verbal niche
i ended with $\frac{21\sqrt{19}}{19}$ if that makes a difference
warm shaleBOT
Joshii
verbal niche
i would have to do extra manipulation to get $\frac{21}{\sqrt{19}}$
warm shaleBOT
Joshii
cyan kite
be safe and have a rational denominator
wanton kraken
how do these lines appear when drawing a graph of a function?
obtuse pebbleBOT
how do these lines appear when drawing a graph of a function?
shut lagoon
Do you mean the asymptotes or?
wanton kraken
uhh
wanton kraken
Do you mean the asymptotes or?
the way I understand is that
lim of f(x) as it approaches -3 from the positive side
goes to +infinity
shut lagoon
Yes that is correct.
wanton kraken
Yes that is correct.
so that makes the line that's from the right, right?
this one
wanton kraken
ohhh
1 is the vertical asymptote
and as f(x) approaches 1 from the + side
it goes to infinity
+inf that is
I get it
ty
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
slate agate
obtuse pebbleBOT
slate agate
Hey yall
My buddy and I have been trying to solve this integral
and I've been working on this for several hours on my own
but i cant for the life of me get this to go where it's supposed to
I originally thought of just yanking out the first two delta functions by jamming them into a delta function, but i think imm supposed to change the p in the exponential function if i do that
final thunder
💀
polar fossil
both of you stop fighting
slim cove
banned
slate agate
Anyways, I think this problem mostly boils down to the fact that I don't really knkow how to handle two dirac delta functions in the integral
One is trivial but two...im unsure how to reconcile that
slate agate
that's correcct. this is for a free particle
i could think of a few physical tricks to solve this
but i'm unsure how to solve it thoroughly from a mathematical perspective
dark stirrup
How does d³p''' work? This feels weirdly written. Are you integrating against p''' three times?
Or do you mean to say dp'''dp''dp'?
slate agate
im sorry im fucking flying all over the place forgive the sloppy notation
p''' p'' and p' are all momentum "vectors", in that they each have a px py and pz component
you could just as well think of p''' p'' and p' as a b and c
dark stirrup
let me review my dirac deltas and free particle momentum equation
Thankfully I have my quantum book near me because I was helping @royal shard a few weeks ago.
slate agate
ok thank you
dark stirrup
No guarantee I can find an answer, but maybe other <@&286206848099549185> already know.
slate agate
no problem thank you for your time regardless
obtuse pebbleBOT
@slate agate Has your question been resolved?
slate agate
well fuck i messed up one of the dirac delta fuctions
it's supposed to be delta(p'' - p''') delta(p''' - p')
ok that don't matter apparently you can switch em around
dark stirrup
ok that don't matter apparently you can switch em around
Yeah they're symmetric
slate agate
Yeah they're symmetric
thanks pardner
think im gonna trust this fuckin guy and slap it down on my paper
.close
obtuse pebbleBOT
dark stirrup
hehe
I'll read my book when I get some time to. I'll message you if I find anything interest, but good luck
obtuse pebbleBOT
Available help channel!
cunning mango
Can someone tell me how to solve 3x+1
obtuse pebbleBOT
Can someone tell me how to solve 3x+1
obtuse pebbleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
cunning mango
so you multiply any number by 3 and then add by 1 if the number is odd, but if it is even then divide by 2. The idea is to see if any number can stop the cycle of 4 then 2 then 1 then 4. Which is a loop that apparently happenes with every number.
fathom flicker
so you multiply any number by 3 and then add by 1 if the number is odd, but if i...
<@&268886789983436800> Collatz
polar fossil
okay, we could be a little less bold with the mod ping and maybe give some grace
@cunning mango this is a very well-known unsolved problem
cunning mango
so you multiply any number by 3 and then add by 1 if the number is odd, but if i...
sorry but my brother asked me this and i can't get it
polar fossil
yeah we think it always goes to 1 but no one's been able ot prove it yet
cunning mango
<@1050189501802221589> this is a very well-known unsolved problem
i have never heard of it
polar fossil
it's called the Collatz conjecture because someone apparently named Collatz came up with it
cunning mango
thanks, ig my little brother gave me a trick question lol
daring elbow
fruit RH?
polar fossil
obtuse pebbleBOT
tardy epoch
obtuse pebbleBOT
🍎 = 154476802108746166441951315019919837485664325669565431700026634898253202035277999
🍌 = 36875131794129999827197811565225474825492979968971970996283137471637224634055579
🍍 = 4373612677928697257861252602371390152816537558161613618621437993378423467772036
Available help channel!
lavish nymph
is my answer A correct?
obtuse pebbleBOT
is my answer A correct?
final thunder
is my answer A correct?
