but it's hard to help if I don't know where exactly there is confusion
#help-23
bold ferry
bold ferry
well divide
like I said.. speed is the distance divided by time
250 miles is your distance
5 hours is your time
bold ferry
almost, but why the ≤ sign?
bold ferry
I understand but
the family wants to travel at least 250 miles
what does that mean to you?
bold ferry
hmm
if your dad told you he wants you to get at least a 50% on an exam, what does he mean?
(it's just a hypothetical)
orchid glen
That i have to get a 50
bold ferry
or more
orchid glen
That too
bold ferry
so if the family wants to travel at least 250 miles
they want to travel 250 miles or more
which means which sign? ≤ or ≥
orchid glen
The left one?
orchid glen
I have a guide but it basically has the same definitions for the others
I told ya
I have a smooth brain
orchid glen
I am
bold ferry
≤ means less than or equal to
≥ means greater than or equal to
orchid glen
So i use the right one then
bold ferry
yeah
orchid glen
Alright done
bold ferry
congratulations
orchid glen
Do ya mind if ya help me out with the rest?
bold ferry
I gtg but I'm sure anyone else here would be willing to help
orchid glen
Alr
safe radishBOT
@orchid glen Has your question been resolved?
orchid glen
Yes
leaden scaffold
May someone help me with this problem?
safe radishBOT
May someone help me with this problem?
leaden scaffold
<@&286206848099549185>
pulsar pecan
May someone help me with this problem?
!status
safe radishBOT
May someone help me with this problem?
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@leaden scaffold Has your question been resolved?
pulsar pecan
May someone help me with this problem?
Which step are you on?
leaden scaffold
Which step are you on?
I think I’m making a tautological mistake
safe radishBOT
I think I’m making a tautological mistake
leaden scaffold
Can you check my reasoning?
pulsar pecan
Can you check my reasoning?
Send it
leaden scaffold
Send it
So when t=0, the vector r(t)=⟨2,−1⟩+0⟨3,2⟩ simplifies to r(0)=⟨2,−1⟩. This confirms that the line passes through the initial point (2,−1). And as t varies from this initial point, the terminal points of r(t)=⟨2+3t,−1+2t⟩ trace out a line with a slope of 2^3, which is consistent with the direction vector ⟨3,2⟩? I feel as if I'm making a tautological mistake with my reasoning..
pulsar pecan
So when t=0, the vector r(t)=⟨2,−1⟩+0⟨3,2⟩ simplifies to r(0)=⟨2,−1⟩. This confi...
2^3? That’s 8
pulsar pecan
How should I do this then?
It should be right except for that
leaden scaffold
It should be right except for that
Really?
leaden scaffold
Do you also understand e?
safe radishBOT
@leaden scaffold Has your question been resolved?
stray socket
Do you also understand e?
It's saying to start at a point and go in the direction of a vector in 3D space
R^n is the nth dimension
astral wind
Hi, I'm trying to figure out a way to generate an infinite set of disjoint sets from a countable collection $X = {x_1, x_2, ...}$ of sets. One idea I had was to encode infinite binary strings as countable intersections: given a string $s = b_1 b_2 ...$, let $y_i = x_1$ if $b_i = 0$ else $y_i = x_1^c$. Define $A_s$ to be $\bigcap_{i=1}^\infty y_i$. Is ${ A_s }_{s \in { 0, 1 }^*}$ guaranteed to be infinite?
safe radishBOT
Hi, I'm trying to figure out a way to generate an infinite set of disjoint sets ...
flat frigateBOT
marshall
astral wind
For example, 0000000... gives us the intersection of all the $x_i$, and 1111111... gives us the intersection of their complements.
flat frigateBOT
marshall
safe radishBOT
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astral wind
<@&286206848099549185> can anyone help with this?
safe radishBOT
@astral wind Has your question been resolved?
dry trench
from which topic and subject?
thin bridge
which subtopic of math
thin bridge
textbooks?
dry trench
Yes I need for geometry @thin bridge if u can recommend
thin bridge
though i wouldn't really recommend buying a textbook for high school
there's plenty of resources on that content online, and you shouldn't have that much trouble finding related questions
dry trench
it's free website
so u can check
ok
yes
for questions it's free
go to the answer tab
hard crest
i like https://math-drills.com/ but I'm not sure if it has any geometry; it's mostly algebra
dry trench
i like https://math-drills.com/ but I'm not sure if it has any geometry; it's mo...
isn't it easy?
thin bridge
do jee
we don't know what level of difficulty you're expecting
we don't know what difficulty you consider to be intermediate
give examples of questions for comparison
just borrow a random textbook then for a large pool of problems
any math textbook that coves the topic you want
try asking in#book-recommendations
safe radishBOT
hard crest
the site i posted has a lot of these
safe radishBOT
Available help channel!
granite flower
Given 2 circles with two different radii
The bigger circle has radius of R and crosses the center of the second circle of radius r
What is the area of the intersection between the 2 circles in terms of R and r
safe radishBOT
Given 2 circles with two different radii
The bigger circle has radius of R and c...
granite flower
Actually I tried a lot in this question but didn't achieve any progress
I mean I don't know how to start
safe radishBOT
@granite flower Has your question been resolved?
weak relic
can someone help me getting through this problem
safe radishBOT
can someone help me getting through this problem
weak relic
i believe i have to use difference quotient but i dont know how to approach it
obtuse plover
U have to replace every x with an h to get f(h)
weak relic
so would it be f(3+4x^2+4)-f(3)/4x^2+4?
flat frigateBOT
Stephen
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rigid path
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@rigid path Has your question been resolved?
