next geyser
Yes
#help-42
plain bone
The requirements of Rolle's theorem are that $f(x)$ is differentiable on $(a, b)$ and $f(a) = f(b)$
potent lotusBOT
King Leo
calm coralBOT
@next geyser Has your question been resolved?
quaint grove
Theres a certain basic math concept Im forgetting, its like a bunch of basic algebraic laws or something but I cant remember them
things like 'if A/B = C then () * () = (_)' or something, Im trying to remember what it was called so I can refresh on it but Im drawing a blank
Does anyone onow what I mean? Iirc its like something very basic but ive not thought about math in a bit
quaint grove
for reference, i was looking up why the circumference of a circle is 2πr and eventually got to 'π= circumference/2r, and solving for that gives us circumference= 2πr' and that made me partially remember
leaden thunder
Theres a certain basic math concept Im forgetting, its like a bunch of basic alg...
quaint grove
thank you, ill read up on this right now, thanks for helping me :]
leaden thunder
If that's not it feel free to ask again with more details
calm coralBOT
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glad lance
Had some prediction exam this week at a county-wide level in order to prepare for the actual exams this summer. This was the only thing that I couldn't figure out how to calculate. (B)
AB is 12cm
the angle ACB is 60 degrees
A and D are diametrically opposed
B means "Show that the length of the circle is egual to 8pi square root of 3cm
calm coralBOT
Had some prediction exam this week at a county-wide level in order to prepare fo...
@glad lance Has your question been resolved?
glad lance
<@&286206848099549185>
calm coralBOT
@glad lance Has your question been resolved?
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@glad lance Has your question been resolved?
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@glad lance Has your question been resolved?
vocal pawn
Had some prediction exam this week at a county-wide level in order to prepare fo...
i was able to figure out the angle but not the proving part
since AD is a diameter
angle ACD= 90
and since ACB is given 60 => BCD = 30
now DAB = DCB (angles in the same segment)
=> BAD = 30
glad lance
i was able to figure out the angle but not the proving part
me too
thats the easy part
glad lance
.close
true blaze
I don't really understand why a random variable X being G-measurable is sufficient to determine the value of X?
mortal orbit
!xy
calm coralBOT
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.
mortal orbit
well we also need the information in G
true blaze
i dont understand what we mean by information
mortal orbit
think about G as a set of events of omega
"knowing the information G" is the same as saying "suppose we know which events of G are true and which are false"
if we know the info G, and if X is G measurable, then X is known
true blaze
oh ok ill think about it
true blaze
if we know the info G, and if X is G measurable, then X is known
Ah so one simple example of determining X given G measurability is when G is ${\Omega, \emptyset}$ (which implies that X is degenerate)
potent lotusBOT
>_<
cinder roost
true blaze
ah i guess i get it now
blazing coyote
Determine which variables are free and which are bound
calm coralBOT
Determine which variables are free and which are bound
blazing coyote
$-3 \in { x \in \R \mid 13-2x>1}$
potent lotusBOT
What a wonderful world!
blazing coyote
here x is a bound variable
sweet stag
what is a bound variable? @blazing coyote
blazing coyote
A varible whoose value has been bound to a certain interval
blazing coyote
the right?
lament sorrel
generating functions
i dont understand the last 2 steps
calm coralBOT
generating functions
i dont understand the last 2 steps
lament sorrel
the -1/2 should be "1"
calm coralBOT
@lament sorrel Has your question been resolved?
next nest
How do I take solve this?
calm coralBOT
How do I take solve this?
next nest
I just took df/dx multiplied by itself but I don’t think it’s right and can’t recall how to take the second partial derivative in this case
calm coralBOT
@next nest Has your question been resolved?
languid elbow
I need help
calm coralBOT
I need help
oak elm
this is like barely readable
calm coralBOT
Show your work, and if possible, explain where you are stuck.
@languid elbow Has your question been resolved?
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lucid knot
did I get these right?
calm coralBOT
did I get these right?
lucid knot
viral patrol
lucid knot
thanks!
calm coralBOT
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lucid knot
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quasi cypress
An equilateral trapezoid is described around a circle with diameter 15, the side of which is 17. Find the larger base of the trapezoid.
quasi cypress
?
ancient grotto
An equilateral trapezoid is described around a circle with diameter 15, the side...
an equilateral trapezoid? is this the same as an isoceles?
calm coralBOT
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lucid knot
calm coralBOT
swift dragon
whats the question?
lucid knot
apparently this is correct- but if the run is -1 and the slope is 3 shouldnt the line be going the other way?
sorry took me a second to type
swift dragon
wdym going the other way?
leaden thunder
apparently this is correct- but if the run is -1 and the slope is 3 shouldnt the...
What are you asking
leaden thunder
Is it related to this problem
lucid knot
-1 is rise sorry
it was related but it was a profoundly stupid thing to ask
yes, it's right
thanks anyways, I figured it out 👍
.close
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cyan moth
Question about the Occupation State Basis for a Fock Space
This may be a physics related question, but as I understand it, one of the basis of a fock state is the occupation number basis. This is an infinite dimensional space, and elements are of the form (n1,n2,n3,...) for ni a set of the positive integers. This basis seems natural, but I noticed that you can have 2 bases sum to a third basis vector in this representation. I never really saw a basis set with this property before and it feels a bit weird since this would seem to imply reducibility. So whats the deal? Is my understanding incorrect?
calm coralBOT
Question about the Occupation State Basis for a Fock Space
This may be a physi...
