I don't know what to do after I reach a point
#help-36
opaque pier
final saddleBOT
I don't know what to do after I reach a point
opaque pier
I reached the point where i*w (where w is a cubic root of unity) = (z+1)/(z-1)
Any hints on how to proceed?
desert mantle
multiply by z-1 and isolate
cold wolf
Is it possible to calculate y (mod 25) while knowing this information?
desert mantle
well not uniquely
cold wolf
Oh right i forgot to mention, caluclate smallest y(mod25)
vernal parcel
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vernal parcel
how would u know when to multiply and add
for this it's 4C3 + 5C2 or is it multiply?
royal swan
for this it's 4C3 + 5C2 or is it multiply?
Multiply, because you need total 5 people
So 3 from women and 2 from men
Where there is an and then it's multiply
mint arrow
how would u know when to multiply and add
When the cases are mutually exclusive add and when they are independent multiply
vernal parcel
how would u know when to use which case
so basically when one case effects the other u add
and when they both don't effect each other u multiply
mint arrow
Yes
final saddleBOT
mint arrow
mint arrow
14! - 11! x 4! all over 14!
For the second part right?
mint arrow
14! - 11! x 4! all over 14!
Yup it's correct
mint arrow
isn't this the worst math topic ever
it isn't it's just that you are doing exercises and not problems from the topic
Combinatorics is the most interesting branch of maths for me
vernal parcel
like binomials?
mint arrow
If you allow me I could give you a question regarding the topic which might invoke some interest
vernal parcel
If you allow me I could give you a question regarding the topic which might invo...
go for it but i haven't done combinatronics to a high level
just year eleven
mint arrow
go for it but i haven't done combinatronics to a high level
Np wait let me check your answer first
mint arrow
this is four right
Yup correct
vernal parcel
thanks
mint arrow
go for it but i haven't done combinatronics to a high level
In how many way can 8 people seated on a circular table shake hands given that no hands cross ( no more than 2 people can shake hands at a time)
vernal parcel
hmm
i've done a similar question but nothing with a circular table
8+7+6+5+4+3+2+1
mint arrow
Are you giving the answer?
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final saddleBOT
how do we reclaim the channel
mint arrow
My advice regarding the problem would be to think that whether there is something special about 8 or it's just arbitrarily given
vernal parcel
i'm not sure how to do it
mint arrow
i'm not sure how to do it
Ok here's another hint - forget 8 do it for smaller numbers like 2 - 4 - 6 so on
|| Can you observe how the prob for 4 is related to 2 ie can you connect them ||
vital crag
how do we reclaim the channel
if your channel was taken over by somebody else, you just copy paste your question and new progress/work.
vernal parcel
alrighty
mint arrow
Ok here's another hint - forget 8 do it for smaller numbers like 2 - 4 - 6 so on...
And thats a advice for all problems when you can't solve for bigger numbers solve for smaller numbers first then go for the bigger ones
vernal parcel
Ok here's another hint - forget 8 do it for smaller numbers like 2 - 4 - 6 so on...
i;m still unsure lol
mint arrow
In combinatorics it might happen that the problem for bigger numbers is closely related to that for smaller numbers ie there exists a || recurrence relation||
vernal parcel
i think i get what you mean
but i'm unsure what the question is asking
how many handshakes can be done with eight people or?
mint arrow
how many handshakes can be done with eight people or?
It's asking for 8 people and I believe I mentioned that in the problem
vernal parcel
7+6+5+4+3+2+1
mint arrow
why so ?
flint parcel
Hello
mint arrow
as one person can shake everyone's hand seven times
shaking of hands takes place simultaneously
vernal parcel
<:sully:651816820122189834> shaking of hands takes place simultaneously
ohh i think i get it
are u asking for the maximum amount of handshakes possible between eight people?
mint arrow
are u asking for the maximum amount of handshakes possible between eight people?
How many ways can 8 people handshake simultaneously given that no hands cross
flint parcel
Is here anyone from 9th grade?
vernal parcel
How many ways can 8 people handshake simultaneously given that no hands cross
i have no idea can u explain
mint arrow
How many ways can 8 people handshake simultaneously given that no hands cross
Nvm if you don't understand the problem leave it
It was my mistake to give you a diff at a starting stage
I just wanted you to understand the problem and then appreciate the slick solution but il do that some other day when you are better in combi
vernal parcel
okay lol
mint arrow
i have no idea can u explain
mint arrow
how would u do this though
Hmm okay so we have a degree 4 polyn and it's given that one of its roots has multiplicity 2 so one part of it must be (x-2)²
And it's given its divisible by x²+x+1 so that forms the other part which gives us the complete polyn as a(x-2)²(x²+x+1)
a is a constant
mint arrow
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tough light
2 rue clos mon désir 69100 Villeurbanne
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2 rue clos mon désir 69100 Villeurbanne
severe canyon
2 rue clos mon désir 69100 Villeurbanne
????