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@rigid path Has your question been resolved?
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@rigid path Has your question been resolved?
granite flower
Given 2 circles with two different radii
The bigger circle has radius of R and crosses the center of the second circle of radius r
What is the area of the intersection between the 2 circles in terms of R and r
Actually I tried a lot in this question but didn't achieve any progress
I mean I don't know how to start
I have drawn it for easy access
safe radishBOT
Given 2 circles with two different radii
The bigger circle has radius of R and c...
@granite flower Has your question been resolved?
granite flower
<@&286206848099549185>
vivid wren
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lusty plume
hello there im searching for formula which would progressively halve number X by N percentage something like this
X*(0.5^(N/100))
and this works but only for integers whereas i need any real number for example 150% would be 1.5 and result for X=1000 would be 375 because it is half of 1000 that is 500 minus half of half of it so 250/2=125 so 500-125=375 any ideas ?
safe radishBOT
hello there im searching for formula which would progressively halve number X by...
final halo
can you clarify what you want to happen
"halve number X by N percent" doesnt make much sense and your example is confusing (or atleast confusingly written)
lusty plume
take any positive number and any positive percentage and for each 100% halve that number
take number 1000
100% = 500
200% = 250
300% = 125
50% = 750
75% = 625
150% = 375
obsidian oracle
the thing you did with 50% is incoherent
if taking 50% gave us 750, then 100% = 50%+50% should give us the same ratio but squared
lusty plume
its always calculated from half of it so half of 1000 is 500 thus take 50% of that that is 250 and substract it from 1000 and that is 750 if it was 100% we would substract full 500 and get 500
obsidian oracle
but then the order of operations matter and the path you take to get to a number
To get to 75% for example
Do you start from 100% and take 25% or do you start from 150% and take half of it?
because those two approaches will give you two different numbers
this operation you're trying to define will not be able to work
lusty plume
always substract that percentage of half that means
75% is not greater than 100% so you take 75% of 500 and substract that from 1000 and you get 625
for 150% you first substract 500 for those 100% and then from remainder (500) substract 50% of half of it that is 125 and you get 375
final halo
you'll want a different formula depending if the percentage is bigger than 100 or less than 100 then i think
obsidian oracle
So you're building a piecewise linear function
final halo
for less than 100 its just X - (X/2 * N/100) i think
obsidian oracle
you'll want a different formula depending if the percentage is bigger than 100 o...
It will depend on the quotient of the percentage by 100%
lusty plume
for 100,200,300 etc X*(0.5^(N/100)) this always works
but i cant figure out how to do it for percentage which is not multiply of 100 like 150
i mean i got program which calculates it but i want to optimize it with help of math
final halo
the second half wont be linear if they wants multiples of 100% to divide by 2^multiple
final halo
right nice yeah i see
obsidian oracle
the directing coefficient will be -X/2^(E(N/100)+1)/100
So f(N%) = X/2^(E(N/100)) -X/2^(E(N/100)+1)*(N/100-E(N/100))
lusty plume
oh right i see i can do it in 2 steps and that will work for any percentage
yes that works 👌
thank you
.close
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true oasis
i have no idea what I'm doing
true oasis
.close
warm crest
I think I'm stuck, I can't figure out where I messed up. If I multiply 1/3 and 512 I get a non whole number
safe radishBOT
I think I'm stuck, I can't figure out where I messed up. If I multiply 1/3 and 5...
marsh walrus
hmm are you able to share any additional context
warm crest
hmm are you able to share any additional context
It's part of a problem where I have to use the disk method to find the volume when the region is rotated
flat frigateBOT
jan Niku
marsh walrus
so $\int _0 ^8 \pi \qty(64 - 16x + x^2) \dd x$
flat frigateBOT
jan Niku
warm crest
I separated the 64(I accidentally wrote it as 8) and multiplied it too pi.
I can try with 64 attached the polynomial
warm crest
did you apply some kind of substitution?
This is what I got
warm crest
No prob
marsh walrus
This is what I got
hmm you have a sign error
this is messing up your result
$-\frac{x^3}{3}$ should be $+\frac{x^3}{3}$
flat frigateBOT
jan Niku
marsh walrus
it comes from (-x)(-x) in the distribution = x^2
marsh walrus
it happens
warm crest
Didn't really change much the final answer is just not a negative
marsh walrus
do you know the answer?