@cyan moth Has your question been resolved?
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@cyan moth Has your question been resolved?
whole hinge
Question about the Occupation State Basis for a Fock Space
This may be a physi...
Can you provide an example of two basis vectors that you think sum to another basis vector here? There shouldn't be any
calm coralBOT
@cyan moth Has your question been resolved?
cyan moth
Can you provide an example of two basis vectors that you think sum to another ba...
yeah the occupation number representation. Its a bunch of sequences with integer entries. So perhaps I have the wrong understanding of this basis
whole hinge
I mean like two specific basis vectors that you think add up to another basis vector
I think you're misunderstanding how the basis vectors work here
There's no vectors in the occupation number basis that add up to another basis vector
cyan moth
(1,0,0,0,...) + (0,2,0,...) = (1,2,0,...) for example @whole hinge
whole hinge
(1,0,0,0,...) + (0,2,0,...) = (1,2,0,...) for example <@531535537362829315>
This is not correct
cyan moth
I think you're misunderstanding how the basis vectors work here
I think so too, unfortunately the found literature about this specific topic is really poor it seems
whole hinge
If it helps, you can instead write those vectors like this
The first is v1 and the second is v2^2. That doesn't add up to the third one, which is v1 v2^2.
The result is simply v1 + v2^2, there's no further way to simplify it
The v1 v2^2 here is a tensor product, not a direct product/direct sum.
cyan moth
vi here is some energy state yes?
whole hinge
It's the wave function representing a particle in the ith energy state, yeah
cyan moth
yeah, ok and the power is the grade of the hilbert space, correct? I hope Im using the right words
whole hinge
If you had v1 + v2^2, you could think of that as like a superposition between having a particle in the 1st energy state vs having two particles in the 2nd energy state, whereas v1 v2^2 is the situation where you have three particles simultaneously, one in the 1st energy state and two in the 2nd energy state.
whole hinge
yeah, ok and the power is the grade of the hilbert space, correct? I hope Im usi...
The grade is the sum of the exponents yeah, v1 v2^2 would be in the third grade (there are three particles)
cyan moth
ye ye, ok so I think I understand the construction well, its the notation thats misleading me a bit
whole hinge
Yeah, the tuple notation makes it look like a direct product. It should really be a tensor product.
cyan moth
so there is no simpler way to write (1,0,...) + (0,2,...)
whole hinge
Yeah, there is no way to simplify that further.
If you wanted, you could use bra-ket notation and write like |1> + |2>^2 or something
cyan moth
yeah admitedly the bra-ket notation makes it more obvious you cant add these things together
ok got it, thanks for the help!
whole hinge
A mathematician's way to write it might be more like
v1 + v2^2 (remember that the ^2 here means a tensor product)
But either way, yeah, you can't add them together like that
cyan moth
gotcha gotcha
whole hinge
Oh and also, since they're identical particles, replace every time I said "tensor product" in this discussion with either "symmetric tensor product" or "antisymmetric tensor product" depending on whether they're bosons or fermions
So if you're dealing with fermions, v2^2 for example is just 0 since the antisymmetric tensor product of v2 with itself is zero.
cyan moth
ye of course. Maybe getting a bit off topic, but I remember reading that these two parity subspaces are not compliments of eachother
but then I remember that this isnt really a problem and that theres some work around?
whole hinge
For the second grade (two particles), you can write any tensor uniquely as a symmetric tensor plus an antisymmetric tensor. For example v1 (x) v2 can be written as
1/2 (v1 (x) v2 + v2 (x) v1) + 1/2 (v1 (x) v2 - v2 (x) v1).
But yeah, in general, this is not possible.
You can convince yourself of this by counting dimensions.
Let's say you have three particles, and each one can have either the state v1 or v2.
If they're distinguishable, then that gives you 2^3 = 8 possible outcomes.
If they're indistinguishable and symmetric, then that gives you the outcomes {v1, v1, v1}, {v1, v1, v2}, {v1, v2, v2}, and {v2, v2, v2}, so 4 possible outcomes.
If they're indistinguishable and antisymmetric, then there aren't actually any outcomes because there are more particles than states, and the antisymmetric product of two repeated particles is zero (the Pauli exclusion principle), so that gives you 0 possible outcomes.
4 + 0 can't get you 8.
So in this case, there are 4 extra dimensions of possibilities which aren't accounted for by just thinking of symmetric and antisymmetric arrangements.
cyan moth
Ah I see, thats a great explanation! Thanks again!
whole hinge
You're welcome, and good luck with things :)
calm coralBOT
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stable hollow
Okay so I know how to normaly so a peacewise function
calm coralBOT
Okay so I know how to normaly so a peacewise function
stable hollow
Like for ex -2x if x 2 (this isnt a real question just showing format)
And 2x if x greater than or equall to 2
But how tf I don't when the graph has this bumpy thing
plain bone
Can you show your y = menu @stable hollow
void umbra
Can you show your `y = ` menu <@818456196943970365>
But yea please show menu frfr
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exotic cosmos
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exotic cosmos
the positive difference between the largest and smallest possible range of grades of all students > 60?
