#help-33
thin frost
marsh citrusBOT
thin frost
some help with this question please, i can see OABC is a rhombus but im not sure where to go from there
marsh citrusBOT
@thin frost Has your question been resolved?
marsh citrusBOT
@thin frost Has your question been resolved?
marsh citrusBOT
@thin frost Has your question been resolved?
keen plover
OABC is a rhombus therefore all its sides are equal
draw a line OC
what can you say about the two triangles OBC and OAC
still temple
I'm getting undefined for the tangent
marsh citrusBOT
I'm getting undefined for the tangent
still temple
I differentiated and got $\frac{8x-3y}{3x+2y}$
elfin berryBOT
still temple
$3(2)+2(-3)=0$
elfin berryBOT
stoic saddle
,w implicit derivative 4x^2 - 3xy - y^2 = 25
elfin berryBOT
stoic saddle
checks out
and you got that y' is undefined at this point?
you can either go through the same song and dance but to find dx/dy instead of dy/dx,
or you could acknowledge that you just have a vertical tangent at this point.
brave spire
Yeah..0 is in the denominator
brave spire
you can either go through the same song and dance but to find dx/dy instead of d...
How does he know it's vertical??
stoic saddle
who's he
still temple
?
still temple
you can either go through the same song and dance but to find dx/dy instead of d...
so the tangent is x=some real number?
stoic saddle
_____ does not have a pronoun role, so i would refrain from assuming he/him pronouns for them
still temple
i dont care about pronouns for myself
stoic saddle
so the tangent is x=some real number?
sure is, and you know exactly what that real number is.
stoic saddle
i dont care about pronouns for myself
then get an "any pronouns" role so there is no question of that
still temple
oh ok
brave spire
\_\_\_\_\_ does not have a pronoun role, so i would refrain from assuming he/him...
Oops sry
still temple
sure is, and you know exactly what that real number is.
by finding dx/dy and then plugging in values?
still temple
oh....
it's just x=2
can u explain what this means though?
this is what the answer key says
brave spire
can u explain what this means though?
It means that on a Cartesian plane the relationship between the x and y of all points the tangent passes thru is given by that equation
still temple
It means that on a Cartesian plane the relationship between the x and y of all p...
Isn’t the equation x=2
Because it’s tangent is vertical
brave spire
Isn’t the equation x=2
Equation for a line must involve both x and y
still temple
Ok
brave spire
Desmos go brrrrr
polar fable
marsh citrusBOT
sinful barn
Sup
sinful barn
How can i approach this question?
lofty gyro
is it given that x,y are integers or what condition?
lofty gyro
integers, right?
sinful barn
Yes
sinful barn
Done
sinful barn
Now i can subsitute it in any of those 2 eq right?
lofty gyro
you can just check the integer values that
(x+1)(y+1)=5 is valid
all those 4 pairs of (x,y)
and plug them back to the original equation to see if they are valid
marsh citrusBOT
@sinful barn Has your question been resolved?
olive gate
marsh citrusBOT
olive gate
Isn't this slide incorrect?
It should be "strongly connected"
Here is the accompanying graph:
the above graph is strongly connected, not weakly connected
Or am I misunderstanding something here?
glass silo
Complete wild guess (and I almost certainly won’t remember any more to help extra), but does strongly connected imply weakly connected?
olive gate
Complete wild guess (and I almost certainly won’t remember any more to help extr...
I'm not sure what you mean here
they are two different states, I believe
weakly connected would be where some vertices only have an in-degree or out-degree, but not both
stoic saddle
an euler circuit is a circuit that visits each edge exactly once, yes?
given that a circuit comes back where it starts, the existence of one does imply strong connectedness and not weak...
so it looks like the slide is in error
olive gate
given that a circuit comes back where it starts, the existence of one *does* imp...
The same error seems to be repeated here as well.
How can there be so many typos that seem to be significant
stoic saddle
ah, no, for an euler path you don't need strong connectedness
olive gate
ah, no, for an euler path you don't need strong connectedness
wait
let me show the accompanying example
this graph is strongly connected, not weakly
this is why I feel this is another typo
stoic saddle
do you mean to claim "this graph is strongly connected and fails to be weakly connected"?
olive gate
or it seems to be based on the example given
olive gate
do you mean to claim "this graph is strongly connected and fails to be weakly co...
yes, a graph can not be both strongly and weakly, afaik
stoic saddle
do you have a definition of weak connectedness on hand? we could check your graph against it.
olive gate
or as far as i have been taught so far
stoic saddle
i think either you misheard your teacher or they chose to misinform you.
as far as i know, strong connectedness implies weak connectedness.
olive gate
do you have a definition of weak connectedness on hand? we could check your grap...
But this is a reason why I feel a graph can't be both.
