I think I’m confusing myself
#help-13
pastel vault
but you already have what z is here
also multiplying z by z...... that's really confusing things
frank prairie
You said Multiply Z on both sides
pastel vault
I did not say that
frank prairie
Wait
Ok I’m delusional
Nvm
So just 0.381 < 0.381
so it’s correct ?
$0.381 \le 0.381$
wraith daggerBOT
Bakudo
frank prairie
Correct?
pastel vault
**Bakudo**
yes
either 0.381 < 0.381 or 0.381 = 0.381
even though 0.381 < 0.381 is false, 0.381 = 0.381 is true
so it's overall true
frank prairie
Tysm for your help
pastel vault
no worries!
plush blade
If i needed to factor this, can i just get rid of the x^2 at the top or bottom or is that againist the rule?
iron wren
try an example for x
and try it when its cancelled out and when its left in
if you get different answers you know its against the rules
plush blade
but for example if we have 5x^5/7x^2 we can factor it as 5x^3/7 so why cant we just do the same here?
tropic oxide
you can do that precisely when the top and bottom are products.
iron wren
you mean if its just $\frac{5x^5}{7x^2}$
tropic oxide
not sums
wraith daggerBOT
ImOakley
plush blade
no i started from 35x^5/49x^2 and i divided by 7 and got that and then got 5x^3/7
its a different example but
iron wren
you can divide x there yes
mental trail
no i started from 35x^5/49x^2 and i divided by 7 and got that and then got 5x^3/...
because both the numerator and the denominator in your example are products, not sums
iron wren
if you have w/x + y/z can you turn it into (w+y)/(x+z)?
no you cant
but you can do that with (w/x)(y/z)
thats why you can cancel them if they are multiplied
plush blade
here is a example i did with number instead of letter and it seems like i cannot do that, how can i solve this then?
lusty osprey
If i needed to factor this, can i just get rid of the x^2 at the top or bottom o...
if you have (2+3)/(2+8), what is this equal to? what if you cancel the 2's, then what is it equal to? now if you have 2*3/2*8, what is that equal to? what happens if you cancel the 2s? see , it's different when you're cancelling something being added vs something being multiplied
lusty osprey
here is a example i did with number instead of letter and it seems like i cannot...
just do it manually
like just add and subtract the numbers
plush blade
so i have to find a way to make the top and bottom same like so i can cancel terms?
lusty osprey
so i have to find a way to make the top and bottom same like so i can cancel ter...
you need to find common factors, yes
plush blade
i see
lusty osprey
how would you go about doing that
plush blade
Here is how i did it
but what if there is no gcf
is there any other way to simplify cause this is quite slow method.
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Hello. Would part c be (4/24) * 11/23)
cedar kilnBOT
Hello. Would part c be (4/24) * 11/23)
crimson sedge
I got 4/24 because there are 4 computers and the total prizes is 24.
I got 11/23 because there are 8 bikes and 4 computers (now 3 computers, seeing Asanja would get a computer) and the sample space wpuld then be 24-1, taking out the computer that Asanja got
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
deep nymph
I got 11/23 because there are 8 bikes and 4 computers (now 3 computers, seeing A...
seems correct
cedar kilnBOT
cedar kilnBOT
Available help channel!
prisma pollen
cedar kilnBOT
tropic oxide
you mean 8 ups and 8 rights?
tropic oxide
no bc on a chessboard we move inside the squares and not on the intersections
to get from a1 to h8 you do really need to go 7 steps up and 7 steps right
cedar kilnBOT
cedar kilnBOT
Available help channel!
vapid grotto
Could somebody just check this
weary ingot
seems correct but i see a few questions written on the paper, do you need help with those?
for the first one, end behaviour is not needed as on the graph you can clearly see that the function is not defined for x<-1 and x>3
so asking the value of the limit as it tends to infinity (on both sides) makes no sense as the function isn't even defined after a certain point
As for the question in section 3, I don't really understand it, could you write it down here in the channel?
vapid grotto
Oh I figure out the question in section 3 I just forgot to erase it
I do have one question about this one problem in my class work. I was looking at the answer key. And it doesn’t make sense to me
weary ingot
And at the end, the difference between end behaviour and left/right limits is the following:
The end behaviour of a function describes how this function acts as x approaches infinity, or negative infinity.
Note that infinity and negative infinity are two different numbers, which is completely different to evaluating the limit from the right or left side.
When I ask you the lefthand limit as x approaches to 3, I'm asking you: "as x gets closer and closer to 3 from the left how does the function act?
When I ask you the righthand limit as x approaches 3, I'm asking you "as x gets closer and closer to 3 from the right how does the function act?
This is fundamentally different to finding the end behaviour, when x tends to positive infinity, it can only do so from the left as nothing is on the right to ("bigger than") positive infinity. When x tends to negative infinity, it can only do so from the right as nothing is on the left to ("smaller than") negative infinity.
weary ingot
I do have one question about this one problem in my class work. I was looking at...
,r
i forgot my commands 
weary ingot
I do have one question about this one problem in my class work. I was looking at...
,rotate
wraith daggerBOT
weary ingot
why do you think it approaches -infinty?
also is the function defined anywhere?
@vapid grotto
vapid grotto
<@695456015805710337>
Oh wait I see it I was going backwards
Sorry this was the first day we have done problems like this
weary ingot
all good! these are good questions to have early on as making sense of limits is the most important task to do before starting calculus.
you should make sure you understand fully everything about this topic before moving on to derivatives and integrals cause otherwise your life will be hell lol
cedar kilnBOT
@vapid grotto Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
empty breach
cedar kilnBOT
empty breach
I am having trouble understanding the concept of the limit being 'continuous' and the limit 'not existing' at a certain value.
Over here, they want us to find the value of a that makes the limit exist. In such a case, don't we have to find the value of the limit from the right and from the left if they are the same, the limit exists at that value?
But here, since it says that x = 0 and x =/ 0, do they expect us to find whether the function is continuous at x = 0 ?