frosty spruce
I think it's simply (100 - 15) - (86 - 63)
woven summit
in how many ways can a party of four be selected from 10 people
frosty spruce
in how many ways can a party of four be selected from 10 people
!occupied
calm coralBOT
in how many ways can a party of four be selected from 10 people
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
woven summit
can someone explain
frosty spruce
all of them get 15?
ah
of course.
largest is 85 and smallest is 0, so the difference is 85
exotic cosmos
but also "divided into three classes"
woven summit
in how many ways can a party of four be selected from 10 people
?
exotic cosmos
so can we really have a range of 0
UGHHHH every question is so ambiguous
i hate it
woven summit
ok
frosty spruce
oh, i thought that part is negligible
frosty spruce
I think it's simply (100 - 15) - (86 - 63)
yep so this is the answer
each classes must have at least 1 student so the range is never 0
exotic cosmos
then how did you get the minimum range of 86 - 63
wait i misread the question
yes that is correct
but my main concern is if min range is 0 or not
frosty spruce
each classes must have at least 1 student so the range is never 0
^
exotic cosmos
no but yeah that depends
if u have 3 boxes
u can distribute 5 objects
such that one box has 5 object
and 2 have 0
there's still 3 boxes there
even though 2 of them have 0 boxes
frosty spruce
i mean since the answer is correct, it could be what the problem indirectly meant
though i would argue that is poorly stated
exotic cosmos
i mean there was another question
same issue
How many ways can 5 people be assigned to 3 distinct teams, with at least one team having 2 members?
how am i supposed to know what to solve for 😭 if the question isn't clear
frosty spruce
you can always argue with teacher about what is missing from the context
they will understand if your reasoning is logical
frosty spruce
in my country, we always have 5 minutes to check for every possible mistake after given paper test. the mistake includes: printing error, missing pages, etc
but the time to check whether a problem is correctly stated is very open
so if a problem has a context error, it's fine to argue about the supervisors (if you still obey the rule of taking exams) and they will call the teachers who made the exams to initiate an emergency meeting, then distribute some teachers to each rooms to make an emergency adjustment
exotic cosmos
frosty spruce
if the error is noticed after the exam is completed, the problem is instantly neglected and everyone has free mark
exotic cosmos
so is the question ambiguous after all?
frosty spruce
yes, it is ambiguous
exotic cosmos
How many ways can 5 people be assigned to 3 distinct teams, with at least one te...
even here?
frosty spruce
well it doesn't say every team must have at least 1 member so one team can have nobody at all
stray tundra
well, it's a school, and they are 5th graders.
You can make the reasonable assumption that there's a minimum of students per class, because otherwise, they simply would be less classes
exotic cosmos
in this sense each team must have at least one person
but there are different schools of thoughts here
otherwise u can think of it as 3 boxes where one box can have 0 objects
so it's all philosophical 😭
stray tundra
idk in your country, but here for most classes there needs to be a minimum of students unless exceptional circumstances apply
exotic cosmos
what about
frosty spruce
but then "assigned to 3 distinct teams"
the "distinct" is, well, just "distinct"
exotic cosmos
How many ways can 5 people be assigned to 3 distinct teams, with at least one te...
this tho
exotic cosmos
the positive difference between the largest and smallest possible range of grade...
this is the question
our question structure is weird
so i just wrote out the question myself
the actual question is just "60"
stray tundra
show the original
exotic cosmos
we have instructions aside for what to do with just that
stray tundra
!original
calm coralBOT
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.
exotic cosmos
the positive difference between the largest and smallest possible range of grade...
It's literally this
stray tundra
that's badly worded, so i can guarantee it's not written like that
exotic cosmos
stray tundra
and the rest?
exotic cosmos
It's literally
just that
our question have different formats
so i don't post it
stray tundra
there's literally no question there
exotic cosmos
dude we have different
formats for a question in class
it's known what the question is
stray tundra
you have MORE instructions than that. I dont care if they are in a different paper, they NEED to be posted
exotic cosmos
the positive difference between the largest and smallest possible range of grade...
this translates to this
i have written it out for u
stray tundra
So basically your instructions are "is A > B"?
stray tundra
so then write that
exotic cosmos
this has nothing to do with what my actual question was
No
it has nothing to do with what i asked
exotic cosmos
the positive difference between the largest and smallest possible range of grade...
besides i wrote this
U have gotten 0 extra information from all this
stray tundra
i have gotten quite a lot from the screenshot actually
exotic cosmos
why is the smallest possible range not 0?
okay then answer this question solely based on the new information you got
stray tundra
we do have a bot command asking for the original context precisely because what "seems" to be the same isnt
exotic cosmos
The point of that is because people post xy questions
I know about it
My question is posted word for word
how the question is formatted has been translated by myself
exotic cosmos
the positive difference between the largest and smallest possible range of grade...
the answer to this is either:
"no"
"yes"
"can't tell"
stray tundra
okay then answer this question *solely* based on the new information you got
The new information is "compute A"
"compare A to B"
Which is basically a 30 second problem
before, it was "wtf is to be done here"
exotic cosmos
but again i didn't want the answer to that. my actual question is if we can't have students all scoring 15 on the test
exotic cosmos
The new information is "compute A"
"compare A to B"
Which is basically a 30 seco...