I guess we can just calculate it huh
,w volume circular pyramid
flat frigateBOT
Requested by janniku
flat frigateBOT
flat frigateBOT
Result:
536.16514621266
,calc 1/3 * 8 ^3
flat frigateBOT
Result:
170.66666666667
,w integrate (64-16x+x^2) from x = 0 to x=8
flat frigateBOT
marsh walrus
warm crest
Oh, ima look at the answer just gotta get the book brb
marsh walrus
should be 512/3 pi
warm crest
should be 512/3 pi
The answering key is in odd number and ima just assume this is correct and email my professor
marsh walrus
what answer are you getting?
the correct, right?
you can kind of trivialize this integral with a substitution if you really want to be sure
warm crest
Aight
Also I'm really tired
Gn
Thank you very much
marsh walrus
yea, its correct
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pulsar mirage
How do i show that this is a ordered base:
safe radishBOT
How do i show that this is a ordered base:
@pulsar mirage Has your question been resolved?
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@pulsar mirage Has your question been resolved?
pulsar mirage
<@&286206848099549185> Ping
upbeat adder
<@&286206848099549185> Ping
still need help?
pulsar mirage
still need help?
yes
upbeat adder
alright, you know what a basis is I assume?
pulsar mirage
I guess, let me tell: A base is a set of vectors with whose you can build R^3 in this case?
upbeat adder
thats a way to put it, yeah
but not just build R^3
it also hase to be the "smallest" set
does that make sense?
pulsar mirage
yes, because if there are for example 5 vectors but you only need 4 of these to build a vector room, then these 4 cecotrs are enough right?
upbeat adder
yes
so for example R^3 is a 3 dimensional vector space because the smallest number of vectors that can give you a basis is 3
upbeat adder
right
upbeat adder
thats one way to do it, yes
pulsar mirage
but i dont know how to put these lements into a matrix
upbeat adder
ok
pulsar mirage
i think the are enough because it would be a quadratic matrix
pulsar mirage
nxn
upbeat adder
yes
pulsar mirage
but i dont know where the coefficients are
upbeat adder
so you could use a matrix and show that the determinant is non zero
but the reason why this works is not very straight forward conceptually
so I could just tell you so that you'd know what to do in this particular case, or try giving you another method that you might understand a bit more
up to you
pulsar mirage
yes very gladly
upbeat adder
so do you want to know how to do the matrix method without necessarily understanding it, or another method that you might understand a bit more?
pulsar mirage
method i might understand a bit ore
upbeat adder
ok
so a basis is a set of vectors that span the whole vector space ( "build" the vector space as you said) in the sense that any vector in the vector space can be written as a sum of elements from the basis
AND that is free, in the sense that no vector in the basis can be written as a sum of other elements in the basis
upbeat adder
something like that
its a theorem (or a lemma or something) that says its equivalent
using lots of different theorems and everything, we know for a fact that if we can find a set of n vectors where n is the dimension of the vector space that is free, OR that spans the whole vector space, then in both cases this set is actually a basis, yes?
pulsar mirage
yes
upbeat adder
so we can either choose to show that our 3 vectors span all of R^3, or show that they are linearly independent (free)
pulsar mirage
exatcly
upbeat adder
if you want to show that they are linearly independent, we can do what you (sort of) mentioned, which is to say, write lambda1*v1 + lambda2*v2 + lambda3*v3 = 0, and show that all the lambdas must be equal to 0
there is a theorem that says that this condition is equivalent to being linearly independent, yeah?
pulsar mirage
yes
upbeat adder
alternatively, we could show that the set spans R^3
now to do that, we can actually use the fact that the canonical basis, {e1, e2, e3} is a basis, and so already spans R^3
if we show that we can build e1, e2 and e3 from the given set, then we can also build any other vector, do you see why?
pulsar mirage
no
upbeat adder
ok, lets imagine we want to build (a1, a2, a3)
this is just a1*e1 + a2*e2 + a3*e3, right?
pulsar mirage
ok
upbeat adder
lets call the set we are working with {v1,v2,v3}, we want to show that it spans R^3
if we can build e1, we know that we can find somes coefficients x1,x2,x3 such that e1 = x1*v1 + x2*v2 + x3*v3
I dont know if this is hard to follow with all the different coefficients
upbeat adder
yeah
pulsar mirage
(1,0,0) etc?
upbeat adder
sure
upbeat adder
well we can build e1 but also e2 and e3
pulsar mirage
do you assume that the e1,e2,e3 in my task are the elemtary vecors?
upbeat adder
lets say e2 = y1*v1 + y2*v2 + y3*v3 and e3 = z1*v1 + z2*v2 + z3*v3
I assume so, but it doesnt really matter if they are or not, as long as they are a basis
pulsar mirage
ok
upbeat adder
so we wanted to build a1e1 + a2e2 + a3*e3
but now we can just replace e1, e2 and e3 by the equalities we established above
and we get the vector we were trying to build, (a1,a2,a3) as a linear combination of v1, v2 and v3
it would be (x1 + y1 + z1)*v1 + (x2 + y2 + z2)*v2 + (x3 + y3 + z3)*v3
make sense?
