Proposed solution to the problem uses Euler's path
#help-13
strange summit
They say: since n is odd, in K_n exists Euler's path, hence we can follow the path and properly direct the edges, that means there is Euler's path in T_n which implies deg in equals deg out
But that doesn't really proof that any graph that fits given properties has a Euler path
crimson sedge
what is T_n and K_n?
strange summit
Tournament of n vertices, full graph of n vertices
strange summit
Indeed
Hence my confusion, the solution the provide besically says, that there exist a tournament with Euler's path
strange summit
Hmm
crimson sedge
I guess we have to use the out degrees are all equal
crimson sedge
They say: since n is odd, in K_n exists Euler's path, hence we can follow the pa...
there's a proof of this claim here https://en.wikipedia.org/wiki/Tournament_(graph_theory)#Paths_and_cycles
wait nvm
that's for hamiltonian paths, not euler
cedar kilnBOT
@wraith basin Has your question been resolved?
crimson sedge
aight, I think I have something
since the outdegrees are all equal, then the sum of all indegrees are is equal to the sum of all outdegrees (each edge has an in and out)
we know the exact out + in degree of each vertex
so we can divide
then I think it turns out the in and out degrees are equal
wraith basin
we do know that
crimson sedge
everything else is a counting argument based on that fact
wraith basin
hm could you show the proof in our own words?
I still don't follow how we got deg_in = deg_out
crimson sedge
since the outdegrees are all equal, then the sum of all indegrees are is equal t...
do you get this ^
wraith basin
indeed
crimson sedge
so outdegrees = (n*(n-1)/2)/n = (n-1)/2
using the fact that all outdegrees are the same
crimson sedge
np
worn compass
cedar kilnBOT
worn compass
What did i miss here
stark cipher
didnt you see that i was already typing here?
tribal junco
Simple percentage question. Say you have two tries at winning a game, and you have a 51% chance to lose try 1, and a 7% chance to lose try 2. How would you come up with your total chance of losing the game? Just multiple the two together?
tropic oxide
wdym "losing the game"
there are four different outcomes:
- win in both tries
- win in try 1, lose in try 2
- lose in try 1, win in try 2
- lose in both tries
tribal junco
okay so if you lose just one of the tries you still win, but if you lose both you lose the game
tropic oxide
okay then yes, the chance of losing is just 0.51 * 0.07
cedar kilnBOT
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azure violet
why does excel keep rewriting 12.55 as time to date
cedar kilnBOT
why does excel keep rewriting 12.55 as time to date
@azure violet Has your question been resolved?
dire geode
why does excel keep rewriting 12.55 as time to date
This isn't a math question
Google Excel formats
.close
cedar kilnBOT
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lone dune
if i had to differentiate something like 2^x^2^x, would I use the chain rule in that case?
stable edge
That's $2^{x^{2^{x}}}$, yes?
bold vine
if i had to differentiate something like 2^x^2^x, would I use the chain rule in ...
Logarithmic differentiation
stable edge
if i had to differentiate something like 2^x^2^x, would I use the chain rule in ...
if y = 2^..., set u = 2^x => y = u^u, then find dy/du and sub 2^x back in.
lone dune
Logarithmic differentiation
oh i see
lone dune
if y = 2^..., set u = 2^x => y = u^u, then find dy/du and sub 2^x back in.
alr gotcha
i was just confused on whether i should use logarithmic differentiation or something like the chain rule while differentiating stacks of exponents
cinder venture
cedar kilnBOT
cedar kilnBOT
@cinder venture Has your question been resolved?