I am struggling to understand this idea.
sullen cipher
Nice name btw
empty breach
Thank you : )
lament mango
I am struggling to understand this idea.
what i am thinking is, to make the limit exist, the left and right side of the function when x=/0 needs to approach the f(x) when x=0
empty breach
Ohh I see, but if the function is approaching the value of 0 from any side, then wouldn't saying that x = 0 be wrong?
old dove
i wanna ask also, why does the value at x = 0 even matter since this limits give you the value infinitely to some number this case 0 but never at 0
lament mango
Ohh I see, but if the function is approaching the value of 0 from any side, then...
what the question is trying to make you find out is the outcome of the function while x approaches 0- and 0+, for instance, if the outcome is 3, then the function when x=0 need to equal 3,
i hope you understand my point and i really hope i answered your question since im quite perplexed too
empty breach
i wanna ask also, why does the value at x = 0 even matter since this limits give...
I didn't get your question.
empty breach
what the question is trying to make you find out is the outcome of the function ...
I understand what you mean. Thank you for the answer!
lament mango
I understand what you mean. Thank you for the answer!
you are welcome glad i helped
old dove
limits dont give a value at a exact number, just infinitely close to it, so why does the value at exactly x = 0 matter
old dove
I didn't get your question.
.
if u have f(x) = { x^2 for x =/= 0
{ 15 for x = 3
the limit when x approaches* 3 is still 9 not 15
drowsy obsidian
option e?
lament mango
if u have f(x) = { x^2 for x =/= 0
{ 15 for x = 3
th...
i dont get it, this wont pass the verticle line test will it
empty breach
wait the limit wont be 9 ?
No, I don't think so.
old dove
im not familiar enough with limits ig
ill look into it myself
not my help channel anyway
i wrote that wrong
f(x) = { x^2 for x =/= 3
{ 15 for x = 3
this is what i meant
lim as x -> 3 should be 9 now no ?
lament mango
f(x) = { x^2 for x =/= 3
{ 15 for x = 3
you cant just make x equals to a constant some somehow make the thing continuous
old dove
well its not continous
why is that a problem
isnt that why we wanna use limits in the first place
when its not continous
lament mango
im even more confused, maybe just figure it out yourself..
old dove
ill open a new help channel
empty breach
Anyway, thank you for your input everyone.
I will be closing this channel.
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
sturdy escarp
cedar kilnBOT
tropic oxide
|u||v|cos(theta)?
you're stating half of a relevant-ish thing
sturdy escarp
u*v = |u||v|cos(theta) where u and v are vectors ?
tropic oxide
yes, looking at the dot product is a good idea.
you can use it, and this formula, to work out theta (the angle between your u and v) and see if it is close to 90°
sturdy escarp
you can use it, and this formula, to work out theta (the angle between your u an...
hmm okay
u dot v is = u_1v_1 + u_2v_2 right
so I would do that on the left then take magnitude for u and v
then move that over to the left side
and then take arccos?
cedar kilnBOT
cedar kilnBOT
Available help channel!
golden raft
i dont get this question what am i supposed to?
cedar kilnBOT
i dont get this question what am i supposed to?
modest escarp
probably sufficient to show that there exists a square such that two of its sides are equal to two sides of the octagon?
undone epoch
This looks like a part 2 of a question. You got the rest?
golden raft
yeah give me a sec
i wouldnt think the others would relate no?
i skipped the bearings question as im using a pc and dont have any measurement tools
odd verge
Use the interior angles, the angles at a point and the fact that they are both equally sized regular octagons
odd verge
and that would up to 360?
Yes
golden raft
is this correct?
odd verge
Anything else?
golden raft
just want to know if my answer was correct
odd verge
Where did you get 4-2 from
odd verge
Yeah
golden raft
thank you thats all
odd verge
Then the sides are equal too
golden raft
how do i close this
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
golden raft
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson dune
Find a basis for the null space of the following matrix
I tried to use gauss-elimination to find the free variables, however when plotting in the coefficients of the 3 vectors I found, it said that the nullspace must be in R^3
crimson dune
hollow trail
hmm the null space of a 3x6 matrix should be in R^6
can you show a full screenshot of the question and any other surrounding context?
crimson dune
can you show a full screenshot of the question and any other surrounding context...
Enter the answer as a matrix with the requested basis elements as columns.
Remember: The null space of a matrix consists of all vectors x
such that Ax = 0.
Hint: The matrix A has 6 columns, 3 rows and rank(A)=3. Together, this means that the null space must have 3 dimensions. So we need 3 vectors in the basis of the null space.```
The question is in a different language, so it could have minor mistakes in the translation, but that's the full context
ancient lodge
<@&268886789983436800>
cedar kilnBOT
@crimson dune Has your question been resolved?
flint plinth
@crimson dune i see at least one sign error, the 4/3 on the second row should be -4/3
aside from that, it looks ok.. where are you stuck?
crimson dune
aside from that, it looks ok.. where are you stuck?
I'm mostly stuck at that the task says that it's not correct. I entered the new matrix now in with the correct coefficient, but it still says that the answer is not correct
flint plinth
that's a row reduced matrix that can be used to find a basis, but it's not a basis itself, right?
did you find a basis?
crimson dune
did you find a basis?
Not yet, I might be a bit confused with how they wish us to give the answer as it reads How to enter the answer: enter the elements of the matrix row by row with spaces between the elements. When you are finished with the row, press Enter to move to the next row.
flint plinth
which matrix do they want you to enter here? can you show the full question?
crimson dune
```Find a basis for the null space of the following matrix
Enter the answer as ...