??????
targetVN
already answered the question lol
exotic cosmos
I think it's simply (100 - 15) - (86 - 63)
^
we are discussing about the ambiguity of the question
exotic cosmos
the positive difference between the largest and smallest possible range of grade...
this is exactly how the question is posed
stray tundra
Anyways.
You got a range of scores.
Since you got said range, it's usually understood that a student scored each end of the range, which makes it so at least 2 students are in each class
exotic cosmos
if my new information provided you new information then can you answer why the smallest possible range isn't 0 solely based on the new information u received? apparently, it was so helpful
stray tundra
for first class, there was a student scoring 15, a student scoring 63, and whatever many students between those values
for the second class, there was a student scoring 64, a student scoring 85, and however many in between that we dont care about
and in the third, there was a student scoring 86, a student scoring 100, and however many we dont care about
exotic cosmos
there was a student scoring 86?
it's just that a score is attained between 86 and 100, inclusive
no?
it can be anything
"fall in the intervals..."
also uhhh i'm still confused why the entire class just can't score between 15 - 63
why are we so sure that there's scores in the other ranges too
if we change the context to:
Lottery winners over the years are divided based on the gifts they have obtained:
Iphone
Macbook
Car
It is possible that no one has won the car yet, for example.
<@&286206848099549185> , could someone confirm pls. thanks
stray tundra
usually no, because then the category would not be included. It's implicit that it has happened
calm coralBOT
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thick sinew
https://discord.com/channels/268882317391429632/1333046990661222461
why don't you simplify here
z² = 1 + 0
z²= 1
--> z e {-1, 1}
elder mesa
No, this is the original problem:
elder mesa
yep
thick sinew
yes
elder mesa
I think my solution is suppose to look something like this:
thick sinew
I'm confused which task you're now asking to be checked
thick sinew
I don't see how they differ in how you approached the problem
elder mesa
Okay, so what is the solution to the 1st?
thick sinew
from the initial post it's the solution to z² = 1
thick sinew
No, this is the original problem:
for the original problem it's the solution to -i*z² = 1
thick sinew
you must divide by -i
dividing by -1 is the same as multiplying by -1
elder mesa
Sorry this is the wrong picture
thick sinew
and dividing by i is the same as multiplying by -i
1/i = i/i² = -i
unkempt drift
yes, that's correct
elder mesa
yes, that's correct
And the first problem?
unkempt drift
And the first problem?
which one?
thick sinew
https://discord.com/channels/268882317391429632/1333046990661222461
ys also right
as stated in the beginning can be shortened
unkempt drift
.close
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thorny swan
Hello, can anyone help with this ? Given a square ABCD and its interior point M. Construct all the segments PQ that have their endpoints on the boundary of the square and the point M divides them in the ratio /PM/ : /QM/ = 1 : 3 .
calm coralBOT
Hello, can anyone help with this ? Given a square ABCD and its interior point M....
@thorny swan Has your question been resolved?
thorny swan
<@&286206848099549185>
flat gorge
So you want us to construct all segments PQ?
thorny swan
maybe some proposal how to do it would help
cause idk how to do it
something like this ?
calm coralBOT
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calm coralBOT
@thorny swan Has your question been resolved?
white edge
This is a Calculus II question on finding the volume of a solid generated by revolving the regions bounded by the graphs y=sqrt(x), x=0, x=3 - this problem uses the disk & washer method to calculate the volume
white edge
I'm attempting to solve the problem concerning a revolution around the y-axis but cannot discern the error in my work
I will post a screenshot of my math soon
idk why it posted sideways like that
there may be a text command to rotate it but im not familiar with the server commands
ember trail
,rccw
potent lotusBOT
white edge
awesome
tidal grotto
you may need to put in precisely what it is
i.e. (sqrt(3)^5)pi/5
like you did in the previous answer
@white edge
calm coralBOT
@white edge Has your question been resolved?
white edge
if someone is able to confirm the math is correct, then that should be fine
I'll probably assume it's a technical issue with the homework system and speak to my professor about it
white edge
mhm
tidal grotto
but what you're doing is rotating this region
what you want to do is rotate the black region, not the yellow region (which is what your math was doing)
technically you can still get the answer with the work you have,
white edge
can you show how my equation is rotating the orange region instead of the black?
tidal grotto
think about it in terms of x (just rotate your reference frame)
so if you have integral x^2 from 0 to sqrt(3) it would be what region
white edge
I think I have that pictured in my head
tidal grotto
it'd look a bit like the yellow region right?
tidal grotto
yes
everything is in terms of y
yes
so y^2, in the frame of reference of y is a parabola
yes?
white edge
yeah
tidal grotto
and you're integrating it from 0 to sqrt(3)
so that looks like the yellow area, yes?
tidal grotto
tidal grotto
would I do 3-y^2?
almost
white edge
If y^2 is the smaller radius in the graph, and the larger radius is 3 (correct me I am wrong on that one), then we need to subtract the smaller radius from the larger radius to obtain the desired radius of the black region
calm coralBOT
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whole token
(Linear algebra)
Hello, I'm having a hard time understanding the definition, formula and use-case (in problems, not applied) for scalar products with orthogonal basis, any help unpacking it all or any help pointing out some important concepts so i can try and unpack it on my own would be greatly appreciated<3
whole token
apologies, i dont think its orthogonal basis, i belive it should be ON-basis, my textbook is in Swedish and I'm having a really hard time translating and researching in english ^^
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lucid knot
calm coralBOT
lucid knot
did I graph the polynomial correctly/ does my algebra check out?