Here is one of the self test questions are teacher gave us during lecture:
as you can see, the options are strongly OR weakly connected
not both
glass silo
Not the way I read the wording “…and if not, whether…”
stoic saddle
^
olive gate
Not the way I read the wording “…and if not, whether…”
well, that's because there is a third implied option
which is "not connected at all"
stoic saddle
as you can see, the options are strongly OR weakly connected
strongly connected means both, in this sense.
stoic saddle
any strongly connected graph is also weakly connected.
so really, it's "Strongly connected", "Not strongly connected, but weakly connected", and "Not connected"
olive gate
so, if this is true, what does this mean for my original question?
stoic saddle
this one?
olive gate
I'm not sure I understand how this negates the potential typo
stoic saddle
this screenshot has a typo. "weakly" should be "strongly" here.
olive gate
because even if we accept your interpretation, then why would the slide read "weakly" instead of "strongly"?
one is listed instead of the other because there is a difference intended to be shown
so, this slide would also have a typo:
stoic saddle
no, i cannot say whether that screenshot has a typo. i know for a fact that there exists a graph that is weakly and only weakly connected, and which has an euler path. therefore the "weakly" there should not be changed to "strongly".
i do not know how else to communicate my point to you...
olive gate
no, i cannot say whether that screenshot has a typo. i know for a fact that ther...
Could you share such a graph?
the example here is clearly incorrect, but maybe the definition isn't
stoic saddle
a -> b -> c -> d
this graph is just a path
its sole euler path is itself
it is weakly connected but not strongly connected
stoic saddle
in what way?
olive gate
stoic saddle
do you think there are not two vertices with unequal in- and out-degrees?
or that there are exactly two of them, but the differences between their in- and out-degrees are not what they should be?
stoic saddle
you mean a doesn't have any incoming edges!
that's different from it not having an indegree at all!
the number zero exists!
olive gate
ok, that's true
a: in: 0 out: 1
b: in: 1 out: 1
c: in: 1 out: 1
d: in: 1 out: 0
ok, you're right
it does match
then, maybe the example is just incorrect
stoic saddle
in what way?
olive gate
the graph is strongly connected
I know you feel this implies weakly connected
but the slides says "weakly"
specifically
not implied
stoic saddle
i do not "feel" that way
it is an easy theorem that any strongly connected graph is also weakly connected
being strongly connected does not mean you fail to be weakly connected too
olive gate
for instance, I'm sure I will get a 0 for a problem that requires an answer of "strongly", but I write "weakly"
this logic will not hold, I don't think
stoic saddle
do you mean problems of the kind you showed?
olive gate
yes
stoic saddle
i.e. "determine if this graph is strongly connected; if it fails to be strongly connected, determine whether it is weakly connected"?
olive gate
this isn't the wording of the problems above
stoic saddle
then indeed, writing "weakly connected" would mean that you determined the graph to be weakly and not strongly connected, and that is what would contradict said graph being strongly connected.
olive gate
stoic saddle
"Determine whether this graph is strongly connected, and if not, whether it is weakly connected."
olive gate
yes, this
stoic saddle
are you or are you not now going to argue that, because my wording isn't the same-to-the-letter as that, i have committed misinterpretation thereof?
olive gate
no, you are likely very correct here
but the issue is answering to my professor's standards
if strongly implies weakly, then, an answer of 'weakly' should be correct
but i will get that marked wrong every time, I assume
stoic saddle
yes, because analyzing a strongly connected graph and following the instructions provided cannot result in an answer of "weak"
olive gate
yes, so the slide's example is incorrect
olive gate
not the description, but the example
I'm trying to keep repeating that to be clear here
stoic saddle
def answer_assignment(G):
if is_strongly_connected(G):
print "Strong"
else:
if is_weakly_connected(G):
print "Weak"
else:
print "Not connected"
FOR THE ASSIGNMENT you are supposed to follow this pseudocode i just wrote here
do you agree or disagree with this
olive gate
i agree
stoic saddle
okay
in that case
let me attempt for the third time to clear up the apparent confusion
stoic saddle
on what
stoic saddle
that will print "Strong"
stoic saddle
yes, but you didn't let me finish.
olive gate
so, the slide is incorrect
olive gate
not to cut you, but why would there be any follow up if we follow the algorithm?
stoic saddle
"answer_assignment(G) prints Weak" is NOT equivalent to "G is weakly-connected".
olive gate
that's all I wanted to inquire
stoic saddle
that's the follow-up.
olive gate
"`answer_assignment(G)` prints `Weak`" is NOT equivalent to "G is weakly-connect...
oh.
hmmm
stoic saddle
our algorithm prints Weak for graphs that are WEAKLY CONNECTED WHILE FAILING TO BE STRONGLY CONNECTED, and no others.
but the definition does NOT call for a graph specifically like that.
it calls for a weakly connected graph, which ALSO INCLUDES STRONGLY CONNECTED GRAPHS.