cinder venture
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obtuse heart
hi can you explain question 8 i don’t really understand how to do as f-1(1) denominator is 0
tribal kite
f^-1(1) means f(x) outputs 1
And x is -2
Thus just sub back
[a(-2)+b]/-3 =1
Since -3/-3 is 1, a(-2)+b=-3
And do the same for f(3)=7/2
[a(3)+b]/1 =7/2
a(3)+b = 3.5
U can see that a cannot be a negative number
(3)-6.5/a=(-2)
6.5/a=5
a=6.5/5
Then use (6.5/5)(3)+b=3.5
19.5/5+b=3.5
b=3.5-19.5/5
b=-0.4 and a=1.3
obtuse heart
the answer is a=2 and b=1 tho
tribal kite
Uhhhh
obtuse heart
u r having problem in inverse/
yeah
tribal kite
Probably made a mistake somewhere
obtuse heart
Probably made a mistake somewhere
yeah i got it
tribal kite
K good
obtuse heart
thanks for explaining
tribal kite
I'm bad with functions lmao
obtuse heart
it really helped lol
tribal kite
U got the explanation tho right
obtuse heart
yep
obtuse heart
I can't calculate without the ,calc
haha same
obtuse heart
.close
cedar kilnBOT
Available help channel!
Show your work, and if possible, explain where you are stuck.
crimson sedge
Looked like a nice puzzle
cedar kilnBOT
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restive flint
hey I was wondering if this is correct an inverse function implies that bijective and that implies it's one to one and u can go the other direction too
vagrant elbow
yes
restive flint
yes
I am a bit confused about this one
so I proved that it's inverse exist therefore it's bijective and therefore it's one to one
but
how is it bijective if the domain contains k elements and the codomain n - k elements
oh wait I think I intrepret it wrong
it meeans the cardinality of the element of each subset is k and the other one is n - k
and I was wondering he did it with the inverse approach but I could also proof injective and surjective and therefore it's bijective and that implies inverse and one to one right?
cedar kilnBOT
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gusty barn
I'm uncertain what I'm supposed to be doing with this problem. If I don't have what the unit vectors are how am I supposed to draw them? Am I supposed to just take the leading coefficients as the magnitudes of the x and y components?
gusty barn
nevermind, I realized that I answered my own question. The hat means they are unit vectors which are always equal to 1, right?
gusty barn
lol, feel dumb for forgetting that the unit vector always equals 1. Apologies for wasting your time.
safe tinsel
sometimes you see i instead of x hat and j instead of y hat
No worries.
No waste of time.
cedar kilnBOT
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cedar kilnBOT
dw about G
rain drift
hi there do you know how to find the slope for a perpendicular line?
old fjord
no i haven’t learned that yet
would you substitute the gradient into M1 x M2 = -1 ? @rain drift
clear berry
yes
old fjord
what about the y intercept
clear berry
find it using the fact that the line passes through the given point
hollow trail
if you know that y = mx + b and are given a particular value of x, y, and m, you can solve for b
fair zinc
Question 2 c part
cedar kilnBOT
Question 2 c part
fair zinc
Idk how to do it when the variable is on both sides
I got the other one but it this one what happens to h
Is it multiplying with b or ab both
tropic oxide
,rccw
wraith daggerBOT
tropic oxide
handwriting could be better but yes
near surge
Is multiplying a matrix by the inverse the same as multiplying an inverse of a matrix to the matrix?
IE: (A^-1)(A) =? (A)(A^-1)
torn wren
wraith daggerBOT
MathIsAlwaysRight
dusk finch
the only 3 properties used in that "proof" were associativity, A * A^-1 = I and A * I = A
cedar kilnBOT
@near surge Has your question been resolved?
near surge
I see, thanks!
frigid kelp
solving for −π ≤ x ≤ π
cedar kilnBOT
solving for −π ≤ x ≤ π
frigid kelp
im familiar with secant but I’m not sure how to go about it
would you do something like this?