pulsar mirage
xD
upbeat adder
since (a1,a2,a3) is an arbitrary vector, we showed that we can build any vector from v1, v2 and v3
and so, by definition, {v1,v2,v3} spans R^3
upbeat adder
well sorry about that then
if you take e1 = (1,0,0), e2=(0,1,0) and e3 = (0,0,1), then the three vectors you are given are (1,0,0), (1,1,0) and (1,0,1)
the matrix is then [[1,0,0],[1,1,0],[1,0,1]] or its transpose, transposing doesnt change the determinant
this matrix is invertible if and only if the vectors form a basis
in particular, the vectors are a basis if and only if the determinant is non zero
hopefully that is easier to follow
pulsar mirage
but only if we assume that e1 etc are the elementary vecotrs right?
upbeat adder
well
not really
as long as its a basis, its completely equivalent
its hard to explain and I havent done any maths over the holidays so I'm a little rusty
but the elementary basis is completely equivalent to any other basis
pulsar mirage
yes but we assume that the vectors are (1,0,0), (1,1,0) and (1,0,1), so here i can calculate det(A). if we dont assume, than i cant show that this set of vectors are a base in R^3 with the determinant solution
upbeat adder
ok but imagine that e1, e2 and e3 are some other basis
then you could "define" (under the hood, you'd be using an isomorphism) (a,b,c) as a*e1 + b*e2 + c*e3
pulsar mirage
wdym
upbeat adder
its essentially a change of basis
this is using the fact that all R vector spaces of dimension n are isomorphic
pulsar mirage
ok thats too deep for me
upbeat adder
yeah I figured
I know this might seem a bit discouraging but I'm doing a very poor job at explaining anything
upbeat adder
well you can just assume e1, e2 and e3 are the elementary vectors
pulsar mirage
yes i guess so because any other task my prof defines what is what, not in this one
upbeat adder
but as I said, if you "define" (a,b,c) to be a*e1 + b*e2 + c*e3, then you can do exactly the same thing
anyway
good luck
loud breach
Hi, how do I answer it?
safe radishBOT
Hi, how do I answer it?
loud breach
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loud breach
<@&286206848099549185>
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lean otter
9.The three types of ants that are in a nest are shown. Take into account the real measurement of the worker and solve.
a. What is the actual measurement of the queen ant that is 1.25 times as long as the worker, if the measurement of the worker ant in the photo is 20 mm? What is the real size of the soldier ant if it measures 3/5 of the photo size of the queen?
b. What is the scale used in the representation of the ants?
I want to know how to get the scale 8:1
safe radishBOT
9.The three types of ants that are in a nest are shown. Take into account the re...
@lean otter Has your question been resolved?
amber shore
$\mathbb{N}={n:n\ge 0\wedge 1\left|n}$
safe radishBOT
$\mathbb{N}=\{n:n\ge 0\wedge 1\left|n\}$
flat frigateBOT
themathboi #2137
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
amber shore
Is this statement true?
split ether
No need for \left there
amber shore
No need for \left there
I don't even know what \left means, so...
But let's talk more algebraically
split ether
You use \left and \right when you want some brackets like () to nicely envelop the content inside it
E.g. compare $(\frac{x^2}2)$ and $\left( \frac{x^2}2 \right)$
flat frigateBOT
A Lonely Bean
split ether
Anyway, yes, the statement is indeed true
amber shore
Anyway, yes, the statement is indeed true
I guess I have indeed defined natural numbers for the first time.
split ether
amber shore
Thank you very much
split ether
The thing is it doesn't work as a definition
How do you define integer division without having the integers defined yet?
amber shore
How do you define integer division without having the integers defined yet?
How would you propose to define them? I am slowly running out of ideas.
split ether
If you have somehow defined the integers before the naturals, then you could simply write $\bN = { x \in \bZ \mid x \geqslant 0 }$
flat frigateBOT
A Lonely Bean
split ether
How would you propose to define them? I am slowly running out of ideas.
Ah I misunderstood what you meant here
I would do it the way I mentioned last time
Equivalence classes of N^2 under the equivalence relation (a, b) ~ (c, d) iff a + d = b + c
The idea is that (a, b) is actually the same thing as a - b but you pretend like you don't know that yet
amber shore
Equivalence classes of N^2 under the equivalence relation (a, b) ~ (c, d) iff a ...
Sadly I am not into this yet
amber shore
We are defining naturals
indeed
amber shore
Let 0 = {} and n = {0, 1, ..., n-1}
I have seen this one, but the thing is, I can't really understand what it is trying to do.
I have also tried the approach with cardinalities of finite sets, but that had worked out as using naturals in the definition of naturals.