olive gate
this is confusing to me so let me follow up with this question
why is "weakly" specifically used here instead of "strongly"?
stoic saddle
here as in where? the euler path slide?
stoic saddle
so the euler path slide, yes.
olive gate
if what you are saying is indeed the case, then there must be a reason why the professor chose one term over the other
stoic saddle
yeah, of course there's a reason.
stoic saddle
requiring that the graph be STRONGLY connected will exclude graphs that aren't strongly connected yet have an euler path.
the slide says "a graph has an euler path if and only if such-and-such conditions."
olive gate
but "strongly" implies "weakly", not vice versa
which is why I don't understand this statement:
stoic saddle
all strongly-connected graphs are weakly-connected, therefore "weakly-connected graphs" includes strongly-connected ones.
olive gate
maybe you can share a weakly connected graph that is also strongly connected?
stoic saddle
okay, sure...
i can't depict it in plain text easily, but take 4 vertices a, b, c, d with edges ab, bc, cd and da
this graph is both weakly connected and strongly connected
does this or does this not satisfy you
olive gate
how is this strongly connected
both vertices do not have an in-degree and out-degree greater than 0
stoic saddle
what "both" vertices? there aren't two of them, there are four.
olive gate
oh, ok
then, that isn't weakly connected
maybe, we have different ideas of what 'weakly' means
do you agree that this is weakly?
stoic saddle
yeah and you have the wrong one
you think that we are only allowed to call a graph weakly connected if it isnt also strongly connected
and that isnt the case
olive gate
olive gate
is this "weakly" to you?
stoic saddle
AND YOU STILL REFUSE TO BUDGE
YES THIS GRAPH IS WEAKLY CONNECTED I NEVER ARGUED AGAINST THAT
olive gate
why must you get so infuriated when someone doesn't understand your position?
it's not that serious
stoic saddle
i've made my position as clear as i possibly could've, several times in a row.
olive gate
and if it is then, perhaps return to this later when you've had a break?
tacit fjord
Are these the defns you are using:
- 2 vertices are (weakly) connected if there exists a path between them
- 2 vertices are strongly connected if there exists a path in both directions between them
olive gate
whats the issue
I feel either this description is incorrect:
OR
the accompanying example is incorrect:
or both, i guess
tacit fjord
Without delving into the graph theory
tacit fjord
All strongly connected graphs are also weakly connected. Yes?
Do you understand this point
olive gate
i think so
olive gate
ok
tacit fjord
this graph is strongly connected, not weakly
in which case what you've said here doesn't make sense
tacit fjord
Prove all strongly connected graphs are also weakly connected
olive gate
in which case what you've said here doesn't make sense
ah, ok
ahh!
I totally see your point now
by "weakly", my professor is just saying that there needs to be a path between the vertices
not necessarily in both directions, just that there is a path
then, my professor was never incorrect in any of the slides
even in my initial query, the slide is correct
"weakly" connected does mean ONLY weakly connected
tacit fjord
will look later if someone else didnt
olive gate
it just means the minimum requirement
great to have this cleared up
now, i don't need to email them
ty
sick mesa
Hi, why is it true please ?
marsh citrusBOT
Hi, why is it true please ?
sick mesa
dire bobcat
If you think about integral as the area under a graph, it might help you out.
marsh peak
Note that for every t in the interval 1/(k + 1) <= 1/t <= 1/k
marsh citrusBOT
@sick mesa Has your question been resolved?
sick mesa
If you think about integral as the area under a graph, it might help you out.
I dont see how it help 😭the area is bigger than theses points
sick mesa
Note that for every t in the interval 1/(k + 1) <= 1/t <= 1/k
Yes but for the integral ?
marsh peak
Note that for every t in the interval 1/(k + 1) <= 1/t <= 1/k
Now integrate these from k to k+1
dire bobcat
marsh citrusBOT
@sick mesa Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
calm anvil
If X is uncountable, equipped with the cocountable topology, how do I show that
proper zodiac
You'll probably have more luck in #point-set-topology btw
wind cloud
marsh citrusBOT
frosty linden
Yes
glacial hedge
if a divides b, then lcm(a, b) = b
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
can we discuss induction
marsh citrusBOT
can we discuss induction
still temple
its like recursion right
lethal bridge
Hi, when completing the square and getting to the square root process. I know that you just remove the ^2 but what happens to the 4?
marsh citrusBOT
Hi, when completing the square and getting to the square root process. I know th...
bleak reef
4 is also a square number
lethal bridge
Does it just become 2
bleak reef
yes
lethal bridge
Alright thanks
bleak reef
np
lethal bridge
Here’s the full thing, do you checking if I’ve done anything wrong?