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crude maple
could sum 1 help me do my 7th grade math homework
final saddleBOT
could sum 1 help me do my 7th grade math homework
acoustic bloom
what's the question
atomic moon
acoustic bloom
you can just add the exponents since the base is the same
crude maple
could i get the answer 🙂
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final saddleBOT
could i get the answer 🙂
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
bold lake
could i get the answer 🙂
Add the exponents over 1 y
lapis wedge
What does homogenous differential equation mean?
final saddleBOT
What does homogenous differential equation mean?
lapis wedge
tried looking it up but I couldnt really understand
I know what a homogenous system is
in case its similar to that
steady yoke
It’s homogeneous if all the parts that depend on y and it’s derivatives compose the equation entirely
In other words, you cld place all the y parts on the same side of the equation, and it’d = 0
It’d be inhomogeneous if there was an f(x) that doesn’t depend on y or it’s derivatives, and f(x) isn’t 0
formal trail
a homogeneous system of linear equations is one in the form
Ax = 0
for example
4x - 3y = 0
a homogeneous linear differential equation is similarly in the form
L[y] = 0
for example
4y' - 3y = 0
is a linear homogeneous linear ode
lapis wedge
oh
steady yoke
The importance of a homogenous DE comes from the fact that any solution forms part of a basis for the solution space
lapis wedge
I think I see so the x vector is composted of y and it's derivatives
and if there was a constant
we would have no variable for that constant essentially and it'd be like
3x + 3 = 0
and that wouldnt be homogenous
and by linear
do they mean
all y and it's derivatives must be raised to only the first power
3y - 4y' + y'' = 0
but 3y^2 isnt linear?
steady yoke
but 3y^2 isnt linear?
This is correct
formal trail
yes, in the same sense that an ordinary linear equation is linear
steady yoke
But linear simply refers to it must be a linear combination of y and it’s derivatives
lapis wedge
oh ok
im taking linear algebra and de currently and this de hw but it seems to incorporate some linear algebra
thats pretty interesting
opal pelican
I may be mistaken, but isn't a homogeneous differential equation one in which the solution function y is an homogeneous function of x?
formal trail
the study of linear differential equations is very dependent on linear algebra
formal trail
I may be mistaken, but isn't a homogeneous differential equation one in which th...
unfortunately there are two senses of the word homogeneous in differential equations which have nothing to do with each other
opal pelican
unfortunately there are two senses of the word homogeneous in differential equat...
By homogenous function I mean a function such that f(kx)k^nf(x)
formal trail
in the context of linear odes homogenous means the same thing as it does in linear algebra
opal pelican
I recall reading something along those lines, but again I may be spouting nonsense
opal pelican
in the context of linear odes homogenous means the same thing as it does in line...
Hm, alright
steady yoke
Homogeneous in context of DE refers to the fact that any solution of the De can for form part of a basis of its solutions space
You’ll find that you can engineer DEs so any type of function satisfies it
lapis wedge
- y' = 3y
- y' = 2 - y should work right
yeah I believe thats right
thanks for the explanation on homogenous and linear
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pine ridge
is there a mistake in this solution because i got 2.56
final saddleBOT
is there a mistake in this solution because i got 2.56
vital crag
show how you got your answer
vital crag
,rotate
soft zealotBOT
pine ridge
hey @vital crag
vital crag
i just plugged into my calculator
yea don't do that
vital crag
use the quadratic formula
pine ridge
ok
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chrome cipher
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rocky tusk
,w (2x^4 + (4-2i)x^3 - (5+4i)x^2 + 5ix)/(x-i)
soft zealotBOT
rocky tusk
no way it doesn’t show the quotient
drowsy epoch
😂
chrome cipher
u again
drowsy epoch
exactly my thoughts
chrome cipher
ok shut up
chrome cipher
not even
drowsy epoch
not f(-x) = f(x) so true
rocky tusk
still don’t get why you don’t just check it
drowsy epoch
me too
rocky tusk
check the answer by submitting it
chrome cipher
its a review one i complete the whole thing then i get see what i missed
rocky tusk
so submit?
chrome cipher
im like halfway done
chrome cipher
drowsy epoch
"just give me the solution"
drowsy epoch
"help me"
chrome cipher
i hate yall
rocky tusk
cool
chrome cipher
thanks
rocky tusk
happy to help
chrome cipher
THen help
chrome cipher
aleifght
drowsy epoch
maya is afraid she will get backstabbed with a knief
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dim hazel
Am I tripping or does no work need to be done here? I’m asked to find the LU decomposition of\$$A=\begin{bmatrix}
2&4&2\0&5&2\0&0&9
\end{bmatrix}$$\
But because A is already upper triangular, doesn’t that automatically mean L is the identity matrix?
final saddleBOT
Am I tripping or does no work need to be done here? I’m asked to find the LU dec...
soft zealotBOT
KySquared
wary copper
**KySquared**
i guess they just want u to write an identity matrix
seems relaly pointless but
ig thats it?