weary vessel
For me, I would do it straight forward
I memorized that sec(pi/4)=sqrt(2)
So I would do this:
sec(x+pi/4) = -sqrt(2) = sec(-pi/4)
Now remove secants
You end up with:
x + pi/4 = -pi/4
x = -pi/2
frigid kelp
i think thats one of the answers
i dont have them so ill have to double check but thanks
weary vessel
Wait
Your method is also very good
You kind of made it into a cosine equation
Just rearrange it
divide by -sqrt(2)
cos(x + pi/4) = - 1 / sqrt(2)
And -1/sqrt(2) has a well-known angle
-pi/4 directly
cos(x + pi/4) = cos(-pi/4)
x + pi/4 = - pi/4
x = -pi/2
Same answer with different approaches
weary vessel
My bad, the angle whose cosine is -1/sqrt(2) is not -pi/4
There are two
pi - pi/4
and pi/4 - pi
Which give you x=pi/2 and x=-pi
fair zinc
cedar kilnBOT
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shell abyss
im so confused can anybody pls help me?
cedar kilnBOT
im so confused can anybody pls help me?
shell abyss
is the website glitched or what
lyric narwhal
10.85 is the semiperimeter, not the area
use the formula given in the top right to solve for the area
lyric narwhal
what do u mean
cedar kilnBOT
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dusty pasture
I'm asked to prove that if $x < y$ , then $x^n < y^n$, given that $n$ is odd.
I started off the proof by stating that if $x < y$, then $y-x$ is positive. I noted that all I would have to do to complete the proof is to show that
$$(y^{n-1} + xy^{n-2} + x^2y^{n-3} \dots + x^{n-2}y + x^{n-1})$$
Is positive, since by closure under multiplication, the product of 2 positive reals is also a positive real.
But I got stuck trying to prove this. I tried substituting $y$ for $x+a$, where $a = y-x$. But a lot of issues pop up: For one thing, you need to prove that this holds for all $n$. You also may need to take cases, such as when both $x$ and $y$ are positive, when they are negative, when one is positive and the other isn't..... I'm stuck. I'm aware that $x^{n-1}$ and $y^{n-1}$ are positive no matter what, and so is any of the terms with even powers, but even then I don't seem to be making progress. Perhaps I'm taking a wrong approach?
wraith daggerBOT
Kiameimon | Welt Rene
stable edge
i think you might be barking up the wrong tree with this y-x stuff
dusty pasture
yee
stable edge
my insinct says proof by induction
dusty pasture
possibly 
stable edge
so prove for n=1 that if x < y, then x<y
and then do some shit to show that if x^n < y^n, then x^{n+2} < y^{n+2}
and do the standard induction crap from there
dusty pasture
uh huh
cedar kilnBOT
@dusty pasture Has your question been resolved?
dusty pasture
... I'm having problem with the induction step- I'm unable to find an expression which will confirm that x^n < y^n implies x^n+2 y^n+2 .... Well, I probably could if I took it case by case, but I don't really like such tactics, and furthermore induction has not been covered yet in the book (it's briefly covered in the next chapter. I am somewhat familiar with induction, but this implies that there's a way to prove it without induction?)
mighty drift
I guess no derivatives ?
because otherwise just prove x -> x^n is strictly increasing if n is odd
mighty drift
because otherwise just prove x -> x^n is strictly increasing if n is odd
the derivative is n x^(n-1) >= 0 and > 0 except for x = 0
This means the function is strictly increasing
dusty pasture
ahh right, that'll work
mighty drift
... I'm having problem with the induction step- I'm unable to find an expression...
Actually the case splitting is really not that bad
||note that sgn(x) = sgn(x^n) = sgn(x^n+2)||
||Hence if sgn(x) != sgn(y), it's trivial||
||otherwise, if they're both positive it's basically known||
||if they're both negative then -y < -x and I let you end it||
as you can see it's not really long
patent sail
How would you partially differentiate this for epsilon1, epsilon2, ..