Oh wait
There should be a +- sign
but I need to get the x by itself right
I can’t leave it as just 2x
bleak reef
you multiplied the whole thing by 4 but you only have 4x^2
lethal bridge
Oh I thought I take the leading coefficient or something during cts
bleak reef
yes but that affects what's inside
lethal bridge
Oh so I should be distributing it inside the square root first, and then removing the square?
bleak reef
I don't know what you mean
try and copmlete the square ont his again
actually it might help to just start from 4x^2 + 7x - 1
lethal bridge
I don't know what you mean
This
marsh citrusBOT
@lethal bridge Has your question been resolved?
still temple
Where should I go from here?
marsh citrusBOT
Where should I go from here?
still temple
lofty gyro
did you try and draw the line y=mx out and see how it cuts the shape?
still temple
Well how should I draw it if I don’t know the slope
O wait
It’s gonna be
Like this
lofty gyro
yea, something similar, you dont really have to be exact, just to get the picture it's okay
still temple
Ok and now I just do the integral
lofty gyro
now that it is divided into 2 parts
still temple
Thanks
lofty gyro
yea
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
So here you'll see the question is already solved, but can someone walk me through how to solve it?
marsh citrusBOT
So here you'll see the question is already solved, but can someone walk me throu...
@still temple Has your question been resolved?
past maple
So here you'll see the question is already solved, but can someone walk me throu...
There are several ways to prove that
Do you know what eigenvalues and eigenvectors are?
still temple
No. We've never discussed it in class or studied it
past maple
So here you'll see the question is already solved, but can someone walk me throu...
Ok
In that case, the first step is to find sequences in the form aₙ = xⁿ which satisfy the first equation, but not necessarily the two other ones
So you have x^n = x^(n-1) + 6 x^(n-2), right?
still temple
not ^ but _.
But yeah
past maple
But
past maple
Ok
In that case, the first step is to find sequences in the form aₙ = xⁿ which s...
We are actually looking for solutions in which a_n equals x^n, for some x ∈ ℝ
past maple
So you have x^n = x^(n-1) + 6 x^(n-2), right?
Then this is a polynomial equation. What are its solutions?
still temple
I don't know
past maple
I don't know
Well
Either x = 0, which is a solution, or x ≠ 0, in wich case we can divide the equation by x^(n-2)
still temple
How do you get those as solutions?
past maple
How do you get those as solutions?
What are you refering to with "those"? The sequences or the number x?
still temple
Where does x = 0 and x ≠ 0 come from?
past maple
Where does x = 0 and x ≠ 0 come from?
That is a trick that can always be used
A number can either equal 0 or not equal 0
still temple
So if x ≠ 0 then why do we divide the equation by x^(n-2)?
past maple
So if x ≠ 0 then why do we divide the equation by x^(n-2)?
To obtain a quadratic equation
Which we can solve
We had a polynomial equation of degree n. To simplify it, we can divide by x^(n-2) to obtain an equation of degree 2, but if we divide by x then x should not equal 0
past maple
So if x ≠ 0 then why do we divide the equation by x^(n-2)?
So if we divide by x^(n-2), what do we obtain?
still temple
So if we divide by x^(n-2), what do we obtain?
It would be something like this, right?
still temple
past maple
That is still wrong
past maple
(a^b)/(a^c) equals a^(b-c), right?
Applying this rule, what would be each of the numbers a, b and c in the left side?
still temple
2?
past maple
Yes
past maple
Therefore, what should be changed here?
still temple
x^2 = x^1 + 6?
past maple
Exactly
still temple
that was embarassing
past maple
that was embarassing
No
Everyone makes mistakes like that one in math
It is not an embarrassing thing, it is indeed very common
still temple
So if we divide by x^(n-2), what do we obtain?
So we have x^2 = x^1 + 6, now what?
past maple
How did you reach that solution?
past maple
This is not correct, what steps did you make?
still temple
I know it's not correct. I'm redoing it
past maple
Ok
still temple
so this right?
past maple
No
I think you wrote twice something inside the square root
There are two 4, but there sould only be one
past maple
Be careful with the - signs
still temple
This isn't correct?
past maple
Be careful with the - signs
And consider this
still temple
So you have x^n = x^(n-1) + 6 x^(n-2), right?
So this and we now know x is 3 and -2
past maple
Ok
In that case, the first step is to find sequences in the form aₙ = xⁿ which s...
Here
still temple
So here you'll see the question is already solved, but can someone walk me throu...
^
still temple
fixed
past maple
So we obtained two sequences
a_n = 3^n and b_n = (-2)^n
What do we know about these sequences?
still temple
Do we need b_n?
past maple
I wrote b_n to use a different letter
past maple
We are not going to choose any of them yet
still temple
Oh
past maple
They are sequences we obtained after solving a different problem from what we originally wanted
We wanted that a_n = a_(n-1) + 6 a_(n-2), that a_0 = 3, and that a_1 = 6
But a_n and b_n satisfy the first one, right?
past maple
But a_n and b_n satisfy the first one, right?