This is the full question
flint plinth
well the columns of that matrix are not a basis for the null space of the original
for one thing, you answer should be 6x3, not 3x6
bitter blaze
Its been awhile since I reviewed Linear, are the free variables x4, x5, x6
flint plinth
yep
bitter blaze
Found basis for null space or Null(A) yet?
crimson dune
Found basis for null space or Null(A) yet?
not yet, trying different approaches
crimson dune
you were almost there with this
Oh thank you lots, that actually satisfied the question
So just to summarize, these vectors multiplied with A will return into the zero vector, making it a null space for A?
hollow trail
well that makes them members of the null space
them being linearly independent and there being three of them makes them a basis
flint plinth
you should write out explicitly what three vectors you want to use
(the basis vectors themselves should not include the coefficients k, w, v)
bitter blaze
I wrote out the solved problem if u wish to see
flint plinth
I wrote out the solved problem if u wish to see
it's better to guide the OP to find their own solution
bitter blaze
Got it
flint plinth
after they have one it's fine to paste your own if you like
crimson dune
(the basis vectors themselves should not include the coefficients k, w, v)
Yeah so those 3 vectors span the null space, correct?
flint plinth
well specifically which 3, can you write them down? just so we're sure we agree which ones you mean
crimson dune
Null(A) = Span { (1, 4/3, 5/3, 1, 0, 0), (-1, -5/3, -1/3, 0, 1, 0), (2, 2, 2, 0, 0, 1) }
flint plinth
yep those work
now all you have to do is make a matrix with those vectors as the columns
(since that's the format the software asked for)
crimson dune
Ah perfect, thank you so much for the help
flint plinth
yw
crimson dune
.close
cedar rapids
cedar kilnBOT
cedar rapids
- Find, if possible, lim an n-> +inf
cedar kilnBOT
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
give me a second
i’ve just posted the problem
I’ve already proven
0 < an < 2
so the first part is done
now i need to find the limit for an
normally you solve these exercises using convergence tests
be that root or quotient theorem
however here it does not seem to be that simple
This is what I have thus far
but I don’t think I can solve using quotient theorem
cedar kilnBOT
@cedar rapids Has your question been resolved?
split sparrow
I thought it was b, can anyone check por favor?
cedar kilnBOT
I thought it was b, can anyone check por favor?
ancient lodge
plug the solution back in and see if it satisfies the original equation
split sparrow
I did, I get 2=2. but my homework grader thingy said I was wrong
sacred anchor
I thought it was b, can anyone check por favor?
maybe an error on your teacher's part?
ancient lodge
I did, I get 2=2. but my homework grader thingy said I was wrong
This looks like it's badly written
they probably meant $\ln((x-10)^4)=2$
wraith daggerBOT
Civil Service Pigeon
split sparrow
This looks like it's badly written
yeah possibly
well thanks for the second opinions, just wanted to make sure I wasn't going crazy
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar rapids
ç
cedar rapids
so i'm asked to analyze conditional and absolute convergence for the series
we'll focus on the first term because its whats giving me trouble
analyzing absolute for the first term gives us:
$\frac{1}{\sqrt{n^2+6n}} = \frac{1}{n}\frac{1}{\sqrt{1+\frac{6}{n}}}$
wraith daggerBOT
ransik (gmdn)
cedar rapids
we can say this diverges due to comparison with the harmonic series (p series with p = 1)
that's for absolute
but then for some reason when use leibniz's criteria for conditional convergence of alternating series it does converge??
i don't get it
you're left with the same series
abstract breach
it's not absolutely convergent, but it converges, yes
it's not the same since you have a (-1)^n
cedar rapids
right but in order to apply leibniz we remove (-1)^n
and analyze the resulting series minus the -1
sequence*
which is the same sequence as the absolute test
abstract breach
you don't analyse the series but the sequence
cedar rapids
so does this mean (-1)^n/n converges conditionally?
but in order to test for that we'd look at 1/n
which we know diverges
abstract breach
you look at 1/n
cedar rapids
and i know leibniz's criteria asks for a decreasing non-negative series
abstract breach
1/n goes to 0
cedar rapids
which 1/n is
surreal cave
you need to prove 1/n decreases monotonically and goes to 0
cedar rapids
1/n goes to 0
the sequence? yeah
agreed on that
you understand where my confusion stems from, right?
abstract breach
kinda
but for the leibniz criterion, you look at the sequence
so it doesn't matter if the series of 1/n diverges
surreal cave
Leibniz Test for Convergence: If ({a_n}{n=0}^{\infty}) is a sequence such that: (a_n>0,\forall n), (a{n+1}\leq a_n,\forall n), and (\lim_{n\to\infty}a_n=0) then [\sum_{n=0}^{\infty}(-1)^na_n\text{ converges}]
cedar rapids
i think i get it now yeah
wraith daggerBOT
PajamaMamaLlama
cedar rapids
ok
so in order to use leibniz all i need to show is an decreasing, an greater than 0
abstract breach
and an -> 0
cedar rapids
well if an is decreasing and greater than 0
oh wait no nvm
could be a non zero number larger than 0
okay i see
okay. still a bit confusing but i get it now
i'll work on this for a bit
thanks for the help
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
indigo lagoon
Please do not troll at help channels
crimson sedge
🙏
wicked mantle
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
earnest topaz
I'm in grade 8 enriched math but i dont know quadratics
And a lot of questions will involve quadratics
for example
how do you completely factor a quadratic expression? I'm stuck on factoring out the common binomial
Im trying to factor this:
6x^2 - 11x - 10
I've got it down to 2(3x+2) - -5(3+2)
First of all is this correct
And second how do I factor out the common binomial 😭
earnest topaz
Please ping when answering 🙂
slender atlas
may I ask for you to show your steps?
earnest topaz
oh
ok
one sec
sorry my steps are kinda messy ima type it out and I'm not very good at showing my steps
slender atlas
do you have a picture of them?
slender atlas
as long as I can see each individual line, it's fine.
tropic oxide
2(3x+2) - -5(3+2)
this looks like it has at least two typos in it
earnest topaz
The right side is kinda hard to see
i've been watching so many fricking youtube videos
yes there are typos
earnest topaz
> 2(3x+2) - -5(3+2)
this looks like it has at least two typos in it
😭
tropic oxide
ok so
earnest topaz
im lost in the sauce
slender atlas
the first group is missing an x in the GCF.
tropic oxide
-15x - 10 would factor as -(15x+10) first and foremost
and then you would have 2x(3x+2) - 5(3x+2) and there's no double minus going on
with these fixed, you can now factor out (3x+2) and get (2x-5)(3x+2)
earnest topaz
im still confused about factoring out (3x+2)
tropic oxide
would you understand if say $2xz - 5z$ were factored as $(2x-5)z$?
wraith daggerBOT
Ann
tropic oxide
it's like distributing but going the other way.
earnest topaz
yeah
tropic oxide
which is like, the whole deal of factorization.
earnest topaz
yeah
i kinda get it?