Do you need to use some kind of chain rule here?
patent sail
∂f/∂x = (∂g/∂x * h - g * ∂h/∂x) / h^2 is the formula apparently but I can't seem to find how they got the nominator
mighty drift
it's just the quotient rule
patent sail
Yeah I just figured ty, lemme try working it out again
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Available help channel!
rain quartz
cedar kilnBOT
rain quartz
I dont have an issue with solving the equation myself rather than inserting the information into the correct format, how would i put this in an online calculator for example?
wraith basin
depends on the calculator
You can just use a calculator designed for this kind of problem
cedar kilnBOT
rain quartz
.reopen
cedar kilnBOT
✅
rain quartz
using wolfram it gave me this, ive never been taught that sign. is there another sign for this?
dreamy sleet
using wolfram it gave me this, ive never been taught that sign. is there another...
it means “and”
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hot sand
Help
tropic oxide
,rccw
wraith daggerBOT
tropic oxide
@hot sand it appears you're good to go
hot sand
Here
tropic oxide
is this answer getting rejected?
cold briar
that should be the simplest form
tropic oxide
so what?
hot sand
So you can minus them
tropic oxide
So you can minus them
you said so yourself
hot sand
No, I'm asking if I can
tropic oxide
and i said yes
hot sand
So how do I do it?
tropic oxide
same way you broke up the fraction into a sum, but in reverse
wraith daggerBOT
tropic oxide
bad notation
hot sand
?
tropic oxide
by saying it in words and not symbols you deliberately remove all parentheses
also since when was there a ^3 exponent
sure, if you want, x^2 y/4 - 3/4 = (x^2 y - 3)/4
hot sand
x^3y - 3 over 4 is that correct?
tropic oxide
do not use words to write down expressions
hot sand
Is that correct, please?
tropic oxide
no and i am telling you how to correct it
hot sand
Ok
tropic oxide
use operation symbols (for division and fractions, that's /) and parentheses (incl. parenthesss that you would not write on paper surrounding the num and/or denom of any fraction)
i have already said how to write down the result of your subtraction properly:
(x^2 y - 3)/4
umbral drum
-reopen
limber flint
cedar kilnBOT
neon moon
This is an optimization problem with a given equation of motion. In this case the first derivative test can be applied, in which you may find critical point by letting derivative is 0 and test if it is a local maximum.
limber flint
This is an optimization problem with a given equation of motion. In this case th...
oh waiitttt its literally just a graph of h vs tantheta
is that it?
idk
i dont understand it yet
fully
ok
raw scaffold
...
limber flint
lmao ur pinging different ppl
raw scaffold
@sweet spoke PLS HELP
oh yes, A Random Asia Boy, why dont you ask A Random Asia boy?
sorry
i am using an iphone
hard to type lol
are you pure chinese btw?
cool
i am a 0.1-year-old boy so i dont know
dreamy sleet
are you new to discord?
it isn’t polite to ping random people
or to chat in the channels meant for helping with homework
That’s because I was replying to you and pointing out something you did
cedar kilnBOT
@limber flint Has your question been resolved?
limber flint
yea uhm i still dont get why its dh/dtheta instead of dh/dtantheta
here is the image
dreamy sleet
yea uhm i still dont get why its dh/dtheta instead of dh/dtantheta
That is because you’re varying the initial angle theta. You want to maximise some function depending on theta, so you differentiate wrt theta in order to find what value of theta gives you the biggest thing.
dreamy sleet
dollars, even
light pine
when we say eigenvectors for distinct eigenvalues are lin independent, does that mean that the set of each eigenspace contains a set of lin indendent vectors?
mighty drift
If you take n eigenvectors for n different eigenvalues, they form an independent family
mighty drift
What do you think ?
light pine
yes
light pine
yh
mighty drift
So if you take random vectors in it, are they lin. indep. ?
light pine
idrk tbh
mighty drift
Think
In math, it's fine to not know. But you should try to figure it out by yourself
light pine
idrk understand what a vector space has to do with it being linearly independent or not
mighty drift
Suppose the eigenspace is 1 dimensional. Can you find 2 vectors in it ? Is it possible for them to be independent?
dreamy sleet
do the eigenvectors for different eigenvalues form a basis for the eigenspace?
light pine
Surely a nonzero one too
yh
mighty drift
specify "eigenvectors"
mighty drift
do the eigenvectors for different eigenvalues form a basis for the eigenspace?