@dim hazel
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delicate sparrow
How do I determine if these graphed functions are negative or positive? For normal straight lines I have learned to use something like x < 3 if it is positive and x > 3 if it is negative. I am stuck on these problems because of how they are graphed
final saddleBOT
How do I determine if these graphed functions are negative or positive? For norm...
delicate sparrow
Same for this
delicate sparrow
the a value of the quadratic?
Wym
sleek quartz
Where the function is positive and negative
oh like the intervals?
delicate sparrow
I think so
sleek quartz
1 < x < 2 or whatever
delicate sparrow
Something like that
"...and describe where the function is positive and negative" is what I need to do
sleek quartz
1 < x < 2 or whatever
yeah this is about it really
i would say that's describing it
delicate sparrow
Can you explain
sleek quartz
"the function is positive when x is less than 2 but more than 1"
so when x < 2 and 1 < x
put together that's 1 < x < 2
sleek quartz
well can you read the graph
sleek quartz
just find the parts that are negative and positive
delicate sparrow
Same for this
Would I also just use the same concept here except it's not a curved graph and just arrows
delicate sparrow
just find the parts that are negative and positive
How
I get the parabola one but an upside down parabola is different
sleek quartz
positive = above the x axis, negative = below the x axis
delicate sparrow
Like the graph is going above the x axis?
sleek quartz
well can you read the graph
well you see why that's true here right
delicate sparrow
Yes
Pretty sure why
But an upside down parabola would be like the same thing unless it's not
sleek quartz
it would indeed be the same thing
sleek quartz
How do I determine if these graphed functions are negative or positive? For norm...
tell me what you get for the second one here
delicate sparrow
So even if it is upsidedown If it goes to the to sides it's positive?
sleek quartz
do you know how to read a graph
delicate sparrow
tell me what you get for the second one here
X > -4 is positive and -3 < X is positive
Yes?
sleek quartz
How do I determine if these graphed functions are negative or positive? For norm...
at x = 0 the line is at y = -6
are you telling me -6 is a positive number?
delicate sparrow
But we read if the graph is positive or negative based on the x axis?
Like in the first picture
Why doesn't that just apply to the 2nd graph
sleek quartz
every value of x has a y value assigned to it
we want to know where that y value is positive
sleek quartz
at x = 0 the line is at y = -6
for example 0 has -6, so it's negative at 0
delicate sparrow
What
sleek quartz
do you know how to read a graph
i think we should circle back to this
delicate sparrow
do you know how to read a graph
Uhmm
Sort of
Yeah I do
I think
Depends what graph
I can read this
sleek quartz
ok let's just look at this for now
can you tell me where y = 0?
delicate sparrow
ok let's just look at this for now
can you tell me where y = 0?
Y = 0 at X = -3 or so
Wait no
delicate sparrow
ok let's just look at this for now
can you tell me where y = 0?
Y = 0 at X = -1
delicate sparrow
Y = 0 at X = -2
delicate sparrow
Y > 0 at -1 < X and X > -2
sleek quartz
very close, the first condition is -1 > x
delicate sparrow
Ok
sleek quartz
which is this region btw
delicate sparrow
Ok
sleek quartz
but yeah the idea is that y is positive in -1 < x and -2 < x
sleek quartz
i saw a really good explanation for why this is a while ago but i can't find it anymore
but "-1 is bigger than x" and "x is bigger than -1" are opposite statements
delicate sparrow
But -1 is less than X and X is greater than -1 is the same thing
sleek quartz
but yeah the idea is that y is positive in -1 < x and -2 < x
wait mbmbmbmb that should be -1 > x
you're right
delicate sparrow
Ok
delicate sparrow
well can you read the graph
I think I get how to do the homework based on this
sleek quartz
nice
sleek quartz
yea
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bright nest
So 2 things: I want to make sure what I’m saying is sufficient enough to prove the statement as I am struggling to construct proofs. And I need help with the last statement F: (A n B = C) - I understand that it’s True but I’m not really sure how I would go about proving that (discrete math)
final saddleBOT
So 2 things: I want to make sure what I’m saying is sufficient enough to prove t...
@bright nest Has your question been resolved?
bright nest
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sturdy frigate
Your answers of a-e looks good to me
For the last part you need to do two things
Let x \in BOTH A and B and show its in C
Let x \in C and show its in BOTH A and B
which shows A intersects B is a subset of C
and C is a subset of A intersects B
bright nest
Let x \in BOTH A and B and show its in C
For this part would I write something like:
Let x in A n B => x=10k
sturdy frigate
Yes thats what you need to show
bright nest
I’m not rlly too sure what I should write after that
sturdy frigate
Yea I realize this is a bit tricky
First of all you have x=5n=2m right?
because it is in both A and B
Then you can look at 5n=2m and see what it means for n
what you really want is x=2(5k)
bright nest
what you really want is x=2(5k)
From there would I basically say that this is equal to C bc C is 2(5k)
bright nest
Not yet I’m still kind of struggling with that
sturdy frigate
I guess it requires some knowledge of divisibility of numbers
From 5n=2m, we see RHS is even (which means it has a factor of 2)
But 5 has no such factor (coz it's prime)
so it must comes from...