Do you understand why?
still temple
So here you'll see the question is already solved, but can someone walk me throu...
Sorry but I need you to refresh me, Where does this come in?
past maple
Ok
In that case, the first step is to find sequences in the form aₙ = xⁿ which s...
Remember what I said here
still temple
So all of this was step 1?
past maple
Yes
still temple
Ah
past maple
But step 2 is shorter
still temple
I see
past maple
Now we have a_n and b_n
And a_n = a_(n-1) + 6 a_(n-2)
And b_n = b_(n-1) + 6 b_(n-2)
Do you understand why?
Remember that a_n = 3^n and b_n = (-2)^n
still temple
So we found sequences in the form of aₙ = xⁿ?
past maple
Yes
And since -2 and 3 are solutions to the equation x^n = x^(n-1) + 6 x^(n-2)
We can substitute x^n with a_n, x^(n-1) with a_(n-1) et cetera
still temple
So what about 6a_n-2?
past maple
You can also substitute x^(n-2) with a_(n-2)
past maple
I will write it in a more clear way
You know that -2 and 3 hold the equation
x^n = x^(n-1) + 6 x^(n-2)
Therefore, the following identities are true:
3^n = 3^(n-1) + 6*3^(n-2)
(-2)^n = (-2)^(n-1) + 6*(-2)^(n-2)
Furthermore, we defined a_n = 3^n and b_n = (-2)^n. Because of that, the previous lines can be rewritten as
a_n = a_(n-1) + 6*a_(n-2)
b_n = b_(n-1) + 6*b_(n-2)
past maple
I will write it in a more clear way
You know that -2 and 3 hold the equation
x^...
Do you understand this @still temple ?
past maple
Yes
still temple
So what is step 2?
past maple
But do you understand why what we have done so far makes sense and works?
Or are you just writing down all what I'm saying, even though you don't understand it?
still temple
I'm confused
past maple
Why are you confused?
still temple
So my professor's solution to the question was a_n = (3/5)((-2)^n) + (12/5)((3)^n)
past maple
Yes, and that is the only correct solution to the problem
So you are confused because we obtained something different
still temple
Yeah
past maple
Well
As I said before, what we have made so far is to solve an auxiliary problem, a more simple one. It is actually a different problem, so of course the solution is different
But we need it to obtain the solution of the original problem
past maple
I will write it in a more clear way
You know that -2 and 3 hold the equation
x^...
What I want is that you understand why this is true, regardless of what we are going to use it for
still temple
I don't.
still temple
I'm so sorry if I'm wasting your time
past maple
I'm so sorry if I'm wasting your time
Don't worry
First, what does a_n = a_(n-1) + 6 a_(n-2) mean?
What is a_n?
still temple
3^n
still temple
Yeah, but how does that relate to my initial question?
past maple
Because it is important to understand what you are doing
You should not just memorize how to solve every kind of problem every time you see it for the first time
Because that is just too difficult
Instead, understand math in general is easier in the long term, because you have to memorize less things
past maple
So here you'll see the question is already solved, but can someone walk me throu...
If you write down how to solve this and memorize it, you may make mistakes when you solve it again, but if you understand why the solution works you don't have to memorize it
still temple
Alright. Sorry but give me a moment
still temple
You should not just memorize how to solve every kind of problem every time you s...
This being said, I'm gonna review on my textbook. I'll understand if you leave
past maple
Ok
still temple
Thanks for your time
marsh citrusBOT
@still temple Has your question been resolved?
brave pilot
Just started a discrete math course, I have a question that I can’t get my head off of.
marsh citrusBOT
Just started a discrete math course, I have a question that I can’t get my head ...
brave pilot
From this post, how does ExE!y differ from E!xEy?
Any help would be greatly appreciated.
still temple
there exists an x and there exists only one y
vs
there exists one x and there exists a y
still temple
yeah
brave pilot
How about E!xE!y?
still temple
yeah thats one the solutions if you scroll down
still temple
yea
marsh citrusBOT
marsh citrusBOT
Available help channel!
upbeat needle
Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?
marsh citrusBOT
Radioactive radium has a half-life of approximately 1599 years. What percent of ...
late pasture
Let the output of this function be in percentage
Then C would be 100
As at t=0, it would be at 100% and then will decay afterwards
So the function becomes 100e^(kt)
upbeat needle
Why is C 100?
late pasture
As at t=0, it would be at 100% and then will decay afterwards
This is why
Do you know the correct answer?
upbeat needle
Yeah it’s 95.76%
late pasture
Yes so, its given that half life is 1599 yrs, so it decays to 50% in 1599 years. So, at t=1599, its output must be 50. Substituting the values we get...