By definition, the eigenspace associated to the matrix A and value lambda is the set of eigenvalues for A and lambda
So it has a basis of eigenvectors
But it's not a basis itself as it's a vector space
light pine
yes?
mighty drift
Suppose the eigenspace is 1 dimensional. Can you find 2 vectors in it ? Is it po...
Let the space be E
Let x != 0 in E
Is 2x in E ?
Conclude on whether there are 2 vectors in E, and whether they have to make a independent family
mighty drift
A basis of eigenvectors yes
light pine
for a matrix
light pine
A basis of eigenvectors yes
and i assume each eiegnvector has to be from a distinct eigenvalue?
mighty drift
No
light pine
an eigenbasis cannot have two e vectors from the same eigenvalue right?
mighty drift
Exercise: find an nxn matrix such that you can find a basis of eigenvectors for the same eigenvalue
The ultimate counter example
light pine
but i thought we said that eigenvectors of distinct eigenvalues are linearly indepenent
hence eigenvectors of the same e value r linearly dependent
mighty drift
Does that mean the reciprocal is true?
mighty drift
Exercise: find an nxn matrix such that you can find a basis of eigenvectors for...
Legit do this exercise btw, it's good conceptual training
light pine
acc wait i have one more question
so
say u are diagnolasing a matrix
is it true that a matrix can be diagonalised iff there consists a basis of eigenvectors?
mighty drift
Direct corrolary of the definition
light pine
ok
so
i did a question
on diagnolaising a 3 x 3
and i obtained three e vectors in total
but two of them were not linearly independent
mighty drift
You failed
mighty drift
and they were from the same e-value
Duh, they're in the same 1D space
light pine
so does that mean it is not diagonalisable
^?
since i dont have an eigenbasis now
of 3 vectors
mighty drift
Just because you failed to diagonalize it doesn't mean it's not diagonalizable
light pine
but i thought we said a matrix can be diagonalised iff there contains a basis of eigenvectors
light pine
im just going off the defintion in my notes
mighty drift
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
@light pine Has your question been resolved?
unkempt cargo
they want the answer in simplest form
cedar kilnBOT
they want the answer in simplest form
unkempt cargo
i have the answer infront of me i js dk how to solve
its 3/5x radical10x
<@&286206848099549185>
odd snow
can you write 3.6 as a fraction
crimson sedge
36/100
odd snow
and do you know how to take something out of the radical
odd snow
yeah
crimson sedge
Continue im gonna switch to the other one
unkempt cargo
omg sorry i didnt seee this
i thought no one would answer
3.6 as afraction isss 36/10
odd snow
yes
unkempt cargo
im so sorry i didnt answer i thought i had notifs on
odd snow
for examle: how do you simplify √(8x³)
same thing but a bit simpler
you know what a square root is right?
unkempt cargo
yes
odd snow
and you should know that √a*√b=√(ab)
unkempt cargo
yea
odd snow
okay
odd snow
they want the answer in simplest form
can you take 36 and x³ out of the radical
how can you take them
36=6² you know and x³=x*x²
take them out
let /10 stay inside
unkempt cargo
do we simplify 36 so it would be 6x^2|x|
unkempt cargo
yea
unkempt cargo
yes
odd snow
we took 36 and x² out of the square root
now it is already simplified but we can simplify a bit further if you want to
we can say that x/10=10x/100
right?
unkempt cargo
yea
unkempt cargo
do we divide both sides by 10?