Does that help you?
bright nest
So n itself has to be even
sturdy frigate
Yes, exactly
bright nest
Yes, exactly
Would I then say something like X = A n B there fore the statement is true?
bright nest
and x is in B
Would this be sufficient enough to say
sturdy frigate
Would this be sufficient enough to say
Yes I guess so
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tired mango
Sorry for the blurry picture. I just want to check my answer. "This statement is true because limits are approaching the value of x=0, meaning that it doesn't matter where x=0 is or if it's defined at all."
final saddleBOT
Sorry for the blurry picture. I just want to check my answer. "This statement is...
soft zealotBOT
icannotdoanymorecauchy
tired mango
If that's true, then is this also true based off the same line of reasoning?
tranquil pine
Yes
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vernal spade
can we say that all the equal sets are actually each others' subsets?
vernal spade
Such as A = {1,2,3}, B = {1,2,3}. Can we say that A subset of B?
distant sleet
Such as A = {1,2,3}, B = {1,2,3}. Can we say that A subset of B?
yes
vernal spade
all equals are subsets but not all subsets are equals?
distant sleet
yeah I think so
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tranquil pine
Sorry guys, I don’t know shit. Can anybody teach me how to do this?
final saddleBOT
Sorry guys, I don’t know shit. Can anybody teach me how to do this?
soft zealotBOT
white sphinx
Sorry guys, I don’t know shit. Can anybody teach me how to do this?
write the dimensions of the inner rectangle
you have the dimensions of outer rectangle and you also know how much they subtracted
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cedar rapids
Hello, I need help with a math homework that I want to solve but I don't understand how to solve some questions.
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Hello, I need help with a math homework that I want to solve but I don't underst...
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cedar rapids
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cedar rapids
ya entendi
tranquil pine
why is weeb
cedar rapids
do you know spanish? or do I say it in English?
This fact that everything is in English is stressing me out :c
unreal anvil
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red basin
I need help on 2 problems. The first one is this: a jet leaves the Charlotte North Carolina airport traveling at an average rate of 564 km an hour. Another jet leaves this airport 1/2 hour later traveling at 744 km in the same direction using an equation to find how long the second jet will take to overtake the first.
final saddleBOT
I need help on 2 problems. The first one is this: a jet leaves the Charlotte Nor...
red basin
The distance?
fast grotto
no the distance is actually gonna be the same because we are setting them up to be at equal distance to see when the faster one overtakes
id think of it like this
the time is what we need to find right
so that can be the thing we change
red basin
Oh ok
fast grotto
when 30 minutes pass
then obviously the plane that started first is far ahead
but slowly after the 30 mins pass and maybe an hour passes in total, the planes might be a bit closer right?
red basin
Yeah
fast grotto
so you can set something up where you get
564*t
t is time
and that is for the first planes total distance travelled
what do you think the equation for the second plane would be
fast grotto
all g what u think
red basin
744(t+30)
red basin
.5 instead of 30?
fast grotto
yeyeye
BUT!
you shouldnt be adding
instead you should be subtracting
cause lets take it at 1/2 hour
then the 564(1/2) will have travelled a good bit
but then with the equation you found
744(1/2+1/2)
that one travelled hella
red basin
I see
red basin
After that wouldn’t it be 564t=744(t-.5)
fast grotto
yep
red basin
Ight
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quiet tiger
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quiet tiger
Can someone help me solve this
floral solstice
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@quiet tiger Has your question been resolved?
quiet tiger
no
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@quiet tiger Has your question been resolved?
fathom stream
This is what Im thinking for (b):
We already know from (a) that a binomial heap has exactly n - alpha(n) edges so now if we were to insert k keys, the total number of edges will be (n + k) - alpha(n + k):
total number of new edges: [(n+k) - alpha(n+k)] - [n - alpha(n)] = k - [alpha(n+k) - alpha(n)] = k - delta(alpha)
Avg cost per insertion ovr the course of k insertions:
(k - delta(alpha)) / k = 1 - delta(alpha)/k
Now im guessing that delta(alpha)/k is small for large k which would imply that avg cost approaches 1 as k increases? idk
final saddleBOT
This is what Im thinking for (b):
We already know from (a) that a binomial heap...
fathom stream
My whole group gave on this subpart
I feel like Im on the right track but im not sure
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fathom stream
fuckit Im done with this question Imma just go with this draft It seems good to me
stoic fable
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tranquil pine
!15min
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vital surge
unfortunate probably
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<@&286206848099549185>
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ancient kestrel
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ancient kestrel
I have no idea where to go
I've tried a ton of different methods, like drawing out the triangles, drawing out the quadrilateral
I dont think it is possible to find the value of x or y separately
stone wagon
no need to
ancient kestrel
So I was thinking we could just find x+y somehow, but cant figure it out either
stone wagon
can you find these angles, or, rather, their sum?
stone wagon
So I was thinking we could just find x+y somehow, but cant figure it out either
if you need another hint tell me
stone wagon
correct!