OoHhHh
I think i get it
this is wrong? Should it be 2x(3x+2) ?
tropic oxide
yes, lute pointed that out already
cedar kilnBOT
cedar kilnBOT
Available help channel!
sacred iron
$\lim_{t\to-\frac{1}{2}}\int_{t+1}^{2et-e+t}\frac{dx}{t+x}$
cedar kilnBOT
$\lim_{t\to-\frac{1}{2}}\int_{t+1}^{2et-e+t}\frac{dx}{t+x}$
wraith daggerBOT
𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³
dire geode
is there anything stopping you from plugging in t=-1/2
sacred iron
Maybe. I thought there might be a singularity or something though
cedar kilnBOT
cedar kilnBOT
Available help channel!
hexed vortex
having trouble following and understanding this proof
cedar kilnBOT
having trouble following and understanding this proof
hexed vortex
Is our hypothesis they mention when proving the identity is "ab^-1 in H and a,b in H"
The theorem says If ab^-1 is in H whenever a and b are in H, then
this whenever represents and right?
so when proving this we can take that ab^-1 and a and b are in H as true?
dawn junco
Is our hypothesis they mention when proving the identity is "ab^-1 in H and a,b ...
yes
hexed vortex
ok and they use that fact to prove e exists
dawn junco
to prove e is in H
hexed vortex
ok I see
thanks
though I dont really understand it inuitively
the steps make sense in the proof now
but the theorem itself I dont see how it could be applied
So when proving a nonempty subset of G is a subgroup we show that if a and b are elements then ab^-1 are elements for all ab?
dawn junco
yes you can do that
it's just a restatement of what it means to be a subgroup
you can show it one way or the other it doesn't matter
hexed vortex
hm what do you mean by restatement
wait let me check definintion of a subgroup again
dawn junco
hm what do you mean by restatement
that it is equivalent to the def of subgroup you have
hexed vortex
wait so if we have a set with a binary operation
and we show if a,b are elements of this set then ab^-1 are elements we've shown its a group?
wait I guess thats what we just did in the proof right
dawn junco
subgroups only make sense if you have a bigger group to talk about
it's like with vector spaces, if you just have a set with an addition and a scalar multiplication and that's it, well you need to show all vector space axioms
if you want to show a subset of a vector space you already know of is also a vector space, then there are a ton of requirements you don't have to show cause you're reusing the same operations, so you get much simpler proofs that way
hexed vortex
hmm im not really understanding how we can talk about inverses when we havent proven there is an identity, isnt that circular? Can we state b^-1 in hyp becuase b comes from G which has an identity?
dawn junco
hmm im not really understanding how we can talk about inverses when we havent pr...
yes
you can talk about identities and inverses because G exists as a group in the first place
that was my point with vector spaces really
hexed vortex
Ok that makes sense thank you
dawn junco
my T key is getting worse and worse holy crap
cedar kilnBOT
@hexed vortex Has your question been resolved?
cedar kilnBOT
primal wigeon
from what i got its either these two
gritty viper
Well everything looks shaded to me
cedar kilnBOT
primal wigeon
primal wigeon
Well everything looks shaded to me
i got these two
y >= 2x is left
but not sure how i can do y >= 2x
gritty viper
You're just posting a graph with like eight different shaded sections and asking what the shaded part is
You got to be more specific
primal wigeon
the zone
livid hound
look for where the shaded parts overlap
primal wigeon
look for where the shaded parts overlap
is y >= 2x above one or down
thats the 1 i got torubles with
gritty viper
If they're trying to find where the shaded parts overlap, they could flip all the inequalities and then look for the white region
But I can't understand what they're asking
livid hound
y=2x would be the line
y>=2x would indicate the line and region above that
you could always test a point to see which side of the line the region will be
primal wigeon
so this?
livid hound
y>=2x by itself or do you mean something else
primal wigeon
x + y >= 180
u see this one @livid hound
these are the feasible region of x + y >= 180 right
its red
cedar kilnBOT
Available help channel!
livid hound
yes
livid hound
how did you do it for the one just now?
y=2x would be the line
y>=2x would indicate the line and region above that
livid hound
also note that there is a really small triangle in the middle that you shouldn't ignore
livid hound
you can also toggle the graphs to show the one(s) you want
primal wigeon
you can also toggle the graphs to show the one(s) you want
how
livid hound
click on the coloured circle
livid hound
don't think left or right
arranged in that form,
that reads as
y is greater than or equal to 2x
y=2x would be the line
y>=2x would indicate the line and region above that
primal wigeon
don't think left or right
im trying to find the zone to cover
livid hound
yes...
and I've told you which one to use multiple times now, and an alternative method as well
primal wigeon
bro im gonna crash out
livid hound
points where the value of y is equal to 2x are on that line
you also want the values where y is greater than
which would be located above that line
primal wigeon
points where the value of y is equal to 2x are on that line
you also want the va...
above the line
black one gith
livid hound
you could also test a point not on the line
e.g (0,5)
if it satisfies the inequality, the side with that point is what you want
primal wigeon
so its either these two
livid hound
no
primal wigeon
which
livid hound
do you mean just the
y>=2x?