unkempt cargo
ohhh okay
odd snow
it will become the denominator
outside
too
after all we have 6x/10 outside and 10x inside
6x/10 can be written as 3x/5
unkempt cargo
thats so simpleee
odd snow
so final answer 3x/5√(10x)
odd snow
you can do the same thing for the rest
unkempt cargo
okayyy
odd snow
look inside of the square root
you must find something that is someones square
for example 36 was 6² here and x³ was x²*x
we took the squares out
unkempt cargo
.close
obtuse heart
for this is the answer x greater than or equal to 0
cedar kilnBOT
for this is the answer x greater than or equal to 0
@obtuse heart Has your question been resolved?
obtuse heart
<@&286206848099549185>
autumn current
for this is the answer x greater than or equal to 0
is that 4x?
if yes, then x-8 = 4x and x-8 = -4x
but then you chuck x-8 = 4x since its value is negative
obtuse heart
is that 4x?
oh its |x-8|, x is a real number
thats g(x)
sorry for my bad handwriting
autumn current
oh
ok i got the question
so |x-8| >= 0
thats just every value of x, this equation holds true for every given value of x
obtuse heart
ahh
obtuse heart
so |x-8| >= 0
wait does | x-8| means that there is no negative value
and so thats why its 0?
granite knoll
the absolute value of any number is >= 0
autumn current
wait does | x-8| means that there is no negative value
yes
obtuse heart
ah ok thanks for your help
autumn current
|| means removing the sign, only getting magnitude
merry beacon
hi
cedar kilnBOT
@merry beacon Has your question been resolved?
neon vortex
if i have a circle inside a square
and i want area of the region in the square but not in the circle
how would u do it
merry beacon
I would not
neon vortex
ok if you were to find area of the region
how would u solve it
area of the square is given
so is the area of the circle
how would u find the area of the region in the square but not in the circle?
@merry beacon
merry beacon
am sorry i learned this a long time ago so i kinda forgot it
merry beacon
i understand what you mean tho
neon vortex
if your house has 10 m^2
and ur room is 5m^2
how much area do u have in your house
just think for a second
neon vortex
yes
now you have area of def correct?
can you find area of dmn?
do you know the concept of similar triangles?
merry beacon
never heard of it
neon vortex
oh
since M and N divide the lines in ratio 1:2
area is also in the ratio 1:2
area of mnef is 2 times dmn*
dmn + mnef is def
merry beacon
m divides DE in the ratio 1:2 and n does the same to DF
neon vortex
dm + me = de correct?
im talking about length here
merry beacon
so dm=4 and dn=8/3
merry beacon
dm + me = de correct?
yes
neon vortex
same goes for dn and nf?
now based of this
can i say
mn divides def in the ratio 1:2
for area
merry beacon
yes
merry beacon
it would be def
merry beacon
oh my bad
neon vortex
its ok
just look at it again
mn divides def in the ratio 1:2
so what is the ratio of area of dmn and femn
@merry beacon
neon vortex
1:2
neon vortex
mn divides def in the ratio 1:2
here
merry beacon
oh
merry beacon
2 times
neon vortex
are you sure
merry beacon
no
merry beacon
half then
merry beacon
yes
merry beacon
72=dmn+femn
neon vortex
and dmn = 1/2 femn
72 = 1/2 femn+ femn
72 = 3/2 femn
72 * 2/3 = femn
48 is femn
merry beacon
so then 72-48=dmn
merry beacon
=24
merry beacon
nice
but here the thing
i asked here because i couldnt really understand the answer sheet
neon vortex
oh i think we've made an error somewhere then
merry beacon
and thats where am confused
neon vortex
hmm let me just see if I've mis read the question
oh my bad I've missed a point here
de and df are divided in the ratio 1:3
1:2*
merry beacon
yep
merry beacon
where did they bring the ratio 2:1 ?
neon vortex
so dm is 1/3 times de
neon vortex
where did they bring the ratio 2:1 ?
its cut into 1:2
2 pieces
which are in the ratio 1:2
so first is half the length of second
so first is 1/3 times full length
so dm is 1x and de is 3x correct?