ancient kestrel
I was running around in circles trying so many different methods lol
Then i figured it wasnt possible to find x & y separately
So was trying to do x + y somehow
stone wagon
I got it, but how did you figure we needed that so quickly?
i know the blue and green angles, so all i need is the sum of the red ones to figure out x+y
idk
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candid cedar
why r=3/5 rejected
final saddleBOT
why r=3/5 rejected
white tiger
why r=3/5 rejected
because 3/5 > 1/2
candid cedar
so what
ionic venture
tropic nymph
Hey can anyone explain this derivation
final saddleBOT
Hey can anyone explain this derivation
vital surge
Hey can anyone explain this derivation
tropic nymph
my natural thought would be more this approach if I see a^x
spark kettle
Here you have a variable to some constant. Previously you had constant to a variable
tropic nymph
Here you have a variable to some constant. Previously you had constant to a vari...
ahhh that makes sense yeah
is variable always a letter?
because what if the thing is 2^2
(d/dx) 2^2
spark kettle
I mean intuition gives you that
$$(x + 1)^n - x^n = n \cdot x^{n - 1} + ...$$
While
$$a^{x + 1} - a^{x} = (a - 1)\cdot a^{x}$$
soft zealotBOT
Pluton
spark kettle
I mean this isnt a derivative ofc but you can see the change
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warm prairie
If a×b <= 36, when is (that fraction + that fraction => 1) true?
final saddleBOT
If a×b <= 36, when is (that fraction + that fraction => 1) true?
warm prairie
(My failed attempt below)
silk wind
If a×b <= 36, when is (that fraction + that fraction => 1) true?
Does it want a range as answer
warm prairie
It just says "when is equality?"
They really badly specified what they want
"Be that a and b are positive integers with ab<=36
Prove that:
(Sum of them fractions => 1)
When is equality?"
drowsy epoch
They really badly specified what they want
Die wollen nur wissen, wann der istgleich fall passiert
hollow sorrel
If a×b <= 36, when is (that fraction + that fraction => 1) true?
here's *a* possible solution
fix a, note that RHS is minimised when b = 36/a, hence it suffices to show it's true for ab = 36
you could then use calculus to minimise a = free, b=36/a
silk wind
Just tried 2 random numbers and it worked but that does not sound too mathemathical
hollow sorrel
you could then use calculus to minimise a = free, b=36/a
^
warm prairie
I know I read everything, Im just trying to understand
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indigo plover
ik some people say its not math sry its chem
final saddleBOT
ik some people say its not math sry its chem
indigo plover
I just watch organic chem tutor
and he use m1p1+m2p2=average atomic mass
what is this formula being used then
foggy wren
what is this formula being used then
thats the same formula
foggy wren
its the atomic mass of the carbon 12 * its abundance
foggy wren
haha
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narrow yew
I have this discrete dataset of a bacteria growth. How can I find an elementary function that aproximates it?
final saddleBOT
I have this discrete dataset of a bacteria growth. How can I find an elementary ...
royal gust
Looks kind of like a quadratic
narrow yew
yeah I got a close quadratic aproximation
but I need more precise
this is as close as I could get
royal gust
You can probably get better with a cubic. Looks like those two right points are at the cubic's inflection point, and the curve will start going up
royal gust
You can make it periodic
narrow yew
But how on earth would I go on to find such coefficients
mint orbit
wouldnt you be better using some model that was informed by the physical medium 
narrow yew
wouldnt you be better using some model that was informed by the physical medium ...
what exactly do you mean?
narrow yew
i mean like, its bacteria right
it's not an actual analysis though they're just simulated numbers
mint orbit
oh and the assignment is just 'find a function that looks like the data'?
narrow yew
well not really but I'm just trying to get extra credit
narrow yew
closest I can get to
mint orbit
you can make it exact
use an interpolating polynomial
usually you dont want your model to be exact
sorry i shouldnt have interjected myself into this 
narrow yew
is that doable by hand or will I need python
mint orbit
you can do it by hand, its not fun but you can do it
narrow yew
sorry i shouldnt have interjected myself into this <:bearlain:762653539092529182...
Dw dw any suggestions I will take
narrow yew
alright, I'll try it out. Thanks a lot for the suggestions!
narrow yew
https://en.wikipedia.org/wiki/Lagrange_polynomial
it worked out great. thanks a lot!
vital surge
it worked out great. thanks a lot!
polynomial interpolation can be / is pretty bad for approximation
vital surge
but I need more precise
why? quadratic is fine for this
mint orbit
yea it has a tendency to behave insanely
vital surge
polynomial interpolation can be / is pretty bad for approximation
for reason why, there is information on here https://en.wikipedia.org/wiki/Runge's_phenomenon
(if this is an assignment i would not recommend using)
final saddleBOT
@narrow yew Has your question been resolved?
narrow yew
why? quadratic is fine for this
it doesn't look that good no?