primal wigeon
oh alright
x + 2y =< 320
which is below the purple line
so i fund it
its this
livid hound
yes
livid hound
make sure you use () when writing points
primal wigeon
alright i found his maximum profit
im able to do the problems but the graph is insanely annoying for me
anyways thank u
.close
livid hound
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
hot mauve
Do you know the definition of bijective?
twilit bison
you need to show that it's (1) surjective, and (2) injective
hot mauve
Yeah, but that's more like a different name for bijectivity, or a vibes-based definition. The more precise definition is that a bijective function is surjective and injective
You need a precise definition in order to prove stuff
Not quite. You mean f(x1) = f(x2) for all x1, x2? That would be a constant function
twilit bison
for injectivity you need f(x1)=f(x2) => x1=x2
hot mauve
Yep 👍 I wasn't sure whether I should give him the definition immediately, or if it would be better to find it himself
twilit bison
yes, it relies on arctan being injective
hot mauve
yes, it relies on arctan being injective
Damn, I was just about to ask him to justify the first line
hot mauve
Lol, no worries 
twilit bison
i thought sheddow might answer
yeah, well the parentheses for the interval are wrong
they should be ()
wraith daggerBOT
brandon
twilit bison
yeah
wraith daggerBOT
brandon
twilit bison
yeah...
hot mauve
i thought sheddow might answer
Sorry, I went away for a minute. Feel free to take over, I won't be offended 
wraith daggerBOT
brandon
twilit bison
i think we also need to show -pi/2 < x < pi/2
oh
i was confused, nevermind
yeah i guess that's one way of showing x =/= -3
makes sense
isn't there something missing?
i think you should argue that there exists z such that arctan(z)=y
maybe just plug it in (sheddow would have been better at this part lol)
what if y = -pi/4 ?
then the x you found doesn't work
oh right
sorry
seems right
wraith daggerBOT
brandon
twilit bison
yeah
wraith daggerBOT
brandon
twilit bison
yeah
i got something simpler
i changed it into sin's and cos's before taking the derivative
but whatever works
you could even just plug in -pi/4 now if you want
at least you can factor out sec^2
i got $\frac{3}{1-2\sin{x}\cos{x}}$
cedar kilnBOT
cedar kilnBOT
Available help channel!
sonic fossil
how to prove any 4 points are at the angular points of a rectangle? is angular point of a rectangle is the point where right angle in formed?
sonic fossil
using coordinate geometry
cedar kilnBOT
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.
sonic fossil
sonic fossil
like where the right angle in formed that is vertex
tepid oar
how to prove any 4 points are at the angular points of a rectangle? is angular p...
Yes. If those 4 points are the angular points of a rectangle, opposite sides must be equal in length and 4 right angles must be formed
unique copper
So you have to prove the 4 given points form a rectangle, you get this?
tropic oxide
so not "any 4 points"
but these specific ones
and then we can understand "angular points" as meaning "corners".
sonic fossil
Yes. If those 4 points are the angular points of a rectangle, opposite sides mus...
I proved this thing already but i think there can be different meaning of the problem
twilit bison
Yes. If those 4 points are the angular points of a rectangle, opposite sides mus...
it's enough to show one angle is 90 degrees
tropic oxide
this would have been false otherwise; obviously not all quartets of points form a rectangle!!!
also i think the easiest way is to example the slopes of the lines joining each pair of points (decide which ones by first plotting the points on a coordinate grid), and then to see that the slopes of e.g. AB and AD are negative reciprocals and so on
sonic fossil
so I think it's enough to prove that opposite sides are equal then and if it's a rectangle then it's angle formed by vertex points are 90°
twilit bison
you have to show at least one angle is 90 degrees
otherwise it could be a parallelogram
sonic fossil
if this like that then by distance formula opposite sides are equal
Which I have calculated
and since it's rectangle and opposite sides are equal( by dist. Formula) then the angles are 90° formed by joining vertex points
is it done?
unique copper
how did you prove that one angle is 90?
hollow trail
parallelograms also have opposite sides equal
sonic fossil
but it is given in question that we are talking of rectangle only
unique copper
you have to prove they form vertices of a rectangle, you can't say that Since they must form vertices of rectangle so the angle formed is 90, you have to prove that exact thing
twilit bison
if you don't want to prove an angle is 90, you can show the diagonals are equal
tropic oxide
what is even being discussed here
unique copper
Given: Coordinates of 4 points.
To Prove: The shape formed by joining the 4 points is a rectangle.
There's nothing else given
tropic oxide
i have lost track of what op wants to ask and can't understand his msgs
sonic fossil
i have lost track of what op wants to ask and can't understand his msgs
I want to ask how to prove this and the clear meaning of angular point which is now cleared
unique copper
what is even being discussed here
The question asks to prove that the given 4 points form a rectangle. To prove it, the OP has proven that opposite sides are equal hence the 4 points form a parallelogram. But to prove it a rectangle, he is saying that since it's given that they form rectangle hence the angle between the two sides of parallelogram is 90° which is ofcoarse wrong as he can't just say that he gotta prove that.
tropic oxide
well yeah it is wrong. the rectangle-ness is a goal not given.
twilit bison
circular reasoning
unique copper
@sonic fossil you can do 2 things:
- Prove atleast one angle is 90°
- Prove the diagonals are equal (parallelogram with equal length diagonals is rectangle)
tropic oxide
(these are options not steps)
unique copper
I think he can use 2nd option, it can be directly done by distance formula, if he wanna prove by 1st option, I can guide but looks like he's not responding now..
sonic fossil
I am doing that exaclty
twilit bison
nice
sonic fossil
Option 1 is interesting
unique copper
also i think the easiest way is to example the **slopes** of the lines joining e...