merry beacon
yeah
neon vortex
so dmn is 1/9 times def actually
i made an error previously
ratio of areas is square of ratio of sides
merry beacon
how did it become 9?
neon vortex
if the sides of a square are in the ratio 1:2 the ratio of areas is 1:4 correct?
merry beacon
yeah
neon vortex
same here
merry beacon
ohh
neon vortex
the sides here are in the ratio 1:3
so area is 1:9
ive missed these 2 points
thats where we went wrong
my bad
merry beacon
thats alright your helping me more than the book
neon vortex
so now do you understand the problem?
now that its 1:9
femn is 8:9
because dmn is 1/9th
and femn is 8/9th correct?
merry beacon
yes
merry beacon
then 72-64=8
neon vortex
its been around 3-4 years since ive solved such questions
neon vortex
then 72-64=8
area of dmn yes
neon vortex
np
merry beacon
.close
ionic yoke
cedar kilnBOT
ionic yoke
would the resulting vector of boats velocity realtive to ground
be
15 i -4 j
which means the boat is traveling at sqrt (241) mph relative to ground?
cerulean star
@ionic yoke verifying solutions is faster when you show your work
cerulean star
So the 15mph should be the magnitude of the resultant vector
Not the magnitude of a cardinal component vector
astral drum
If a relation is symmetric, antisymmetric, reflexive and transitive is it a equivalence relation?
dire geode
A relation probably can't both be symmetric and antisymmetric?
astral drum
Rly?
What about this relation p on the set of S {(1,1),(2,2)
It would be antisymmetric since no two distinct elements are symmetrically related
But it would be symmetric since (1,1) is equal to (1,1)
Right?
dull oxide
If a relation is symmetric, antisymmetric, reflexive and transitive is it a equi...
You just need reflexive, symmetric, and transitive for and relation
astral drum
Ok so it is a equivalence relation right?
dull oxide
What are the exact set and relation?
astral drum
The set S ={1,2} and the relation u ={(1,1),(2,2)}
dull oxide
So 1R1 and 2R2
astral drum
Ye
dull oxide
Yes it is an equivalence relation
astral drum
And was I right in saying it’s both symmetric and antisymmetric?
dull oxide
It is also a partial ordering because, you are correct, it is antisymmetric
astral drum
Ok right wait what partial ordering again?
dull oxide
A relation is a partial order if it is reflexive, antisymmetric, and transitive.
dull oxide
I think you would write them as {{1}, {2}}
astral drum
Oh right yeh ok thanks again u saved me
dull oxide
Or [1] and [2]
crimson sedge
cedar kilnBOT
dusk helm
No, x could be 14,47 though, but there's another solution
and I don't get where the < symbol is coming from
,w graph (x-10)^2+(y-4)^2 = 36
wraith daggerBOT
dusk helm
you see the two points intersecting w the x-axis? those are your two solutions.
crimson sedge
and I don't get where the < symbol is coming from
Because if it’s greater than that value it’ll be outside of the circle therefore I believe it won’t be a solution
Yea
Ohhh
I get it
Alr thanks
dusk helm
np
crimson sedge
.close
crimson sedge
I am not really familiar on how to do the work for this problem
dire geode
,tex .maclaurin
wraith daggerBOT
riemann
dire geode
Pain I left out arctan
Do you know the Maclaurin series for arctan
It's very similar to 1/(1-x)
lapis maple
you could figure it out right
crimson sedge
It’s 1/1+(x^2) dx
runic garnet
I mean yea u integrate that series to get arctan series
fervent crag
i am trying to find the domain of (x-5)^2 = y+3, but how is there a domain if its x^2 and not like sqrt(x)? i cant think of a number that would not satisfy this equation
crystal raptor
if you cannot think of a number that is not in the domain, then what do you think the domain is?