I mean I don,t really see phenomenon in the lagrande interpolation I did
vital surge
it doesn't look that good no?
an approximation is an approximation, I would not say it looks bad
the problem says “elementary function” so ideally quadratic is preferable to such degree polynomial
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narrow yew
.reopen
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✅
narrow yew
the problem says “elementary function” so ideally quadratic is preferable to suc...
I should of said algebraic.. My bad
vital surge
the problem says “elementary function” so ideally quadratic is preferable to suc...
if u really wanted to be precise about the “approximation” u would define some weird graph that looks like this
narrow yew
I mean honestly I think I'm making a big deal out of this rn but I found "Chebyshev nodes" that I can apply to fix this little issue
vital surge
if u really wanted to be precise about the “approximation” u would define some w...
but ofc nobody actually expects u to do this
vital surge
I should of said algebraic.. My bad
ic
narrow yew
I think I'll be fine with what I have rn. Thanks for the advice!
Have a good night or day or idk
.close
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tranquil pine
A line makes angles $\alpha, \beta, \gamma, \delta$ with the four diagonals of a cube then $\cos^2\alpha+\cos^2\beta+\cos^2\gamma+\cos^2\delta$ is equal to
final saddleBOT
A line makes angles $\alpha, \beta, \gamma, \delta$ with the four diagonals of a...
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yajat
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@tranquil pine Has your question been resolved?
limpid egret
@tranquil pine you can solve it by using direction cosines
example, one such diagonal connects the point (0,0,0) to the point (1,1,1) in a unit cube (where each side of the cube has a length of 1).
limpid egret
ok np
In a cube, each of the four space diagonals connects a pair of opposite corners. All the space diagonals are identical in length and make equal angles with the coordinate axes due to the cube's symmetry.
Because of the symmetry of the cube, the angles that the diagonals make with each axis (x, y, z) are the same. The fact that the line makes equal angles with all four diagonals implies that the problem is symmetrical.
send ok if you understood the stuff I sent you
tranquil pine
ok
limpid egret
you know the direction cosine identity ?
limpid egret
it states that the sum of the squares of the direction cosines of a line is 1
tranquil pine
yea well i know that identity
limpid egret
so using the above concept and the direction cosine identity it can be stated that :
cos^2 α + cos^2 β + cos^2 γ + cos^2 δ=1
tranquil pine
yea but ok
i mean
if there would have been 10 angles, would it be the same?
like just add the other angle part
limpid egret
all those 10 angles should be on the same line or equal lines
for this direction cosine identity to be applied
as here all 4 diagonals are equal
got it ?
limpid egret
well then as mentioned in above concept all angles are equal
tranquil pine
why are the angles equal
limpid egret
cube is symmetrical
limpid egret
In a cube, each of the four space diagonals connects a pair of opposite corners....
.
tranquil pine
oh ur talking about the diagonals
i thot u were talking about the line
yea wouldnt they make 45 degrees
tranquil pine
why can it be anything if its a cube?
limpid egret
also regarding that doubt of yours of 10 angles
tranquil pine
nah wait nvm
limpid egret
If there were 10 angles (say, angles a line makes with 10 different directions or lines), the situation would be different. These angles would not correspond to the angles with the coordinate axes, but to some other set of directions (perhaps diagonals, or arbitrary lines). In that case, you wouldn’t use the direction cosine identity directly.
limpid egret
so using the above concept and the direction cosine identity it can be stated th...
as for this equation
cube is a 3d object
so it is located on an xyz plane
so we will only write cos^2 α + cos^2 β + cos^2 γ = 1
Reason on why δ not included :
In this case, δ represents an additional diagonal, but the three direction cosines α, β, and γ fully describe the geometry of the cube's diagonal with respect to the coordinate axes. There is no need for a fourth direction cosine, cosδ, because in three-dimensional space, only three angles can define the orientation of a line or vector.
it is just not needed
understood ?
vital crag
can i close now?
you can close anytime it's your channel
limpid egret
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@tranquil pine Has your question been resolved?
shell plover
Ik this is a weitf question but if I integrate a velocity function into a position function and plug in my numbers and I'll get my position value. But since it is an indefinite integral wouldn't you put a + C and the end of your answer?
final saddleBOT
Ik this is a weitf question but if I integrate a velocity function into a positi...
formal trail
yes, which is why you need to know the position at some point in time so you can solve for the correct value of C
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@shell plover Has your question been resolved?
quartz pelican
Hey! So i am in the 8th grade and doing algebra 1 so my question is why is f(x-2) called* shifting to the right instead of shifting to the left?
final saddleBOT
Hey! So i am in the 8th grade and doing algebra 1 so my question is why is f(x-2...
shell mica
If the minus is inside the function, it shifts opposite way. If it's outside it, it's same way.
shell mica
Exactly
quartz pelican
but whenever its f(x-5) its counter intuitive
shell mica
Yes, that is the exact rule
Remember, f(x-5) isn't changing the x value, it's still changing y
So you want to know at what x value will the y height be the same as originally, if that makes sense? Honestlly transformations can be really hard to explain, typically you just learn it
quartz pelican
Oh
So basically like
If its f(x-3)
you have to add 3 to x to get back at f(x)?