<@&286206848099549185>
peak estuary
I have seen this one, but the thing is, I can't really understand what it is try...
well its defining some sets and calling them 0,1,2,...
and in that way is defining what 0 and 1 "are"
split ether
Yeah I can't describe that method without saying that it just defines natural numbers to be those inductively constructed sets
amber shore
Yeah I can't describe that method without saying that it just defines natural nu...
Are there any other methods of defining naturals?
split ether
Hmm let me look up
amber shore
Ok, I'll be right back too
split ether
There is one using Peano axioms
peak estuary
well there are probably other ones but this is presumably one of the simplest
well peano axioms are of the form "if they exist, then natural numbers are this"
split ether
Look up natural numbers on wiki and it's under the title "format definitions"
shy lynx
There's also the Zermelo ordinals:
0 = {},
n = {n - 1}.
split ether
Yup, but it seems difficult to define cardinality with that
Actually no nvm, but still looks like you need to mention {0, 1, ..., n-1} for that
safe radishBOT
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amber shore
Actually no nvm, but still looks like you need to mention {0, 1, ..., n-1} for t...
Sorry for the late reply, but from my first idea, can't just division and divisors be defined on the set of real numbers and used to make up the definition of naturals?
split ether
Have you defined reals yet?
amber shore
<:thonk:406575732563902485> Have you defined reals yet?
You have.
amber shore
I don't think you need naturals to say "Any number that can find a place on the number line belongs to R ".
(at least that is the definition you quoted from wolfram alpha)
split ether
Hm? I never mentioned wolfram alpha in this conversation
amber shore
sorry, maybe it was math stack exchange then
split ether
Anyway I don't think you can define reals before/without naturals
amber shore
Anyway I don't think you can define reals before/without naturals
Sorry for being so obsessed with the topic, but maybe we can start with Z ?
peak estuary
defining what real numbers are takes a lot of work. and you need to define N before doing that
what is the number line supposed to be
every definition of what "numbers" are starts by defining N. in the way we did here
amber shore
every definition of what "numbers" are starts by defining N. in the way we did h...
Or Z to get to N
peak estuary
I havent seen a single definition of what Z is without knowing N
amber shore
I havent seen a single definition of what Z is without knowing N
Maybe we can just say that N is the set containing 0 , S(0) , S(S(0)) , S(S(S(0))) , ....
It just creates an arithmetic series.
peak estuary
well but what is S
and what is 0
the point of the set definition is to give a meaning of what 0 and S are
0 being the emptyset
and S(n) being n union {n}
amber shore
I guess I cannot find anything simpler than the organic definition.
but thanks anyways
.close
lean otter
\dm
if $\map f x$ is a differentiable function and $\map g x$ is a double differentiable function such that $\abs{\map f x} \le 1$ and $\map{f'}x=\map g x$. If $\map {f^2}0 + \map {g^2}0 = 9$. Prove that there exists some $c \in (-3,3)$ such that $\map g c \cdot \map {g''} c < 0$
safe radishBOT
\dm
if $\map f x$ is a differentiable function and $\map g x$ is a double differ...
flat frigateBOT
lean otter
so this bad boy is really not clicking in my head on how to go about doing it
any ideas, hints, whatever will be nice
safe radishBOT
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peak estuary
tricky. so basically g(0) has to be quite big in absolute value but then it has to get smaller because otherwise f would grow too fast
but damn, how do you make that in any way precise
safe radishBOT
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plucky elk
Sounds like IVT or MVT. Try setting up a function that uses those on (-3,3)
lean otter
Sounds like IVT or MVT. Try setting up a function that uses those on (-3,3)
f(x)=x^3 maybe?
well guess not
uh
yeah maybe x^3 with a constricted domain I guess
unique bison
mellow lodge
I’d check sinusoidal functions
A cos(kx) function seems like it would work
It would need to be shifted though
safe radishBOT
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lean otter
I checked cos but I didn't find anything that is suitable
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
@lean otter Has your question been resolved?
toxic stratus
\dm
if $\map f x$ is a differentiable function and $\map g x$ is a double differ...
good one
lean otter
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wraith prism
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restive plover
do you know the definition of a two sided relation
wraith prism
Never heard of it
But i guess it is binary operating
You are my brother, i am your brother
Answer 1?
Or maybe m
restive plover
oh, so symmetric relations?
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umbral solar
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umbral solar
hello
restive plover
What is the context?
umbral solar
maximisation of profit in monopoly
and MR(y) must be = MC(y) Marginal cost
but to get MR we need derivate total revenue
flat frigateBOT
rafilou2003
umbral solar
hmmmmmmmmmmmmmmmmmmm
obsidian oracle
The second term, "P", results from keeping P and differentiating Y, which gives P × 1
umbral solar
oh
Woah!
@obsidian oracle but why is this this rule? Because its like 2 functions?
grim plover
<@246787399991033858> but why is this this rule? Because its like 2 functions?