?
<@&286206848099549185>
ancient grotto
derivatives? 
lucid knot
derivatives? <:blobcry:971797574916907028>
whats wrong?
ancient grotto
whats wrong?
did you take the derivative of F and mistakenly taken another derivative thinking you hadn’t taken it yet
lucid knot
did you take the derivative of F and mistakenly taken another derivative thinkin...
i dont think so?
i got two
let me try that bit again it does look weird you are right
lucid knot
did you take the derivative of F and mistakenly taken another derivative thinkin...
.close
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oblique kiln
Let the sequence $ (a_n)_{n \geq 0} $ of real numbers satisfy the inequality:
$$
a_n < a_{3n+5} + a_{n + \left\lfloor \frac{n}{2} \right\rfloor}, \quad \forall n \in \mathbb{N}
$$
Compute the following limit:
$$
\lim_{n \to \infty} \sum_{k=0}^{n} a_k
$$
potent lotusBOT
radwkw
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oblique kiln
@trail epoch
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whole hinge
<@823462958079803432>
What have you tried so far?
calm coralBOT
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stable hollow
calm coralBOT
leaden thunder
The top is blurry
stable hollow
I can read it fine
stable hollow
The top is blurry
leaden thunder
For area wouldn't it just be (x+6)(2)
area of a rectangle is length times width
where does (x+6)*2 come from
calm coralBOT
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stable hollow
where does (x+6)*2 come from
Sorry I was talking about perimeter
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stable hollow
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prime rapids
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prime rapids
Can anyone help me with part C
My professor Said it was not correct
She Said the part b Would guide me
jolly pilot
Lets start with the part a. If you put the x as some value very close to 1, but less than 1, can you tell me whats that integral gonna be?
prime rapids
Constant ?
prime rapids
It Will be 0
jolly pilot
Constant ?
you gotta tell me the value of the constant
jolly pilot
It Will be 0
And how does that work with your formula for a??
prime rapids
I am asking about C
prime rapids
Ohh
jolly pilot
Your formula gives you the integral from 1 to 1 as 2 + 2x. If you put x = 1, it yields 2 + 2 =4
which should actually be 0
prime rapids
I dont get it
jolly pilot
Do you know these properties? Especially the 1st
prime rapids
Yes
jolly pilot
You have dark mode? Thats gonna mess up the image
prime rapids
Yes I do
prime rapids
Yes
jolly pilot
So, what I mean to say is you have calculated $\int_x^1$ when you needed to calculate $\int_1^x$
prime rapids
So it should be 2x-2 ?
potent lotusBOT
Facter10Br4g
jolly pilot
So it should be 2x-2 ?
Ooops, didnt see that between there. Yea, this is correct
jolly pilot
So, you should notice, the integral is negative when x is small
so you cant have F positive in the interval (-inf, 2)
since x is negative, F = 2x-2 is also gonna be negative
The integral x to 1 is positive, but F is negative of that, so the value of F is gonna be negative
Maybe you should try plotting F against x first to get a better idea
prime rapids
Maybe you should try plotting F against x first to get a better idea
Like i did in part a ?
jolly pilot
If you mean b, then yes
jolly pilot
This is what I mean
but this time, keep this rule in mind
jolly pilot
I mean, I only see a graph sketched for your answer to part b
prime rapids
How about C?
prime rapids
Ohh okay
jolly pilot
You need to calculate other values
prime rapids
So it is x>1?
jolly pilot
?
prime rapids
jolly pilot
F is decreasing between 1 to 3, and increasing from 3 onwards
Your answer doesnt capture that
prime rapids
F is decreasing between 1 to 3, and increasing from 3 onwards
Also -inf,1 ?
For increasing
jolly pilot
Your part C asks for positive
Not if its increasing or decreasing
And we are still on part C
jolly pilot
F is 0 at x = 1
And then, for the interval x = (1, 3), you have $F = \int_1^x (-2x+4)dx$
potent lotusBOT
Facter10Br4g
prime rapids
**Facter10Br4g**
How ?
prime rapids
Where you got that
jolly pilot
we know the line is between the points (1,2) and (3,-2)
Thats the equation we get for a line between 2 points right? I may have made some calculation mistakes, but I dont think so
prime rapids
Ohh so we have to make it from the LINE to LINE ?
jolly pilot
Yeah
Thats how f(x) is defined
Divide the integral into different parts of its domain
prime rapids
But my professor told me to use the geometric intepretation
jolly pilot
I mean, integral is jus the area
The area keeps on changing
Initially, as x increases from 1 to 2, the area increases
Then from 2 to 3, it decreases
and then becomes 0 at x = 3 (which you correctly calculated)
Then goes on decreasing, yet still being negative till x = 5
At x=5 onwards, it starts increasing, but is still negative
Becomes 0 at x=7 and so on
The point being, Area of region below x axis is negative
Area of region above x axis is positive
jolly pilot
No.... We already showed from part a, that F is always negative for all x < 1
jolly pilot
Complete this for values of x greater than 1
Thats why I asked you to complete this graph
prime rapids
I have made for (1,3)
jolly pilot
(If you did the integration) First off, the integral would be -x^2 + 4x. So its definitely not negative at x = 1
(If you did geometrical area calculation) The area of the trapezium that forms for x in (1,3] is never negative
So I have no clue how you got F
prime rapids
Can you give the solution ?
jolly pilot
!nosols
calm coralBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
prime rapids
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strange crown
After doing the ferris wheel question, my equation came out a little different than the answer.