so its called shifting to the right because of that?
shell mica
If memory serves correct then yes
Honestly, it's just easier for your sanity to remember that if it's in the bracket, it's the opposite, if it's outside it, it's the same
It could be easier to visualise if you try it with a couple of random functions
shell mica
But just learn the transformations that should be in your textbook and you'll get it!
quartz pelican
Thanks! We took notes on it today, also I just really think math is interesting and im trying to learn alg 1 to pre cal by the end of the year
.close
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wet kelp
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wet kelp
Hello, i need help with tge following equation, i have no clue what im doing wrong
As you can see ive tried bith the big and the small quadratic formulas and got the same exact result
I dont understand
solar birch
81+40=121=11^2
solar birch
np
solar birch
Im gonna throw myself out tge window now
Pls don't
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vital sinew
$gcd(a, b) = c \implies gcd(a/c, b/c) = 1$??
final saddleBOT
$gcd(a, b) = c \implies gcd(a/c, b/c) = 1$??
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kaxi
fallen vigil
kak
vital sinew
😢
fallen vigil
i think so
vital sinew
@fallen vigil its cookedjoever
?
can i do this
and considering k < n, k neq 0
tyring to say that the number of k is exactly d
which seems almost ovbious kinda
vital sinew
wdym
fallen vigil
i mean i dont understand
final saddleBOT
fallen vigil
that is equ to
for some r, s,
ra+sb=c
if they are all divisible by c then u can simplify it by dividing yea
@vital sinew
vital sinew
its joever ngl 😔
fallen vigil
joever
fallen vigil
lol
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vital sinew
let $G$ be a cyclic group of order $n$, generated by the element $a$.
\begin{enumerate}
\item (3 pts) For any integer $i$, determine the order of $a^i$ in $G$ (in terms of $i$ and $n$).
\item (3 pts) Show that every subgroup of $G$ is cyclic and that for any $d\mid n$, $G$ has a unique (cyclic) subgroup of order $d$.
\item (3 pts) The Euler $\phi$ function is defined by
[
\phi (n) = | { 1\le a \le n, \ \gcd(a,n) =1 }
]
Give a formula for $\phi(n)$ in terms of the prime factorization of $n$ and show that $\phi$ is multiplicative, i.e., $\phi (mn) = \phi (m) \phi (n)$ if $ \gcd (m,n) =1$.
\item (4 pts) Show that for any $d \mid n$, the number of elements of $G$ of order $d$ is exactly $\phi (d)$. Deduce that
[
\sum_{d\mid n} \phi (d) = n.
]
\item (3 pts) Show that $\Aut (G) \simeq (\Z/n\Z)^\times$, where the latter is the multiplicative group of classes mod $n$ that are coprime to $n$. In particular, $|\Aut (G)| = \phi (n)$.
\item (4 pts) Let $m$ and $n$ be positive integers. Show that $C_m \times C_n \simeq C_{mn}$ if and only if $m$ and $n$ are coprime.
\end{enumerate}
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let $G$ be a cyclic group of order $n$, generated by the element $a$.
\begin{en...
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kaxi
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vital sinew
Specfically, for 4., how can this statement be true?
$\phi(d)$ for $d = n$ is $\phi(n) = n$?
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kaxi
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vital sinew
😔
ivory vessel
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velvet condor
i need help 😦
final saddleBOT
i need help 😦
rustic sinew
i need help 😦
!status
final saddleBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
3
rustic sinew
Can you show your work?
ivory vessel
i need help 😦
third degree polynomial, yet 6 roots 
rustic sinew
i went by the formula (a-b)(a^2+ab+b^2)
!original
final saddleBOT
i went by the formula (a-b)(a^2+ab+b^2)
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.
rustic sinew
Can you show what you mean by a is a^3?
final saddleBOT
rustic sinew
whoops i meant x^3
You were on the right track, I hope you got it
velvet condor
yeah i had to use the quadratic formula
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low storm
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low storm
Yea
tranquil pine
what did you try
tranquil pine
can you show your work?
low storm
Are you asking if i am allowed to?
tranquil pine
no, i meant "please show your work"
tranquil pine
you dont know how to substitute ?
low storm
Nver really focused on it
tranquil pine
i would recommend watching a video on youtube to clear your concepts
and then attempting the question
low storm
Uh
tranquil pine
unless you have a lot of time and wanna mess around with every method you can
final saddleBOT
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sullen relic
I've been trying to do this problem with the surface area formula I've learnt (attached in image), but I'm having trouble integrating it. I've gotten up to the point where I plugged everything in, and now im unsure where to even start from. Any advice would be appreciated.
final saddleBOT
I've been trying to do this problem with the surface area formula I've learnt (a...
formal trail
note that the expression inside the square root is a perfect square
final saddleBOT
@sullen relic Has your question been resolved?
gritty nest
Apologies in advance if my explanation isn't clear.
Say you have a bracelet of 12 equally spaced out beads or similarly a regular dodecagon.