look at this. for 1st option you have to use the fact that slopes of perpendicular lines have relation m1 × m2 = -1
try to find slopes of adjacent lines then prove they are perpendicular by this
sonic fossil
Yes m1*m2 = -1 is valid
as m1 = 1 and m2 = -1
on calculating
it think proof is done
.close
fair stag
if idon start studying 6-7 hr daily from now , i will be doomed
how to study man
i study only 3-4 hr .. class 10th board im talking about
indigo lagoon
just.....hop off discord and keep on grinding
There's really nothing much we can do
cedar kilnBOT
@fair stag Has your question been resolved?
cedar kilnBOT
@fair stag Has your question been resolved?
trail skiff
bro stop stressing out
chill
we all gave boards it's easy
By studying 2-3 hrs daily you will get 90% easily
you have classes? Yh listen to them and give the test honestly, no cheating. Revise what you got wrong and bamm you passed with good marks
cedar kilnBOT
cedar kilnBOT
Available help channel!
lime rain
cedar kilnBOT
lime rain
.rotate
CD = 15cm, if AB is in line with DF and AD is in line with BF then the length comparison of DE and EF is
indigo lagoon
,rotate
wraith daggerBOT
tropic oxide
prisma pike
You can start by spotting some similar triangles
prisma pike
Yeps
lime rain
im really bad at finding comparisons
cedar kilnBOT
@lime rain Has your question been resolved?
visual basin
do i just need to work out the magnitude of each droplet of water, multiply by the mass and then add them together for the total momentum?
sonic fossil
do i just need to work out the magnitude of each droplet of water, multiply by t...
firstly, did you check in which direction on collision the net force is zero?
visual basin
no
how do i do that?
sorry, i'm in a first year class and i have no idea what i'm doing
dry root
taking the whole setup as system the net force is zero
it means here conservation of momentum is valid
ts in 3d bruh
sonic fossil
x,y,z
dry root
conserve the momentum of drops along all three axes
sonic fossil
yo help him out
i am thinking on it
visual basin
do i need to scale up the velocity vectors by their respective masses?
sonic fossil
but firstly you have to analyse
cases
consider this :
case 1) when they are going to collide:
case 2) when they collide and stick
visual basin
you mean momentum before and after the collision?
sonic fossil
v1 = i + 2j + 3k and v2 = 2i - j
sonic fossil
you mean momentum before and after the collision?
yes
in case 2, do you agree that the final mass is now 8mg
visual basin
yeah
that's what it says in the question
wait, no it doesn't
but yeah, it sounds reasonable
pastel vault
Blackidoz helping people? W
sonic fossil
Blackidoz helping people? W
lol i am trying
visual basin
is that the velocity vector after the collision?
dry root
yeah
dry root
is it correct?
dry root
oh then dont rely on this answer i just did what was in my knowledge
visual basin
thank you anyway
dry root
np
visual basin
.close
cedar kilnBOT
sonic fossil
i had one answer
dry root
yeah pls share
sonic fossil
i am caclulating
cedar kilnBOT
✅
sonic fossil
110i + 70j + 50k = p3
visual basin
p3/v3 = m3 = 8, right?
sonic fossil
i think there is mistake in my answer
dry root
@dense stirrup
dense stirrup
Yo
visual basin
mg is milligrams
which is kg^-6
dry root
upr ek ques h wo dekhio
dry root
do i just need to work out the magnitude of each droplet of water, multiply by t...
.. this one
dense stirrup
do i just need to work out the magnitude of each droplet of water, multiply by t...
Itna lamba que
Bc phy chal rhi h
dry root
mg is milligrams
which is kg^-6
omg i didnt realised i did the conversion wrong
well that didnt matter anyway
dense stirrup
Hahaha
visual basin
but the answer seems to match up between both of you (minus the conversion)
so it's probably right?
dry root
i did something
u can refer to this answer just make the 10^-3 as 10^-6
sonic fossil
This answer is correct because p is vector and he multiplied each mass by its velocity vector
sonic fossil
howd u get those numbers
I have doubt in that
dry root
I have doubt in that
ohh
visual basin
.close
mental hemlock
Hello, I am kinda stuck at part d can’t get it at all
cedar kilnBOT
Hello, I am kinda stuck at part d can’t get it at all
indigo lagoon
Hello, I am kinda stuck at part d can’t get it at all
Have you finished a, b, and c in the first place?
mental hemlock
Yup
cedar kilnBOT
@mental hemlock Has your question been resolved?
cedar kilnBOT
@mental hemlock Has your question been resolved?
crimson sedge
Hello, I don't understand conditional statment or implication p->q
crimson sedge
I don't understand why it's true for both false and when p is false
wraith meteor
It says that if p is true q is true but if p is false we don't know q (it can be true or false)
wraith meteor
It does not. May I ask what you mean by default to?
crimson sedge
floral arrow
It's called a "vacuously true" statement
wraith meteor
Well it can be true or false.
floral arrow
If p is true, q must be true for the implication to hold; that's the point of an implication
If p is false, then it doesn't matter what q is, the implication still holds
It's like saying that something false can imply anything
crimson sedge
I got that but I am confuse why it's value should be true
I also know about vacously true
floral arrow
For example, if you consider the statement "1=2" to be true, then you can imply a lot of things that we know to be false; because that assumption "1=2" is false
crimson sedge
it's just that I am not willing to accept that it should be true it's just sound absurd
@floral arrow can you define the word implication to me?
floral arrow
Well, that's where it gets tricky
There are multiple definitions
Generally, especially when you're just learning logic, the implication is a relationship between statements that holds true when one statement logically follows from another
crimson sedge
um I just want to ask did you get the feeling that you have understand the conditional statement ?
floral arrow
If you want to go deeper, you can learn about these:
https://en.wikipedia.org/wiki/Material_conditional
https://en.wikipedia.org/wiki/Strict_conditional
https://en.wikipedia.org/wiki/Vacuous_truth
crimson sedge
while learning it ?
floral arrow
Not really, I accepted the vacuous truth because there are quite a few examples of vacuous things in maths
Like the empty product equaling 1 (a^0 = 1 for all non-zero a)
crimson sedge
oh, okay I am thinking I should just accept this for now and move on into the content. I hope later it make sense to me for now just acceptance.
