finally he gets the equations and solves when n =5 but for some reason he writes the total length as 1/3, why is that?
#help-10
wanton oar
everything makes sense until I see the arrows pointing to 1/3
how is he calculating the length?
timid silo
taking limits to infinity
wanton oar
wouldnt it go to inf/inf?
wanton oar
ah lhopitalls
I see
yeah I got 1/3
awesome
so is actual length and actual area the same?
wanton oar
.close
obtuse pebbleBOT
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Available help channel!
potent ivy
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potent ivy
what does it mean by warning
obtuse pebbleBOT
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amber kraken
YOu have to ask a question
Well thats just one case
THere's no why
You are asking the wrong question
X is not a constant
So any equation can be correct
The question you should be asking is
What x value makes that correct
Exactly
So to find the x value
you just do some simple math
subtract 5 from both sides so you get 2x=17-5
nocturne minnow
Because it's given
nocturne minnow
It literally states that 2x + 5 = 17. It equals 17 because it's a given piece of information
amber kraken
Yeah
nocturne minnow
Do you know what the addition property of equality is?
You should look it up. They are terms the solution has, meaning you should understand that
hearty pendant
hi guys im precalculus guy, i was thinking that as we know we use real valued function and do derivative ; so is there any proof that any nth derivative of a function willl always be real valued nth derivative . just thought out of blue
obtuse pebbleBOT
hi guys im precalculus guy, i was thinking that as we know we use real valued fu...
kind hawk
well assuming the nth derivative exists, yes
by induction
assuming you start with a real valued function of course
royal basin
so is there any proof that any nth derivative of a function willl always be real valued nth derivative .
can you repeat this but in a more comprehensible manner
"Is there any proof that the n'th derivative of a function will always be an n'th derivative?"
spring trail
real*
hearty pendant
by induction
ohk so it will hold true for real function u mean?
hearty pendant
"Is there any proof that the n'th derivative of a function will always be an n't...
i m asking if that nth derivative we got will be real valued derivative
trail musk
so basically you want to ask if the derivative of a real valued function is real valued
ruby path
$\dv{x}\cos x = -i\frac{e^{ix} - e^{-ix}}{2}$
warm shaleBOT
NEONPerseus
hearty pendant
hi guys im precalculus guy, i was thinking that as we know we use real valued fu...
gonna ask gpt a quick
<@&286206848099549185>
got this
ty tho
tardy epoch
<@&286206848099549185>
don't ping helpers for help with your chatgpt responses
also don't rely on chatgpt for math help
tardy epoch
then close
tardy epoch
do .close
spring trail
i got my prob
have would be better here 💀
plucky sinew
.close
obtuse pebbleBOT
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Available help channel!
half pecan
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half pecan
I got A but confused on part 2
adding scalars to B I get this
but i don't understand why this person didn't join c4 and -c3
since they are both on the v4 vector
obtuse pebbleBOT
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half pecan
wait so since A is independent
-C1 and -C2 are =0 right
meaning C1 and C2 are 0
so C1+C2+C3 =0 turns to 0+0+C3=0
so C3 = 0
and then C4-0 = 0
so C4 = 0 as well
obtuse pebbleBOT
@half pecan Has your question been resolved?
sonic forum
you're right
obtuse pebbleBOT
@half pecan Has your question been resolved?
compact gate
Why are straight lines called linear equations?
obtuse pebbleBOT
Why are straight lines called linear equations?
teal turret
linear
haughty coyote
an equation y = f(x) is said to be linear iff f is a linear function
that amounts to saying that for every vectors u, v and scalar a,
f(u+v) = f(u) + f(v) and f(au) = a f(u)
notice that f(x) = mx is a linear function
teal turret
wow really?
Hope so
timid silo
compact gate
Hope so
I suppose I never realized because I pronounce it lin - ne - ar, and not line - ar
teal turret
Ye ikwym
obtuse pebbleBOT
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flat rune
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split granite
Hey everyone. A bit more of a conceptual question here. What exactly is group isomorphism, and how do you identify group isomorphisms? This is referring to group theory btw
obtuse pebbleBOT
Hey everyone. A bit more of a conceptual question here. What exactly is group is...
kind hawk
think about the group {0,1} with operation addition and 1+1=0 and another group {odd, even} with again addition in the usual way
split granite
here's a question as an example
kind hawk
these are essentially the same thing, right?
and a group isomorphism is a map to translate from one of the groups to the other and back
split granite
fair. How would one go about identifying them?
split granite
think about the group {0,1} with operation addition and 1+1=0 and another group ...
yeah I guess
kind hawk
well try to find some groups which "look" the same except that the names of the elements might be different
split granite
so like all the subgroups of order 2?
kind hawk
well maybe
split granite
as in, does that mean that for example all subgroups of order 5 are isomorphic to each other, or is that not right?
kind hawk
(all groups of order 2 are isomorphic but that's just because 2 is small. will not be the same for other numbers)
split granite
oh ok ok
civic zealot
a group isomorphism is a function between two groups that is one to one, onto, and maintains the group structure/relations, i.e. f(a+b) = f(a) + f(b)
There are also a bunch of properties of group isomorphisms that should hold.
split granite
what does that notation represent?
as in is f(a+b) just applying b to a or is it something else?
civic zealot
if f is an isomorphism from group G to group H
if a and b are elements of G, then a+b is also an element of G (by group closure)
f(a+b) is saying, apply the function to the element a+b whatever that element is.