Is this a test?
obtuse pebbleBOT
@lavish nymph Has your question been resolved?
dark stirrup
is my answer A correct?
what the heck is elimination tool? 
restive thorn
obtuse pebbleBOT
fickle shell
yes
restive thorn
yes
is that what you would do
Uh
we can separate the terms from each other right
sqrt2 * 2sin *cosx - sqrt2 * cosx
can the cosx’s subtract
but I assume not cuz PEMDAS
is this right
gleaming socket
Are you supposed to prove this or find x?
restive thorn
find x
gleaming socket
Youre correct then
gleaming socket
Eh wait
restive thorn
I dont get the last part
if I divide 2sin - 1
to factor it out
it should be sqrt2cosx - 1 right
gleaming socket
Its (2sinx-1)(sqrt2cosx+1)
restive thorn
oh yeah ok
One more
do we consider the two terms we move from the right side
as a term
I have it as just 2sinx - 1
But would u put it as (2sinx-1)?
or does it not matter
gleaming socket
Doesnt matter
restive thorn
You can divide by 2sinx-1 regardless
gleaming socket
You mean subtract?
restive thorn
I mean divide 2sin-1 to factor it out
gleaming socket
But would u put it as (2sinx-1)?
Then u should use parentheses
shut lagoon
This is almost right, but you're missing a set of solution since sin(2pi/3) = sqrt(3)/2 as well.
restive thorn
This is almost right, but you're missing a set of solution since sin(2pi/3) = sq...
how did I solve it wrong
What do I do to solve it correctly
shut lagoon
I mean looking at a trig circle you would see that there are 2 solutions straight away.
shut lagoon
Apart from that, if you use arcsin, I think you would do arcsin(y) for you first solution and pi - arcsin(y) for the second.
shut lagoon
I set 2x = to both angles
Yes, then you'll have like pi/6 + 2npi and pi/3 + 2npi
restive thorn
Yes, then you'll have like pi/6 + 2npi and pi/3 + 2npi
Ok perfect
I assume this is missing something right
its better written as pi/6 + npi
same with pi/3
my professor said to add the general solution while solving and not at the end
so 2x = pi/3 + 2npi
why?
gleaming socket
so 2x = pi/3 + 2npi
So you can insert the n and get all the answers immediately
x = pi/6 +npi
n = 0: pi/6
n =1: pi/6 +pi = 7/6pi
That apply to the 2pi/3 also
shut lagoon
I assume this is missing something right
Yeah I forgot to divide by 2 at the end.
obtuse pebbleBOT
@restive thorn Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
#3. no idea where i went wrong
probably some integral or derivative
i know i should use trig identities but theres no way im memorizing those again 
aw shit
i messed up the first v
should just be -cos(tau)
gonna leave this channel open incase its still wrong, which i think it is.
robust raven
$sin\alpha\cdot sin\beta=\frac{1}{2}\left[ cos\left( \alpha-\beta \right)-cos\left( \alpha+\beta \right) \right]$
warm shaleBOT
Joanna Angel
robust raven
this formjal helps you
timid silo
yeah dude im gonna be honest i dont want to use trig identities 😭
robust raven
no other way , durign integral
youhave there =
sin(tau) * sin(t - tau)
so you must use it
timid silo
theres no other option? like its mathematically impossible to not use trig identities?
timid silo
i believe you. trying it right now 
robust raven
🙂
timid silo
thanks for all the help btw. you have saved my ass a few times so far
robust raven
yvw 🙂
timid silo
i got -sin(t) - t + 1 lol
that is.. very wrong
this is the answer 🫡
it should be possible though. IBP using t-tau as u, du=-d(tau), dv=sin(tau)d(tau), v=-cos(tau)
robust raven
maybe letters mistake somewhere ) you have to calcualte it once again
timid silo
i have no clue
robust raven
$\frac{1}{2}\left[ \frac{1}{2}sin\left( 2x-t \right)-xcost \right]_{0}^{t}=\\\frac{1}{2}\left[ \frac{1}{2}sint-tcost+\frac{1}{2}sint\right]=\frac{1}{2}\left( sint-tcost \right)$
warm shaleBOT
Joanna Angel
timid silo
do you know how to do it using integration by parts? so no identities.
i think it can be done
robust raven
no, becasue
timid silo
if we set u = t-tau and whatnot
robust raven
sina 8 sinB, when you try by pats, you will go in a cricle
robust raven
yea
timid silo
hmmm, am i getting the u & v wrong then? here was my idea:
u = t - tau
du = -d(tau)
dv = sin(tau) * d(tau)
v = -cos(tau)