100e^(1599k) = 50
=>e^(1599k)=0.5
=>k=-ln(2)/1599 = 0.000433
Are you getting it till this?
late pasture
Ya sorry k=-0.000433
upbeat needle
All good
late pasture
So, now putting k back in equation, we get
100e^(-0.000433t)
Now we need to find the decay percent at t=100 years, so substituting t=100 in it, and you'll get the answer 95.76%
Got it?
upbeat needle
And the y value is the half life percentage at t= amount of years
And I’m assuming half life is always 50%?
late pasture
And I’m assuming half life is always 50%?
Yes
lavish owl
can anyone help me with this?
marsh citrusBOT
can anyone help me with this?
lavish owl
its urgent
vale panther
can anyone help me with this?
There are multiple ways you can solve this
But the best (for me) is using the equation
Thank you
stoic saddle
vale panther
Bruh
stoic saddle
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
elfin berryBOT
Ann
weak tulip
Backward slash
vale panther
Backward slash
Sorry forgot
stoic saddle
given that this is a mulitple choice question
vale panther
I mean in general
stoic saddle
it might be less headache to simply expand all the answer options and see which matches
vale panther
When it comes to solving complex polynomials this is literally the only way but in this case there are faster ways
wheat sedge
you could look at the coefficient and constant
wheat sedge
yea and that will make +7.x and -4.x which is d
you could check this by looking at the constants, 7*-4 is -28 so it checks out
vale panther
Or you could do trial and error on each of the answers (try multiplying the numbers together to see if it matches the c coefficient and summing up together to see if they match the b coefficient
wheat sedge
Or you could do trial and error on each of the answers (try multiplying the numb...
yea as you said there is a lot of ways to do this
scarlet blaze
x^2 + 7x - 4x - 28 = x(x + 7) - 4(x + 7) = (x + 7)(x - 4)
wheat sedge
You can even draw squares to find it
hold my ms paint
vale panther
Lol
lavish owl
x^2 + 7x - 4x - 28 = x(x + 7) - 4(x + 7) = (x + 7)(x - 4)
where do you get the 4 from
vale panther
He re-writes 3x as 7x-4x
wheat sedge
did it
lavish owl
but its positive in the equation
wheat sedge
but its positive in the equation
wdym
scarlet blaze
where do you get the 4 from
I wrote 3x as 7x - 4x, because 7 * (-4) = -28 and 7 - 4 = 3
lavish owl
I wrote 3x as 7x - 4x, because 7 * (-4) = -28 and 7 - 4 = 3
i kind of get it
wheat sedge
yea just try the factors of -28 constant and sum them
wheat sedge
because of the 3 coeficcient in 3x, 4,-7 does not work because 4+(-7) would make -3
lavish owl
thats what i get
wheat sedge
so it would be -3x instead of +3x
lavish owl
because of the 3 coeficcient in 3x, 4,-7 does not work because 4+(-7) would make...
ohhh
wheat sedge
yep
lavish owl
so -4*7?
wheat sedge
yea
marsh citrusBOT
placid oak
How do I start?
marsh citrusBOT
@placid oak Has your question been resolved?
marsh citrusBOT
@placid oak Has your question been resolved?
marsh citrusBOT
@placid oak Has your question been resolved?
elfin berryBOT
sage pollen
What next?
Can you cancel anything?
elfin berryBOT
placid oak
.close
lethal zinc
differentiate w.r.t x
marsh citrusBOT
differentiate w.r.t x
lethal zinc
serene parcel
use quotient rule
lethal zinc
i'm just learning derivatives and i'm not sure about if i'm supposed to leave the answer without simplifying it or simplify it cause the question just asks to differentiate w.r.t. x
still temple
Is there a function where the derivative is undefined everywhere, by any chance?
still temple
and by "everywhere" i mean for all points of the function's domain
nova totem
Is there a function where the derivative is undefined everywhere, by any chance?
(-1)^x
On the reals plane
nova totem
The among us function
sage heath
perhaps a fractal
but fractals can be continuous right? or am i missing smtg
outer arrow
yeah but u have more than 1 value at every x
hollow quest
continuous doesnt mean differentiable
sage heath
yeah but u have more than 1 value at every x
ic, so u mean some fractals?
because some fractals can be conti iirc
marsh citrusBOT
@still temple Has your question been resolved?
outer arrow
marsh citrusBOT
vale marten
@marsh citrus
marsh citrusBOT
Available help channel!
placid oak
Let W={(x,y,z)∣x=2y+z} be a subspace of R³. Let β={(2,1,0),(1,0,1)} be a basis of W.