Comes from limit definition of derivative I think
obsidian oracle
<@246787399991033858> but why is this this rule? Because its like 2 functions?
You can prove it from the limit definition
$\frac{f(x+h)g(x+h) - f(x)g(x)}{h} = \frac{f(x+h)g(x+h) - f(x+h)g(x)}{h} + \frac{f(x+h)g(x) - f(x)g(x)}{h}$
flat frigateBOT
rafilou2003
obsidian oracle
So $\frac{f(x+h)g(x+h) - f(x)g(x)}{h} = f(x+h)\frac{g(x+h) - g(x)}{h} + g(x)\frac{f(x+h) - f(x)}{h}$
flat frigateBOT
rafilou2003
obsidian oracle
Taking the limit as $h\to 0$, we get :
$(fg)' = fg' + gf'$
flat frigateBOT
rafilou2003
grim plover
There's a much simpler geometric proof btw
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nocturne spade
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nocturne spade
isnt A the same as D?
and isnt B the same as C?
restive plover
isnt A the same as D?
and isnt B the same as C?
The tangent may not go through the origin
because the function curves slightly, it isn’t a straight line
restive plover
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sacred wadi
hello
sacred wadi
how i find a b and y ?
I have to make a system A 3 equation with 3 unknown?
i is a root of p(Z) P(1)=-4i, the remainder of the division of p(Z) by z+i is -8i
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burnt notch
Use the info given
Suppose I give you P(z) = az+2. If I tell you that P(1) = 5, what is the value of a?
sacred wadi
a+2=5 so a=3
burnt notch
but there is 3 unknown
Indeed, you have 3 pieces of information to find the 3 unknown coefficients
sacred wadi
i^3-a+bi+y=0
@burnt notch i can replace the "a+bi" by Z or no ?
it change nothing
-i^3-a-bi+y=-8i
i^3-a+bi+y=0
1+a+b+y=-4i
i can substitue no ? @burnt notch
sacred wadi
-i^3-a-bi+y=-8i
like a=-i^3-bi+y+8i for this
it will change nothing ?
i dont know how to find value when there is 3 unknown
burnt notch
Do one step at a time, I'm not following you sorry
Pick the first info, that's P(i) = 0
burnt notch
Yep, now what's i³ ?
burnt notch
Perfect, this is P(i)
But we were given that P(i) = 0, hence we have the 1st equation, which is -i-a+bi+y=0
Now, go on with the second info
burnt notch
You should get to ||1 + a + b + y + 4i = 0||
burnt notch
1+a+b+y=-4i
This is correct, but it's better to have equations with a 0 on the RHS
sacred wadi
Ok
1+a+b+y+4i=0
last info is
the remainder of the division of p(Z) by z+i is -8i
thats means p(-i)=-8i ?
burnt notch
That's what's written there, yep
sacred wadi
so i-a-bi+y+8i=0
burnt notch
So you should reach the equation i - a - bi + y + 8i = 0
burnt notch
so i-a-bi+y+8i=0
Exactly
Now, the last step is to write all these 3 in the standard form off a system of 3 equation in 3 unknowns
sacred wadi
burnt notch
Yep, now I believe you can add the first and the third eqn.s and see what you get
Things should cancel nicely
burnt notch
Exactly
Now from the first you can get for example y in terms of a
So that you can then subsitute this value of y into the second equation below
burnt notch
You coorectly found that 1 + 2a + b = 0, nut I don't understand what you want to do
sacred wadi
i can substitue again ?
burnt notch
You mean to use b = -1-2a and plug that into the other equations?
burnt notch
Yes, of course you can do it
sacred wadi
to find y
sacred wadi
i replace the -1-2a here ?
burnt notch
No, to find a
You have y in terms of a and you also have b in terms of a. This means you can get an equation in the only unknowna (and solve for that)
burnt notch
i replace the -1-2a here ?
This doesn't work, it gets you to what you already know
Change equation where you plug stuff in
sacred wadi
i dont understand where i need to place the b=-1-2a
burnt notch
In the third equation (from the top) here
sacred wadi
it's give me this
i can't replace the y by -4i+a
so what can i do
hmm
i need to substitue again ?
burnt notch
Yes, here you substitute y = -4i + a
sacred wadi
i can replace the y by -4i+a ?
burnt notch
Yes
sacred wadi
so 9i+1+a-4i+a=0
burnt notch
Yes
burnt notch
You should get $a = -\frac{5}{2}i -\frac{1}{2}$
flat frigateBOT
Alberto Z.
sacred wadi
yes
burnt notch
And this is your value of a
burnt notch
Now you can use what you found to find y and b as well
burnt notch
Yeah I think you understood what to do, right? I'll let you do it on your own 👍
sacred wadi
yeah i understood thanks you bro
burnt notch
You're welcome 🤗
sacred wadi
This doesn't work, it gets you to what you already know
but i did not understand why i cant replace here
burnt notch
but i did not understand why i cant replace here
Because you used that equation to find what you are replacing. This leads you to 0 = 0, which of course is correct but that doesn't give you additional information
burnt notch
Yep
sacred wadi
ok i understood everything
if i have this in a evaluation tomorrow i will do it without problem
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full oracle
full oracle
Could u help me with this
exotic bolt
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grizzled oxide
How do you prove that rank (A+A^2+A^3)<=rank A?
safe radishBOT
How do you prove that rank (A+A^2+A^3)<=rank A?