I checked them out in desmos, my graph/equation(Blue) has the rider do a full rotation(starting from the bottom and ending at the bottom), in 3 minutes. The graph of the answer(Red), does a full rotation in 6 minutes. Am I misunderstanding the question?
calm coralBOT
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@strange crown Has your question been resolved?
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proud bronze
After doing the ferris wheel question, my equation came out a little different t...
I think ur solution is correct
calm coralBOT
remote mural
The easiest way u can think of
Is to just substitute the value of a = bc from the first equation
Into the following two equations
tall moon
multiply the second and third equation (why does this feel illegal lol)
wdym how TwT
b×c=c(a+2)×b(a-2)
calm coralBOT
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vital cosmos
molten pendant
what's the trig form for this complex exponential
calm coralBOT
what's the trig form for this complex exponential
tacit moat
$e^{i\theta}+i$
potent lotusBOT
Sepdron
potent lotusBOT
anti-algebraist 𝔸dωn𝓲²s
eternal shard
i has pi/2 angle so e^(i * pi/2) and you can now plug it in in the trig formula
calm coralBOT
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blazing coyote
Trying to integrate this
calm coralBOT
Trying to integrate this
blazing coyote
I was thinking of $x+2y=u, y-x=v$
potent lotusBOT
What a wonderful world!
blazing coyote
so the integrand is $u e^v$
potent lotusBOT
What a wonderful world!
potent lotusBOT
calm coralBOT
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steel kraken
how do i do this question ?
calm coralBOT
how do i do this question ?
steel kraken
im unfamiliar with these types of questions so i'd like to know how to start it in the first plac
*place
frosty spruce
For the first problem, you can use coordinate system to solve it
For the second one, you can also use coordinate system to solve it
Although, you can base on the first one to solve the 2nd one
polar frost
Use polar coord if u want something more challenging
potent igloo
im unfamiliar with these types of questions so i'd like to know how to start it ...
This looks like it wants you to use vector addition
frosty spruce
If you dont want, you can solve the 2nd problem first using Thales theorem, then base on it to solve 1st one
flat gorge
how do i do this question ?
OP = OA + h(OC - OA) = 0.5 OA + k(OC + 3/4 OA - 1/2 OA)
Can you figure h, k?
frosty spruce
but they're doing vectors though
I got taught about thales before vectors so idk
flat gorge
**OP = OA + h(OC - OA) = 0.5 OA + k(OC + 3/4 OA - 1/2 OA)**
If you don't get this, you can ask :o
calm coralBOT
@steel kraken Has your question been resolved?
steel kraken
If you don't get this, you can ask :o
alrgive me a second
steel kraken
If you don't get this, you can ask :o
why 2/3 OB ?
steel kraken
This looks like it wants you to use vector addition
yep
this is how i did it buts its wrong
flat gorge
why 2/3 OB ?
Corrected. Not 2/3 OB but 3/4 OA
steel kraken
Corrected. Not **2/3 OB** but **3/4 OA**
im pretty sure i did as was shown in ur working
but i get the wrong answer for some reason
steel kraken
oh my god
i am stupid how did i not see that
thank you @flat gorge
idk how to give praise or points here if thats a thing but thank u
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restive pier
This will sort of be a two part question:
First, why does this highlighted portion matter? What is the problem trying to teach? Second, what if it was something like 4 < √500? Would I be manipulating the sign of the square root number instead?
dull wagon
(piecewise) definition of absolute value
the goal is to express what you have without those abs val bars
and to do that you would need to consider whether the inside is positive or negative
restive pier
Piecewise portion helpful - will have to read
Third follow up: is there only one answer to this problem?
For example: |3| is either 3 or -3
Would -4-√5 be a valid answer?
dull wagon
Would -4-√5 be a valid answer?
no to that as well
restive pier
Ok so I shouldn't be thinking of abs like this? I should be thinking of solving abs problems like . . . their own thing?
dull wagon
Third follow up: is there only one answer to this problem?
one simplified answer/value, yes
$|\text{this}| = \begin{cases} \text{this}\ &\text{if } \text{this} > 0 \
-\text{this} \ &\text{if\ } \text{this}\leq 0 \end{cases}$
potent lotusBOT
ℝαμOmeganato5
coral leaf
Hi, im having trouble with a question, i seem to be fine with all the other ones but this question (the top bit of the image, and solution being bottom bit) all i need to know is how theyve managed to get the y^2 on the other side, because when ever i do it and integrate it i end up with -1/y on the right and dunno what to do from there, please help!
calm coralBOT
Show your work, and if possible, explain where you are stuck.
coral leaf
1 second
i get stuck here, not sure how to turn it into what the answer should be, im not very good at rearranging so maybe im missing a step?