If f is an isomorphism, wherever the function sents f(a+b) should be the same as f(a)+f(b),
notice that f(a) and f(b) are elements of H, and f(a)+f(b) is an element of H (by group closure)
(also I'm using + here, but it's whatever operation exists in G and H. But + is easier to type)
kind hawk
f is the translation between G and H. the equation is saying that you can either first apply the group operation and then translate to the other group, or first translate to the other group and then apply the group operation there. and either way you get the same result
split granite
ahhh right I think I get it. Gonna take some time to digest but should be good. Tysm guys hope you have a lovely evening/ morning or whatever time it is for you
obtuse pebbleBOT
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winter flame
hey, i got this paper with few math problem could someone help me with it?
royal shard
yeah
royal shard
!status
obtuse pebbleBOT
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3. I got an answer but I'm told it's wrong
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6. None of the above
~Martin
obtuse pebbleBOT
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edgy cradle
obtuse pebbleBOT
edgy cradle
How would I find the anti derivative at the specific points
old isle
,rotate
warm shaleBOT
strong pike
How would I find the anti derivative at the specific points
The antiderivative is a sort of “accumulation”. The physical implication of an antiderivative is the area under a curve. Hence the antiderivative at a given point is the accumulation of the area under the curve of a function. @edgy cradle
I suggest you start with f(-5). It’s probably easier.
edgy cradle
Would f(-5) just be 0
edgy cradle
And then f(5) would be 3pi/2 +5/2
strong pike
Basically the area of the two semicircles + the area of the triangle - the area of the triangle below from x=4 to 5
strong pike
And then f(5) would be 3pi/2 +5/2
Yeah I think you got it, you did 3-1/2 right?
strong pike
Np
obtuse pebbleBOT
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lucid salmon
.help is this right?
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No command called "is" found.
lucid salmon
.help
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last lark
I was doing some graphing on desmos, and I realized that when I have something like f(x) = x^2/x, the value of f(x) is undefined when x is 0. But I don't really understand why it would be undefined because x^2/x = x (cancel out the x) and when f(x) = x, the value of f(x) is 0 when x is 0. Can someone explain why this happens?
obtuse pebbleBOT
I was doing some graphing on desmos, and I realized that when I have something l...
timid silo
I was doing some graphing on desmos, and I realized that when I have something l...
Even though x^2/x=x indeed, Desmos still recognizes that 0^2/0 has a division by 0 which isn't possible
last lark
So does that mean Desmos is inaccurate?
timid silo
In most cases you should
Just be wary of these specific cases
This can be important sometimes:
Say you were solving the equation x^2=x
You might divide both sides by x and get x=1, however x=0 is also a solution. You could not see that solution because you divided both sides by x, which assumes x is not 0. Hence, when dividing both sides by a variable that can be 0, you should split it into 2 cases:
- That variable is 0 (do whatever is appropriate in that case, which depends on your exact problem)
- That variable is not 0 (just divide both sides by that variable as you planned)
last lark
Oh ok, that makes sense
thank you
so generally I should note when the denominator portion equals 0
timid silo
Yeah
Also I guess you should also be wary of multiplying both sides by a variable as well, for example a/x=1 (a is a constant, solve for x) has one solution which is x=a but that solution doesn't work when a=0 (because 0/0=1 is wrong). The reason for that is that when a=0, our solution would give x=0, but multiplying both sides by 0 leads to 0=0 which is true regardless of the values of x and a
I bet someone's made a paradox involving that
sleek mural
obtuse pebbleBOT
sleek mural
Could someone plz help me w/ #32?
I’m not sure how to draw it out
But I’m pretty sure it’s become a triangle some sort
nocturne minnow
Why would it be a triangle?
One, it shows the little parallelogram next to the letters.
Two, it's labeled as 4 letters, meaning 4 vertices, hence 4 sides
sleek mural
One, it shows the little parallelogram next to the letters.
Two, it's labeled as...
No, I mean
It creates a triangle within the quadrilateral
Doesn’t it? @nocturne minnow
obtuse pebbleBOT
@sleek mural Has your question been resolved?
obtuse pebbleBOT
@sleek mural Has your question been resolved?
half crown
just used the formula area of parallegoram = absin0
u would get area of pallegoram then again use the formula
area of parallelogram = base * height (where base is given in question and area u have u would get height)
fathom flicker
I'm looking into what it means if a square matrix A has all of its singular values in the SVD equal to 1.
obtuse pebbleBOT
I'm looking into what it means if a square matrix A has all of its singular valu...
warm shaleBOT
AustinU
fathom flicker
and U, is composed of the basis vectors of A in the column space
V, is composed of the basis vectors of A in the row space
warm shaleBOT
AustinU
fathom flicker
In particular, I am wondering about if A might be: singular, symmetric, orthogonal, positive definite, positive semidefinite, or diagonal
any ideas?