Let T : W→R be a linear transformation such that T(2,1,0)=(1,0) and T(1,0,1)=(0,1).
marsh citrusBOT
Let W={(x,y,z)∣x=2y+z} be a subspace of R³. Let β={(2,1,0),(1,0,1)} be a basis o...
placid oak
How do I prove that T is an Isomorphism?
obsidian shard
It maps basis to basis so it must be an isomorphism
placid oak
T(x,y,z)=(y,z) or T(x,y,z)=(x-y-z,x-2y)
obsidian shard
If you want to show a bit in detail, you would wanna prove 1-1 and onto
But notice the dimensions are same so proving either 1-1 OR onto is enough
obsidian shard
That would be a bit hard to find, a better option is to consider inverse transformation T' : R2 -> W
then the transformation is easy to find
placid oak
But notice the dimensions are same so proving either 1-1 OR onto is enough
How do I prove T is one-one without knowing the transformation?
obsidian shard
well, there's a theorem which says that T is 1-1 if and only if T maps linearly independent subsets to linearly independent subsets
but anyway, since you're given the explicit transformation that should be used
ionic owl
[\frac{d}{dx}\frac{x^2 + x}{x^2 -x}]
[(x^2 - x)(2x+1)-((2x-1)(x^2+x))]
[\frac{-4x^2 + 2x^2}{(x^2 -x)^2}]
[\frac{-2x^2}{(x^2 -x)^2}]
marsh citrusBOT
\[\frac{d}{dx}\frac{x^2 + x}{x^2 -x}\]
\[(x^2 - x)(2x+1)-((2x-1)(x^2+x))\]
\[\fr...
obsidian shard
T(x,y,z)=(y,z) or T(x,y,z)=(x-y-z,x-2y)
my bad, use the first one
obsidian shard
They might be equivalent but as per my calculations I got the 1st one
placid oak
If T is the first one, then T(1,0,0)=(0,0) and T(0,0,0)=(0,0). So they are not one-one?
obsidian shard
nah cause (1,0,0) doesn't lie in W
anyway get a different channel, I didn't notice you closed the channel
obsidian shard
Where is my mistake?
I think you answer is correct
It's just that wolfram simplified it by cancelling x
,w diff (x+1)/(x-1)
elfin berryBOT
obsidian shard
basically same as you got above
you might as well cancel x in the first place cause x won't be 0
@ionic owl
marsh citrusBOT
@ionic owl Has your question been resolved?
ionic owl
you might as well cancel x in the first place cause x won't be 0
Alright thanks
twin ether
hi is this
marsh citrusBOT
hi is this
obsidian shard
what's the question?
twin ether
what's the question?
simplify
obsidian shard
I think you should be able to cancel some stuff before performing the fraction substraction
twin ether
yep
obsidian shard
Hmm, looks correct to me
obsidian shard
as in the domain restrictions?
twin ether
yesss
obsidian shard
yep
obsidian shard
sure
obsidian shard
the one at the right is my answer, is it correct as well?
yes, it is correct. I got the same.
twin ether
yes, it is correct. I got the same.
thanks a lot, last question, am I just going to plug d^t and d^0 then solve for 1/f?
1/x^2-4x - 12 + 1/4x+8
like that
obsidian shard
weird question but I think it does mean that only
twin ether
weird question but I think it does mean that only
alr, that's what I got, right?
obsidian shard
yep, got the same
gritty wren
Hi there can someone tell me how to deal with sine double angle identity
gritty wren
Like how is 2sin(x/2)cos(x/2)=sin(x)
late geode
x/2 is half of x
$\sin(\text{this}) = 2\sin(\frac{\text{this}}{2})\cos(\frac{\text{this}}{2})$
elfin berryBOT
ℝamonov
gritty wren
Ohhhhh i see, thank you so much!!!
uneven musk
how much do you need to get 9664 to 10058 help pls im stupid
marsh citrusBOT
how much do you need to get 9664 to 10058 help pls im stupid
cobalt sentinel
So u want to do 10058 - 9664?
knotty trellis
10058-9664
cobalt sentinel
What’s troubling you with that
shell hill
Btw
shell hill
@quaint hill there's an easier
Solution for the problem I had
U remember it right?
$\lim_{x\to\infty}x^0 = 1$
elfin berryBOT
RulzerFly.
shell hill
.close
frosty linden
if $p$ is prime and $p²+8$ is prime, Prove that $p^{3} + 8p + 2$ is prime too. Can someone gives me a hint?
marsh citrusBOT
if $p$ is prime and $p²+8$ is prime, Prove that $p^{3} + 8p + 2$ is prime too. C...
elfin berryBOT
phoestaclies
devout mauve
consider mod 3
frosty linden
I think I don't get the idea ?
devout mauve
when in doubt, try examples
go through the first few primes p, check if p^2+8 is prime and if yes check if p^3+8p+2 is prime
frosty linden
yes I did that with 3 and 7
marsh peak
p^2 + 8 is not prime when p is 7
devout mauve
if 2 examples is not enough then maybe do 4 or 5
frosty linden
euh yes sorry mb
devout mauve
p^2 + 8 is not prime when p is 7
tell that to grothendieck
marsh peak
To whom?