dull wagon
don't forget + c
swift dragon
you forgot the +C
coral leaf
yh i was bout to mention, that was my bad, however once i add c, i still have -1/y on the left however the answer says it should be y (my foundational maths isnt very good so i could be missing some easy rearranging or something)
mild hedge
Yes, you need to rearange so y is by itself in the numerator, a first step could be to multply both sides with y
swift dragon
$\frac{-1}{y}=\frac12x^2+C$
potent lotusBOT
Bonk
swift dragon
then rewrite into y=???
coral leaf
i see, im very bad at rearranging however thank you for pointing out where my error is
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molten sphinx
Can someone explain how to find the correct amount of mass?
calm coralBOT
Can someone explain how to find the correct amount of mass?
swift dragon
!show
calm coralBOT
Show your work, and if possible, explain where you are stuck.
tender pelican
Can someone explain how to find the correct amount of mass?
ft^3 🤮
molten sphinx
I know that Density = Mass x Volume
swift dragon
I know that Density = Mass x Volume
thats wrong
molten sphinx
I typed it wrong mb
tender pelican
Mass = Density x Volume
molten sphinx
Mass/Volume is Density
swift dragon
look at your units
molten sphinx
I gotcha
tender pelican
look at your units
you dont need to repeat after me
not repeat
he has a brain
you dont have to tell him exactly what to do
molten sphinx
I didn't convert the units, that's what I did wrong
tender pelican
i typed it at the same time bro
i sent my message at 20:22:33 and you sent yours at 20:22:59
glad parrot
Lmao got trapped
tender pelican
i sent my message at 20:22:33 and you sent yours at 20:22:59
UTC+1
clear sapphire
i sent my message at 20:22:33 and you sent yours at 20:22:59
And?
molten sphinx
How do I get to 1.75 x 10^3?
swift dragon
did you convert the ft^3 into cm^3?
tender pelican
mass = density x volume
molten sphinx
I understand that
I coverted the cubic feet to cubic meters
6754 x 0.0283168 = 191.2516672
Is that correct?
swift dragon
,w cubic feet to cubic meters
potent lotusBOT
molten sphinx
Gimme a moment
Ok, so I multiplied what I got by 10^6 (to make things shorter) and got 11251.667.2
swift dragon
is this the final answer?
swift dragon
indeed
zealous verge
Can someone explain how to find the correct amount of mass?
6,754 * (30.48^3) = 191,251,982 --(1ft^3 is equal to 30.48^3cm^3)
191,251,982 * 0.917g = 175,378,067g (correcting the density)
175,378,067g / 1000 = 175,378kg (converting grams to kg)
175,378kg = 1.75kg * 10^5 (simplified)
unborn sentinel
hi
pallid halo
the notation is ambiguous, does it mean $\frac{28\sqrt{15}}{21\sqrt{20}}$ or is it one of those dumb memes where the order of operations is something else?
potent lotusBOT
Bungo
unborn sentinel
what?
pallid halo
what what
unborn sentinel
the notation is ambiguous, does it mean $\frac{28\sqrt{15}}{21\sqrt{20}}$ or is ...
speak english pls
pallid halo
not one of those words was non-english (even "meme" is in the dictionary, alas)
unborn sentinel
bruh
can u repeat that again
without being a nerd
is that the right command?
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rancid creek
Can you do the study of this function?
f(x)= 2 ln(x) - ln^2 (x)
eternal shard
Can you do the study of this function?
f(x)= 2 ln(x) - ln^2 (x)
What do you wanna study of this function?
It's okay Leo
eternal shard
What have you tried so far, any workings?
eternal shard
For the zeroes you need to do f(x) = 0
plain bone
It's okay Leo
You sniped this question first, so ill let you have it lol
eternal shard
you can perform a substitution for example u = ln(x)
rancid creek
I already did
eternal shard
You sniped this question first, so ill let you have it lol
no please
i need to go anyway
rancid creek
Is it 1 and e
plain bone
Lol ok
rancid creek
?
eternal shard
e wrong
rancid creek
e^2
plain bone
Can you do the study of this function?
f(x)= 2 ln(x) - ln^2 (x)
@rancid creek do you know how asymptotes of a logarithmic function work
rancid creek
Not really
calm coralBOT
@rancid creek Has your question been resolved?
vale garden
calm coralBOT
vale garden
I believe this is simple, the equation is this
and because Diophantine equationsa are of the general form:
I get this equation and with these solutions?
im pretty unsure about a_{0,0,0,0} and a_{1,1,1,1}
vale garden
I get this equation and with these solutions?
and I dont know if this is correct
this is the next question I have to solve but I dont want to get started without being sure of the above first
thick sinew
Note that a_0000 is the coefficient for the term
x1^0 • x2^0 • y1^0 • y2^0 in your polynomial
So it's the constant term
vale garden
so that would be 1 - 2(1) + 1 - 12?
thick sinew
nono it is independent of the other coefficients
it's just because you have - 12 as constant term
- 12 is the same as - 12 • x1^0 • x2^0 • y1^0 • y2^0
meaning a_0000 must be 0
since -12 is the coefficient for the term with all exponents being 0
And if you look at the sum that you're given:
x1² - 2y1³ + y1y2³ - 12
There is no term having x1x2y1y2
thereby a_1111 = 0
likewise there is no term having x1x2y1y2² for instance
vale garden
thereby a_1111 = 0
yes thats how I got this
thick sinew
so a_1112 = 0 too
thick sinew
kk
vale garden
sorry could you
rexplain the a_0000
im a little confused
i thought since -12 is the coefficient for the term when all exponents being 0 => that a_0000 = -12?
thick sinew
yeah that's correct
vale garden
meaning a_0000 must be 0
but is it 0?
thick sinew
I get this equation and with these solutions?