What would be the general formula for the amount of possible ways a fixed triangle can fill the vertices of this bracelet/regular dodecagon with its shape and without occupying the same vertex?
Also, inversions or mirror images are considered the same.
The image posted is an example of one possible configuration of this.
In this example there's a triangle whos fixed shape occupies all vertices once. Of course given its a triangle filling a 12 sided shape in such a way, you will always need four of them.
However, this is apparently one of many configurations that this triangle can make to fill the vertices of the bracelet.
I tried applying a combination of consecutive and non consecutive selection, but I got stuck in trying to figure out how to maintain a fixed shape. Perhaps there isn't a general equation to this question and needs to be solved using several different steps.
final saddleBOT
Apologies in advance if my explanation isn't clear.
Say you have a bracelet of ...
@gritty nest Has your question been resolved?
steep timber
Well, 2 triangles are equal if and only if all 3 sides are equal, and the chords of a circle are only equal if they have the same arc length
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@gritty nest Has your question been resolved?
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@gritty nest Has your question been resolved?
restive beacon
C)
terse crypt
+c
spare hazel
(1-x^2) or (1+x^2)?
spare hazel
oh
spare hazel
differential equation
restive beacon
?
spare hazel
correct answer is -1/4*(1-x^2)^2 +C
spare hazel
expand (1-x^2)^2
spare hazel
solve it
restive beacon
spare hazel
correct
restive beacon
Ye, But i wonder what i did wrong with the substitution
spare hazel
Ye, But i wonder what i did wrong with the substitution
integral is correct
restive beacon
Ok But what i needed to do is just expand it
spare hazel
yea
restive beacon
And then solve for C
spare hazel
yes
scenic pendant
How can i graph xy-y-2x ≥ -1
final saddleBOT
How can i graph xy-y-2x ≥ -1
gentle barn
Isolate y
shrewd mist
Let (S, <=) be a POSET then for x, y E S, "x <= y" and "y <= x" are equivalent right?
final saddleBOT
Let (S, <=) be a POSET then for x, y E S, "x <= y" and "y <= x" are equivalent r...
shrewd mist
because x <= y means that either (x, y) E <= or (y, x) E <= and same thing goes for y <= x
barren hound
scarlet sequoia
"x <= y" and "y <= x" are kinda the opposite of equivalent
the only x,y that verify both at the same time are such that x = y
an order is antisymmetric
and x <= y only means (x,y) is in your relationship set
shrewd mist
Let (S, <=) be a poset and x,y E S, y covers x if x <= y, x != y and there are no elements z E S such that x < z < y
In the above definition
they have mentioned specifically about "x <= y" and not "y <= x"?
scarlet sequoia
uh huh
shrewd mist
So if S = {1, 2, 3} and P(S) denotes power set of S, P(S) = {phi, {1}, {2}, {3}, {1,2}, {2,3}, {3,1}, {1,2,3}}
(P(S), <=) is a POSET where <= denotes the set-subset relation
how does {1} cover phi?
scarlet sequoia
well
(first of all emptyset's notation is usually not a phi just to be clear)
we do have emptyset as a subset of {1} right?
and a proper subset at that
shrewd mist
we do have emptyset as a subset of {1} right?
yes, empty set is a subset of {1}
scarlet sequoia
ok
so " x <= y, x != y"
is there a proper subset of {1}, call it z
such that emptyset is a proper subset of z?
shrewd mist
but for {1} to cover empty set, x = {1}, y = empty set, x !<= y
as {1} is not a subset of an empty set
shrewd mist
ohhhh
scarlet sequoia
but for {1} to cover empty set, x = {1}, y = empty set, x !<= y
so not that
shrewd mist
yess
scarlet sequoia
we wanna know if {1} covers emptyset
shrewd mist
so an empty set does not cover {1} right?
scarlet sequoia
so emptyset = x
scarlet sequoia
so an empty set does not cover {1} right?
no
because {1} is not a subset of emptyset to begin with
we wanna know if {1} covers emptyset, so emptyset = x and {1} = y
we do have x < y
is there some z such that x < z < y?
shrewd mist
also, just to clear some confusion, in a poset, x <= y implies that (x, y) must exist in <= right?
scarlet sequoia
also, just to clear some confusion, in a poset, x <= y implies that (x, y) must ...
aRb always means (a,b) is in R, in that order
shrewd mist
is there some z such that x < z < y?
no
similary {1,2} does not cover empty set as z = {1} exists such that empty set < z < {1,2}
scarlet sequoia
yep
shrewd mist
also why are posets even studied? Like what do they represent? I heard its something about comparing elements to each other
scarlet sequoia
an order relation is literally a "hierarchy" between elements
imagine S = employees of a corporation
and <= being "takes orders from"
that'll create multiple chains of command
with for example the CEO at the top (I'm guessing)
where two people don't necessarily take orders from one another
but if you have A taking orders from B
and B taking orders from C
A technically needs to take orders from C as well
shrewd mist
Oh I see, you can set <= as some sort of a comparision and then represent models of data using hasse diagrams