@grizzled oxide Has your question been resolved?
devout shale
How do you prove that rank (A+A^2+A^3)<=rank A?
do a 2x2 example with arbitrary values a,b,c,d to convince yourself
grizzled oxide
I get that, but how do you rigorously prove it?
tacit yew
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tacit yew
im looking at the last bit
why can you just switch the -1 to -3 without changing inside the brackets
quiet juniper
You're multiplying all of (x-5)^2 - 1 by 3
Because you want the roots to still be x = 6 and x = 4
You don't do anything to the inside of the brackets just cus that's not how distributive property works
Multiplying by a constant won't change the roots
3(x-4)(x-6) still has roots 4 and 6
bright carbon
how do you do this?
safe radishBOT
how do you do this?
quasi bison
the point (4,7) lies on the line x+3y=k
what happens if you plug that point into the line's equation?
lean otter
how do you do this?
x + 3y = k
Passes through (4,7)
Put x and y, find k
quasi bison
x + 3y = k
Passes through (4,7)
Put x and y, find k
too late
bright carbon
I got so tunnel visioned on the circle equation
lean otter
I did the questions first
lean otter
I got so tunnel visioned on the circle equation
Ye happens
Its the reason it was put there
it is the reason , when i get confused i read the question backwards
starting from what i want to what i have
bright carbon
.close
umbral fossil
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split ether
Open a new channel, this one is about to close
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clear trench
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clear trench
Is this correct?
split ether
Did you mean to write $\frac1{1 - e^u}$ instead?
lilac patio
you didnt even integrate after you substituted
clear trench
Because one of the us cancel out?
flat frigateBOT
A Lonely Bean
lilac patio
integrate -1/u^2 first then plug u back in
clear trench
1/u + C?
split ether
Yes
lilac patio
yes
charred yew
Is this correct ?
safe radishBOT
Is this correct ?
charred yew
For q 2 a
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pure agate
Is this correct ?
In this format, the coordinates of the vertex of the parabola are given to you.
$y = (x - h)^2 + k \text{, where } h \text{ and } k \text{ are the x and y coordinates of the vertex.}$
flat frigateBOT
Kookiemon
untold ore
Hey I need help with my HW. I just wana make sure everything is right. Someone told me earlier that 2(c), 2(d), and 2(f) are wrong. can someone explain why or am i right?
safe radishBOT
Hey I need help with my HW. I just wana make sure everything is right. Someone t...
untold ore
<@&286206848099549185>
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Please read #❓how-to-get-help
dire fjord
!15min
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
dire fjord
That's the correct command
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split fulcrum
Why should car Y rebound if it had more mass?
safe radishBOT
Why should car Y rebound if it had more mass?
split fulcrum
Wouldn’t it be Car X that rebounds off
plucky elk
That's a physics question
split fulcrum
yeah but people here know this stuff too 
plucky elk
yeah but people here know this stuff too <:catThin4K:811354320460578896>
#old-network for physics server
split fulcrum
I’ll just wait here and see if anyone is able to help because I and many other people before has gotten help on not so math questions before 
worthy hemlock
Why should car Y rebound if it had more mass?
Because Newton's third law
It'll rebound less of it was heavy but it still rebounds
split fulcrum
oh okay
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royal oxide
How do I find the slope of a regression line??
safe radishBOT
How do I find the slope of a regression line??
tardy copper
Where can I go from here?
safe radishBOT
Where can I go from here?
tardy copper
.close
tight marsh
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inner obsidian
What is the question
inner obsidian
Ok well
You have to combine all the values that are x^2
All the values that are just x
and then the ones without a variable
tight marsh
ye mb
inner obsidian
All good
tight marsh
so those two
inner obsidian
-14x squared
Yep
tight marsh
does it matter for the order its in?
inner obsidian
The order of the final equation?
tight marsh
ye
inner obsidian
Yeah, put the largest exponent at the front
tight marsh
so next to the =
inner obsidian
Yeah
tight marsh
flip it??
tight marsh
you said the largest exponent next to the = tho
or you clarified it idk
ohhh
alr lemme fix it
inner obsidian
well i didnt see the equal sign on the paper so I figured it was on the left
tight marsh
oh wait a second
there isnt an equal sign
so what do i do in this situation
soooo
nothing?