But it's not in this image?
vale garden
right no im saying is what i put down correct? or is a_0000 = 0?
vale garden
oh gotcha lol
cool
are you able to provide any insight for part 2 btw?
do I just construct a polynomial that makes it true?
like P(x_1 .... x_j, y_1 .... y_k) = x - 2y is what one of my friends said made sense
but i dont know if this is how we prove it
since its a biconditional i only wrote this down so far:
thick sinew
Hm yeah you need to construct a polynomial that essentially tests if all x_i are even
because then you can argue the other way around too
vale garden
do you have any insights for b) and c) since I have no clue where to begin
for those
stoic oyster
j=1 for question a), you only need a test for one number
vale garden
j=1 for question a), you only need a test for one number
gotcha
stoic oyster
like P(x_1 .... x_j, y_1 .... y_k) = x - 2y is what one of my friends said made ...
and yeah x is even means that there exists y such that x = 2y, x-2y=0
vale garden
wait does that need justification?
stoic oyster
it's straight up from the definition of even really
vale garden
oh yeah if it works for 1 it works for all
thick sinew
For c) the forward implication remains simple, since if (x1,...,xj) e A union B, then there exists an according polynomial either for A or B depending from where (x1,...,xj) was drawn
stoic oyster
for b) try to restate x < y as an equality (introduce another variable ||which would act as the difference between x and y||)
vale garden
hmm
stoic oyster
it's roughly like a), just provide a polynomial that works
stoic oyster
aight
vale garden
for assistance if im still stuck
thick sinew
I'll put a note here so you can compare after your attempt
||With x1 = x and x2 = x+d, where d must be greater than 0, we can choose P(x1,x2,y1) = x2-x1-y1. Notice that b picking y1 = d, the polynomial becomes 0. Likewise for the backwards implication: if there exists y1 such that x2-x1-y1 = 0, then y1 = x2-x1, but since y1 is natural, x2 must be greater than x1, therefore belonging to the desired set||
calm coralBOT
@vale garden Has your question been resolved?
stoic oyster
you have to provide P still
what do you want to prove if P is just some random polynomial floating in the air
stoic oyster
alright alright
calm coralBOT
@vale garden Has your question been resolved?
vale garden
||With x1 = x and x2 = x+d, where d must be greater than 0, we can choose P(x1,x...
shouldnt the equation be x2 - x1 -y1 - 1?
this what i ended up with for a) and b)
thanks for the help for part a) and b) @thick sinew @stoic oyster
dont know if i needed to specify j = 2 for part b
west horizon
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west horizon
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calm coralBOT
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west horizon
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ripe coral
Hi quick question
calm coralBOT
Hi quick question
keen sapphire
Geometry right
ripe coral
geometry/trig
keen sapphire
Gotta grab my old notes from last yr
I remember this but it's been a while
Over a year
ripe coral
just need help understanding
kindred estuary
I dont understand how you can multiply that by 5
What exactly are you asking?
keen sapphire
5 has to be multiplied on both sides since you're cancelling out the denominator of opposite/adjacent
ripe coral
I dont get how you can multiply tan(65 degree) cuz its a degree
keen sapphire
Leaving with 5 x tan 65
kindred estuary
I dont get how you can multiply tan(65 degree) cuz its a degree
tan(65) results in a value
ripe coral
which is what
keen sapphire
On the calculator try tan (65) x 5
kindred estuary
Did you type it into a calculator?
ripe coral
yes but i wanna know how it works
keen sapphire
It'll be a weird ass decimal but most of those are gonna be decimals and depending on how you gotta round it you'll have your answer
All you're doing is multiplying tangent by 65 because that's the angle you have
And then you multiply that by 5
kindred estuary
yes but i wanna know how it works
How what works?
keen sapphire
Your answer is also always going to be in degrees at this level
Tangent is a numerical value
Think you're multiplying a number by 65 and then times 5
But tan is the number and if you press the "TAN" button on the calculator it should give it to you
If you know how to find sine cosine tangent on a triangle you've already done 80% of the work all you need to do now is put it over and cancel terms out
ripe coral
i get confused cuz from what ive learned recently tan is opposite/adjacent and the 65* kinda confuses me
calm coralBOT
kindred estuary
i get confused cuz from what ive learned recently tan is opposite/adjacent and t...
So $\tan(\theta) = \frac{Opp}{Adj}$ is correct. Basically tan(65) returns the ratio of what Opp/Adj
potent lotusBOT
CaptainNova22
kindred estuary
For example, tan(45) equals 1, that means the ratio of the opposite side divided by the adjacent side equals 1
ripe coral
I think im starting to understand, rn im imagining the 65 as levering the hypothenuse up and down to cut off the opposite side
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rigid hollow
After making my truth table, the final column was all false
So now, i'm confused
How to find the DNF? 😭
calm coralBOT
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rigid hollow
<@&286206848099549185>