thank you for the time
floral arrow
I do recommend going deeper if you still don't feel like accepting it as is (after learning the current material)
crimson sedge
I have time I should
floral arrow
There isn't a single unique logic system
It's interesting to compare them, even though you usually only need the basic one
crimson sedge
okay, So, I have learn about Vacuous truth and also Material conditional and Strict Conditional ?
floral arrow
Yeah, and you can also take a look at this list
https://en.wikipedia.org/wiki/Logic#Systems_of_logic
It's a lot though, so take your time; and you don't have to restrict yourself to Wikipedia either
crimson sedge
I am currently learning a book called "Discrete Mathematics and its application" by Rosen. I will dm you when I understand the concept
or I will just ping you -_-
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Hello. I am verifying my answers please
cedar kilnBOT
Hello. I am verifying my answers please
cedar kilnBOT
@crimson sedge Has your question been resolved?
neat dune
For the first problem P(Brian gets a bike or a washing machine) = P(BuW) (for convenience) = P(B) +P(W) -P(BnW), not just P(B) +P(W)
Then also, BuW and Asanja getting a computer (let's call the latter event C) aren't entirely independent events. So you either calculate P(Cn(BuW))=P(C|BuW)*P(BuW)= P(BuW|C)*P(C) (the former is probably easier if you've already calculated P(BuW).
Not just P(C)*P(BuW).
crimson sedge
Ohh
yes
The thing is, for part 1 , wouldn't P(B N W) = 0?
So it would be the same 10/69
neat dune
The thing is, for part 1 , wouldn't P(B N W) = 0?
oh yeah nvm
Anyways I think your 1a) looks good
crimson sedge
Great
crimson sedge
Is this what I h ave correct for the first part
So like (4/24 * (8/23 + 12/23 + 0)
neat dune
So like (4/24 * (8/23 + 12/23 + 0)
yeah the numbers look good there also.
You seemed to have calculated P(BuW|C) implicitly
crimson sedge
yeah the numbers look good there also.
Great
crimson sedge
You seemed to have calculated P(BuW|C) implicitly
I guess
crimson sedge
I did this too for b and c
neat dune
b) looks good
crimson sedge
Nice
neat dune
c) looks good also, now that I see the "after" blurb it's not implicit at all, but explicit 
neat dune
Looks good
crimson sedge
Awesome
Thank you so much
I have more to do but I am going to pause now
.close
copper owl
Hi, someone was helping me to think this through but they had to leave. I just want to check if I finished it right.
Using (1+x)^n (1+x)^n = (1+x)^n, I had to prove that sum (c(n,i))^2 = C(2n,n)
Started by:
(1+x)^n(1+x)^n = sum c(n,i)c(n,k-i) = c(2n,n)
because of the RHS, k = n, so the sum becomes
sum c(n,i)c(n-i), and for symetry, C(n,i)=C(n,n-i)
So, going back to the sum
Sum C(n,i)C(n,i) = C(2n, n)
Sum (C(n,i))^2 = C(2n, n)
proud vigil
Hi, someone was helping me to think this through but they had to leave. I just w...
First statement should have 2n on the RHS
copper owl
where?
proud vigil
Using (1+x)^n (1+x)^n = (1+x)^n
frail citrus
Hi, someone was helping me to think this through but they had to leave. I just w...
better you couldve maybe tried using the formula-
copper owl
it was (1+x)^n(1´x)^n = (1+x)^2n
proud vigil
ah yeah that was a copy mistake
Other than that it looks fine
Though I would love to see an elaboration for
(1+x)^n(1+x)^n = sum c(n,i)c(n,k-i) = c(2n,n)
frail citrus
where $\binom{n}{r}$ denotes $\frac{n!}{(n-r)!r!}$
wraith daggerBOT
Dhairya
copper owl
Though I would love to see an elaboration for
> (1+x)^n(1+x)^n = sum c(n,i)c(n,...
it was to get the coeficients of (1+x)^n (1+x)^n
cedar kilnBOT
cedar kilnBOT
Available help channel!
analog summit
cedar kilnBOT
cedar kilnBOT
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
Please wait for 15 minutes before pinging.
analog summit
ok srry
wraith meteor
Np
Sorry does nor seem like something I can do(or I am just rusty with inverse matrixes). Other helpers probably can help you better.
lofty sand
Sorry does nor seem like something I can do(or I am just rusty with inverse matr...
What’s your question ?
frail citrus
what does the prev line to the qn imply?
analog summit
what does the prev line to the qn imply?
do you mean det(M) = det(DA - BC)?
frail citrus
do you mean det(M) = det(DA - BC)?
analog summit
what this implies?
it's just the size of the matrices
i was gonna say
M^-1 = third matrix ^-1 ...
frail citrus
never learnt or saw this anywhere
analog summit
but the inverse of the two matrices arent that easy to find?
analog summit
never learnt or saw this anywhere
it's literally just the sizes of the matrices
M is a bloc matrix
frail citrus
so u mean to say that M is n by n matrix consisting of only real elements
analog summit
yes
frail citrus
very sorry i wont be able to help u out
cedar kilnBOT
@analog summit Has your question been resolved?
analog summit
<@&286206848099549185>
unique copper
I am thinking you can use 1.a. to find adj M in terms of adj of the three matrixes and then divide both sides my determinant of M to get M^-1 on LHS and simplify the RHS to get something
analog summit
I am thinking you can use 1.a. to find adj M in terms of adj of the three matrix...
we never used adj before
unique copper
without that how would you find inverse here 
unique copper
nvm I searched it doesn't work here
lofty sand
Can you try MM-1 = In+m and see where it leads ?
Also split the matrix M^-1
A’ B’
C’ D’
analog summit
Can you try MM-1 = In+m and see where it leads ?
what is m?
ah ok
shouldnt it be just In
ah no
ok
wait
it's In right?
lofty sand
I mean just assume M-1 exists. Format it accordingly (so you can do the products, and see what happens
No the size of M is n+m
So if M^-1 exists it should have the same size
analog summit
so how does it have an inverse?
lofty sand
so how does it have an inverse?