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worthy hemlock
.close
lean otter
Need help understanding
safe radishBOT
Need help understanding
lean otter
sequence formulas
last heath
watch a video
safe radishBOT
@lean otter Has your question been resolved?
royal isle
What is the derivative of x?
safe radishBOT
What is the derivative of x?
upbeat ridge
Have you learned power rules yet?
royal isle
yea
upbeat ridge
What's the power of x?
royal isle
nothing
upbeat ridge
????
royal isle
like
lean otter
if you are unsure, check the definition of the derivative
royal isle
f(x)-> 9x^2 -4 the derivative would be 18x
upbeat ridge
if you are unsure, check the definition of the derivative
It's not that
She's not understanding the power of a normal constant
If a number or a variable doesn't have a power written
It means that constant or variable has a power of 1
In which x will have a power of 1
Does that make sense?
upbeat ridge
Yes!!!
x is a variable
You can think of constants being the lowest hierarchy in the caste system... haha
Derivatives are removing a power down by 1 in a sense
x^2 -> 2x^1
2x^1 -> 2
2 -> 0
royal isle
You can think of constants being the lowest hierarchy in the caste system... hah...
ok so the product rule of x^2 - x cos (x) would be (2x-x cos x)+ ((1) -sin (x))?
royal isle
the product rule
upbeat ridge
Like
Tell me how you've got there
Product rule is just a way of solving derivatives
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tacit cosmos
Prove or disprove: (P ∧ ¬Q =⇒ F) ⇐⇒ (P =⇒ Q) is a tautology. Here F represents a contradiction: some proposition which is always false.
safe radishBOT
Prove or disprove: (P ∧ ¬Q =⇒ F) ⇐⇒ (P =⇒ Q) is a tautology. Here F represents a...
tacit cosmos
This is my question
So I have never heard of the term tautology before
I don't know how I'm supposed to prove this
I am completely lost..
restive plover
So I have never heard of the term tautology before
tautology is something like (this box is not completely red) or (this box is completely red)
either way, this statement is true
because either the box is completely red, or it is not completely red
one of the two must be true
tacit cosmos
one of the two must be true
But what if the box is half red
Like we don't consider these cases?
restive plover
But what if the box is half red
Then it’s not completely red
restive plover
Like we don't consider these cases?
I thought of that
tacit cosmos
Its not like probability where the sample space S = 1 and the two cases here divide the space by 0.5 and 0.5 right
tacit cosmos
one of the two must be true
What makes one of two must be true?
tacit cosmos
I thought of that
Are you there
I am solving this but
could you check if im doing it right
restive plover
What makes one of two must be true?
a box could be any color. If it is completely red, then it satisfies the statement. If it is not red, or it is striped, then it still satisfies the statement
restive plover
could you check if im doing it right
Sure
restive plover
Is a truth table an actually legit method
Yes, just as legit as all the others
but sometimes they require you to manipulate the logical expressions
restive plover
Prove or disprove: (P ∧ ¬Q =⇒ F) ⇐⇒ (P =⇒ Q) is a tautology. Here F represents a...
have you tried expanding using the definition of implies
tacit cosmos
Hmm
tacit cosmos
have you tried expanding using the definition of implies
What do you mean by this?
restive plover
What do you mean by this?
do you know the definition of implies using and and not
tacit cosmos
do you know the definition of implies using and and not
no..
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obtuse plover
Could someone check if I did A correctly and help me with part B please?
obtuse plover
lean otter
did u check the answer for part a?
obtuse plover
no i dont have an answer key
lean otter
i see gimme a sec
obtuse plover
👍 thanks
lean otter
it should be alright
correct me if im wrong
u found out the total no of ways to take out 4 balls which is basically total outcome
first
tiles*
dire fjord
i think you should prob use permutations not combinations
dire fjord
no he is using combination
lean otter
i think u messed up at a place
lean otter
no he is using combination
he is not man
obtuse plover
i think you should prob use permutations not combinations
we havent learned anything else other than this (just started my intro to probability class)
dire fjord
you should have 14P4 not 14C4
lean otter
whadda
man he is choosing
not arranging
ofc it will be c why p?
but i think u messed up the place where u chose 2 Es together
dire fjord
no event C wants him to draw 2 E 1 A and 1 N he should compute in how many ways can he get this
and then he will divide by total ways to get probability
lean otter
and then he will divide by total ways to get probability
for that u have to get the numerator and deno using permutations right
dire fjord
yea
obtuse plover
and then he will divide by total ways to get probability
isnt that what i did?
dire fjord
maybe both ways give same answer lemme check something
lean otter
but i think u messed up the place where u chose 2 Es together
u see i think u gotta make that 5c1*4c1
since u pick up one after another
wait i think theres more to it than meets the eye
dire fjord
oh ig i am wrong about this
lean otter
well the answer might be alright
but u see the 4! multiplied in the numerator?
thats what i was thinking about
obtuse plover
hmm i see
obtuse plover
https://math.stackexchange.com/questions/4002853/a-bag-of-scrabble-tile-contains...
this one right
lean otter
well part b makes it more confusing
its not easy to write it in chat
u got telegram?
lean otter
any social media?