frosty linden
ok I will try to test other, and see what I get ty 🙂
marsh peak
Btw I noticed that p^2 + 8 is most of the times divisible by 3
frosty linden
.close
marsh citrusBOT
devout mauve
Btw I noticed that p^2 + 8 is most of the times divisible by 3
way to spoil the fun
marsh peak
What/Who is grothendieck?
marsh peak
Actually I once picked 57 as prime for some reason as well 
marsh citrusBOT
devout mauve
it does look quite primelike
devout mauve
as general advice btw, if any claim says "this formula will always be prime", then either the claim is false or the hypothesis only hold for finitely many cases
in 99% of cases anyway
frosty linden
ok thanks
marsh peak
That is what is meant in the remaining 1%
frosty linden
yes i saw that
main idol
everyone shitpost until bot queue's this job up
devout mauve
abusing wilsons theorem to give integers or not I guess with the cosine there
marsh peak
everyone shitpost until bot queue's this job up
Every time that happens I just edit my last message to add what I want to say lol
frosty linden
.close
main idol
bot's just slow
knotty trellis
Stupid bot
main idol
devout mauve
10 minute timelimit before bot can move channel again
frosty linden
I wasn't thinking about the consequences of my question
devout mauve
how dare you
marsh citrusBOT
Available help channel!
narrow kite
does anyone know how'd you maximize a function of this type?
marsh citrusBOT
does anyone know how'd you maximize a function of this type?
sand vigil
night mica
try to use the formula for geometric series ..then you get a simpler function on N
narrow kite
try to use the formula for geometric series ..then you get a simpler function on...
the formula (1-r^N+1)/(1-r)?
if so, good point. Thanks for help
night mica
yes but i think you have to add a -1 because the series doesn t strat from 0
narrow kite
yes but i think you have to add a -1 because the series doesn t strat from 0
yeah
alr how do I close this?
.close
marsh citrusBOT
narrow kite
yes but i think you have to add a -1 because the series doesn t strat from 0
thanks
night mica
np
marsh citrusBOT
Available help channel!
kindred spear
could someone give me pointers for this
marsh citrusBOT
@kindred spear Has your question been resolved?
kindred spear
<@&286206848099549185>
kindred spear
higher probability and stochastic processes
marsh citrusBOT
@kindred spear Has your question been resolved?
kindred spear
can u tell more
marsh citrusBOT
@kindred spear Has your question been resolved?
flat raft
what's a geometric series
I think here you just need to show that Q(A) satisfies all of the axioms of a probability measure
which honestly I constantly forget, but it should be something like Q(emptyset) = 0, Q(the whole space) = 1, countable additivity, and nonnegativity
countable additivity is where you might need to use monotone convergence
tacit fjord
<@&268886789983436800> could you check this person's msg history along with their deleted msgs
Seems to just be trolling
kindred spear
countable additivity is where you might need to use monotone convergence
right I was thinking along those lines
I'll try it out
kindred spear
which honestly I constantly forget, but it should be something like Q(emptyset) ...
so for the case of Q(empty set) = 0, could we consider a decreasing sequence of events where the limit would be the empty set
kindred spear
right
im guessing for a set A in the collection of events H, the measure Q outputs a number [0,1]
kindred spear
read the definition of Q
do you think you could help with my understanding of Q (the numerator regarding that 1_A)
flat raft
im guessing for a set A in the collection of events H, the measure Q outputs a n...
you don't know that this is a measure
you need to prove that it is a measure
flat raft
do you think you could help with my understanding of Q (the numerator regarding ...
do you know what 1_A means
kindred spear
do you know what 1_A means
no
flat raft
why didn't you just look it up
kindred spear
i was trying to but i couldnt find smth explaining it
flat raft
how do you expect to do a problem if you don't even know what it's saying
flat raft
it's never defined in your textbook?
kindred spear
why didn't you just look it up
what's it called
flat raft
it's called an indicator function
so what have you been wasting your time on
if you don't even know what the problem is saying
no it is not
do you know what a sample space is
let's say A is an event
do you know what an event is
do you know the definition of event
bruh
go review
kindred spear
sure
flat raft
an event is a measurable subset of Omega
it is a set of outcomes
"measurable" means it belongs to H
no it is not
you need to review the definitions of sample space, probability measure, random variable
H is the set of all measurable sets
do you know how expectation is defined
do you know what a Lebesgue integral is
do you know what a random variable is
you kinda need to know the definitions
to do something that depends on them
after you review everything, to check your understanding, come back with an explanation of why E[1_A] = P(A)
marsh citrusBOT
@kindred spear Has your question been resolved?
flat raft
you need to show it for general random variables
using the definition of expectation given by the Lebesgue integral
flat raft
it's basically the same thing, because 1_A is a discrete random variable
but you need to understand what the Lebesgue integral is and where the formula for discrete RVs come from