Assume it does and see what it should loook like
analog summit
Assume it does and see what it should loook like
but if we assume it does then we also assume M is square no?
lofty sand
M IS square
analog summit
so why dont we just write In?
lofty sand
By definition
lofty sand
Because we’re looking for identity of size (n+m)
analog summit
yes
so this is identity
MM^-1
wait
no
i forgot the " ' "
so this is identity if M^-1 = (u, v, w, x)
lofty sand
I’m not sure you understood
analog summit
AU+BV = In
lofty sand
Give me a second
analog summit
I’m not sure you understood
i should've used the product we found in question 1?
cedar kilnBOT
@analog summit Has your question been resolved?
azure nacelle
Can help me with this one
I need to find the pdf of Z where Z=SQRT(X^2+Y^2) and X and Y are uniform distributed between -1<=X<=1 and -1<=Y<=1
I understand the part 0<=Z<=1 but i do not understand the part where 1<Z<=SQRT(2)
wicked mantle
just post
cedar kilnBOT
@azure nacelle Has your question been resolved?
cedar kilnBOT
@azure nacelle Has your question been resolved?
zenith grail
is there a solid way to memorize the double angle, sum and difference, power reducing and half angle trig identities? so far ive memorized the easy ones like reciprocal, quotient, pythagorean, co function and even odd but im having trouble with these. ive looked around but nothing has worked well.
zenith grail
for example, reciprocal, quotient and pythagorean were mostly common sense so i didnt really need to memorize those. co function is essentially just the other "version" of the function so like sin(..) => cos and vice versa. same thing with csc(...) => sec so thats how i remembered that. and for even/odd i just remembered if its something involving y like sin, tan, cot or csc, it becomes negative on the outside and everything else just stays positive. are there tricks like that for the others?
cedar kilnBOT
@zenith grail Has your question been resolved?
zenith grail
<@&286206848099549185>
sacred anchor
is there a solid way to memorize the double angle, sum and difference, power red...
the double angle and half angle formulae can be derived from the sum and difference formulae. The power reducing formulae can be derived from the pythagorean identities
so at minimum you only need to memorise the sum and difference formulae, given that you already have the pythagorean identities
tough finch
cedar kilnBOT
@zenith grail Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
void escarp
11.59 The system shown starts from rest, and each component moves with a constant acceleration. If the relative acceleration of block C with respect to collar B is 60 mm/s2 upward and the relative acceleration of block D with respect to block A is 110 mm/s2 downward, determine (a) the velocity of block C after 3 s, (b) the change in position of block D after 5 s.
void escarp
cedar kilnBOT
@void escarp Has your question been resolved?
cedar kilnBOT
@void escarp Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
zenith lintel
cedar kilnBOT
zenith lintel
this vector question seems very easy but im not sure how to approach it
im thinking something involving using a projection?
sullen cipher
Seems alright
past jungle
im on this question atm and im lost on where to go with it.
My process was:
P(A/B) <= PA
P(A/B) = P(AnB)/P(B)
P(AnB) = P(A) since A c B
P(A)/P(B) <= P(A)
1/P(B) <= 1
P(B) > = 1.
idk how to answer the original question given this
dreamy sleet
im on this question atm and im lost on where to go with it.
My process was:
P(A...
what you did is assuming P(A|B) =< P(A)
tranquil oracle
im on this question atm and im lost on where to go with it.
My process was:
P(A...
you derived that something's wrong with the conclusion ig?
but you don't really want to assume the conclusion to work out what's going on
dreamy sleet
you derived that something's wrong with the conclusion ig?
no, it’s possible, because you could have P(B) = 1
tranquil oracle
yeah that's really the only possible result for the conclusion
which should tell you something's wrong with the conclusion
there's a relatively simple way to show it's false, which is to construct a counterexample
the simple way to show it's true, is to prove it
past jungle
uhh idk how to do that 💀 . Isn't the question basically stating that event B could have or could have not altered P(A)
how can i prove a statement which is asking me for both
past jungle
uhh idk how to do that 💀 . Isn't the question basically stating that event B co...
Cuz if P(A|B) value comes out less than P(A), that means that they are not statistically independent. But, if P(A|B) = P(A), then they are statistically independant
unless that's the reason why it's false
💀
dreamy sleet
how can i prove a statement which is asking me for both
to prove that it is false, all you have to do is give an example of a sample space S, and sets A and B contained in S such that P(A|B) > P(B)
You can try considering extreme cases, like having B equal to S, or A equal to S, or A being the empty set, and so on
past jungle
so
S = {1,2,3,4}
A = {1}
B = {1,2}
P(A) = 1/4
P(B) = 2/4 = 1/2
P(A|B) = 1/4/1/2 = 0.5
0.5 > 0.25
therefore false?
if i use an extreme like B = S i think it becomes true
dreamy sleet
so
S = {1,2,3,4}
A = {1}
B = {1,2}
P(A) = 1/4
P(B) = 2/4 = 1/2
P(A|B) = 1/4/1/2...
this is indeed a counterexample
past jungle
i hope that's an acceptable answer on an exam 💀 my prof lowk useless and hasn't provided grading info
past jungle
this is indeed a counterexample
element mentioned something about proving it if it's true. would my steps from earlier be an example of proving it
or would i need to grab an example again. I feel like using examples for proof of truth is harder
since u would have to make it so it's right for x number of cases
dreamy sleet
element mentioned something about proving it if it's true. would my steps from e...
you have exhibited a counterexample, which shows that it is false. To use an analogy, it’s like disproving the statement “all of the ground is wet” by pointing at a dry floor tile
dreamy sleet
element mentioned something about proving it if it's true. would my steps from e...
Your steps from earlier derive a consequence of the statement “P(A|B) =< P(A)”