storm bone
you don't solve equation by thinking. use formula
fervent crag
@storm bone what formula?
dusk helm
there is no specific formula for the domain.
fervent crag
well i thought x could be equal to anything, but the answer is somwhow x>= 5
crystal raptor
do you have a picture of the original question?
fervent crag
yes ill type it out
f(x) = 5 + sqrt(x+3) what is the domain of f^-1(x)
i substituted x in for f(x), and y in for x; then isolated y and got y = (x-5)^2 - 3
crystal raptor
the domain of a inverse function is the range of the original function
fervent crag
and the range is any possible output of the funciton?
crystal raptor
yeah all the values it can (and does) achieve
fervent crag
okay that makes a lot of sense
because the square root would have to be positive, and 5 is outside of that
so anything above 5
or 5
crystal raptor
yeah thats the range of f
fervent crag
sick, thanks dawg
crystal raptor
your initial thoughts werrent quite right becasue you werent thinking of your function as the inverse of some other function
cedar kilnBOT
cedar kilnBOT
Available help channel!
flat thicket
I NEED HELP!!!
cedar kilnBOT
I NEED HELP!!!
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
1
dire geode
,tex .transformation rules
wraith daggerBOT
riemann
crimson sedge
:goodtex:
dire geode
God I wish that didn't take 187 seconds to compile
Feel free to keep uploading that image Toby. I need to work on optimization that snow set up
crimson sedge
Feel free to keep uploading that image Toby. I need to work on optimization that...
or post an image of precompiled bot outputs, thus negating the factoid system all together
cedar kilnBOT
@flat thicket Has your question been resolved?
flat thicket
yes
muted bear
Its poorly written
exotic verge
nvm, it is 0
exotic verge
If we were to use it tho, what would that look like?
sage badge
It would be the long way around
You would take the integral and evaluate the difference between when x=π/2 and when x=0
And that leads to a constant
exotic verge
ye
exotic verge
Well FTC can't be used here right?
sage badge
That’s… the upper limit
exotic verge
yes
sage badge
Use F(upper)-F(lower)
It’s part of the FTC
Do the integration first
Then differentiate
long swan
it's 0
long swan
it's a definite integral so it just becomes a constant
sage badge
Not trying to be rude
long swan
yeah. not tryna be rude either but you're kind of spreading misinfo
sage badge
I think the helpee is offline
exotic verge
Nah, I'm tryna do it using FTC rn
exotic verge
So, when would we use the FTC?
sage badge
When definite integral
exotic verge
Ah I see
sage badge
If your problem is solved, you can close the channel
cedar kilnBOT
cedar kilnBOT
Available help channel!
ebon aurora
cedar kilnBOT
ebon aurora
i been stuck on this for ages
thorn furnace
ewll youre told its a quadratic sequence so maybe write out some sort of equation that tells you the nth term is a quadratic in n
obsidian coral
obsidian coral
3n squared + something
Yes part of the formula is 3n^2
You need to find the rest
Use the resources I presented
cedar kilnBOT
@ebon aurora Has your question been resolved?
real crane
help
real crane
i need help understandingthis whole thing
kindred bridge
do you know what a coterminal angle is?
cosmic steppe
Keep on subtracting or adding 360° until you get a value between 0 and 360
Coterminal angles are exactly what they sound like: they terminate at the same "spot" (they have the same reference angle)
cedar kilnBOT
@real crane Has your question been resolved?
cosmic steppe
I spoonfed you how to do it
What else do you want me to do? Chew the food for you?
bold hazel
cedar kilnBOT
bold hazel
I'm assuming that this question is asking how many digit strings do not have 2 consecutive zeroes?
in any possible place they could be?
bold hazel
total 5 digit strings: 10^5
and then subtract the strings with consecutive zeroes
looks like that is C
pretty confident that's it
it wasn't 😭
fiery whale
why 9^3
cedar kilnBOT
@bold hazel Has your question been resolved?