<@&286206848099549185>
obtuse pebbleBOT
@fathom flicker Has your question been resolved?
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@fathom flicker Has your question been resolved?
spare jewel
obtuse pebbleBOT
spare jewel
i made this question after finding a similar one in my exam
how do you find only a and b
i was able to find only c because all 3 of the intersections have been given
these 2
and also this
empty hull
you need everything in the venn diagram to add to 100
assuming there are no values outside the diagram
spare jewel
so 100 - (1+0+7+15) gives this area
empty hull
not quite
spare jewel
empty hull
since the 1 and 7 are in an overlapping region you have to count them twice
since its 1 from C and 1 from A and 7 from C and 7 from B
empty hull
yes
empty hull
for A you have 38 left because one is in the C intersection
for B you have 43 by the same logic
if you solve 38 + 43 = 69 - x then x should be the intersection
spare jewel
for A you have 38 left because one is in the C intersection
but wouldnt you have to consider this as well
empty hull
if you solve 38 + 43 = 69 - x then x should be the intersection
yeah i said that part is x
you need x to find the rest
obtuse pebbleBOT
@spare jewel Has your question been resolved?
spare jewel
ah alr
timid silo
How do I do this?
obtuse pebbleBOT
How do I do this?
royal basin
make a diagram
royal basin
perhaps find the coordinates of both ships in a coordinate system that places the port at (0,0) and has the y-axis running south to north
ok lets see
,rccw
warm shaleBOT
timid silo
Mb
royal basin
no as in my comment is small
you should make the slash in km/h more visibly slanted
as is it's too close to vertical
anyway arithmetic check
,calc 9.6 * 3
12.7 * 3
warm shaleBOT
Results:
28.8
38.1
ok cool
yeah so far so good
now you just need to calculate 38.1^2 + 28.8^2 - 2 * 38.1 * 28.8 * cos(82°) with your calculator
and take its square root
timid silo
now you just need to calculate 38.1^2 + 28.8^2 - 2 * 38.1 * 28.8 * cos(82°) with...
that would be 44.4 km if using cos82
royal basin
the angle in your triangle is 82° yes
you've written it down that way and it is correct
jovial merlin
obtuse pebbleBOT
jolly ginkgo
Ok which note from lecture disagree with this?
jolly ginkgo
Yeah
jovial merlin
So it's true, they are not sublattices ?
jolly ginkgo
Yeah
jovial merlin
But why? They have sup and inf
What's that photo grr
What define sublettice in signature (01) then
jolly ginkgo
But why? They have sup and inf
What are the sup and inf here?
jovial merlin
Like from my example, if I get it correctly 0ad1 is sublattice, and I also have note that if lattice is line sublattice is any other line if I take out one element
O and 1
There is nothing higher than 1 and nothing lower than 0 so I guess it has to be them
And in internet I found many examples where they skipped sth but not exact ones
jolly ginkgo
There is nothing higher than 1 and nothing lower than 0 so I guess it has to be ...
01 does not belong to lattice
I'll be back later
jovial merlin
I'll be back later
Unlucky, later it might be to late I'm trying to get the answer before my exam :/. And I can't rely on sth I don't understand yet
jolly ginkgo
Ok just wait for couple of mins
jolly ginkgo
Ok so can you translate this?
jovial merlin
A sup b=1 and Ainfb=1
So it's saying if I compare 2 elements theyr sub and inf are 0 and 1
jolly ginkgo
A sup b=1 and Ainfb=1
That's join and meet
jovial merlin
jolly ginkgo
So does it says $b \in A$ if $a \lor b = 1$ or $a\land b=0$
warm shaleBOT
fäf
jolly ginkgo
Yeah in hasse diagram
jovial merlin
But a and b can't be equal 0
jolly ginkgo
In your diagram only $a \land 0 = 0$
jovial merlin
Both of them can't be the same because to be lettice there can be only one min
jovial merlin
Yes but then why in presentation there would be a^b =0 if they both can't be equal it
jolly ginkgo
Yes but then why in presentation there would be a^b =0 if they both can't be equ...
Who said this?
Which diagram are you referring to?
If 0 joins both a and b then a^b = 0
jovial merlin
Hmm so it's like v is showing that I have 2 branches up an ^ two branches down?
jolly ginkgo
Hmm so it's like v is showing that I have 2 branches up an ^ two branches down?
You have b and c meeting at 1 above so bvc = 1
If you have 0 joining b and c then b^c = 0
jolly ginkgo
So it's not 0
So what's not 0?
jovial merlin
A is not 0
jolly ginkgo
But in my example b,c,d,e joins a
So we have $b \land c = a$
warm shaleBOT
fäf
jovial merlin
If we take of a we have b^c=0 so why it's not sublettice
jolly ginkgo
If we take of a we have b^c=0 so why it's not sublettice
No that's not what we have then
jovial merlin
Why not?
jolly ginkgo
b ^ c is a , but if we remove a from L and keep b and c then b^c = a doesn't belong to L so L is not a sublattice
b^c is fixed depending on lattice
It's supposed to be same for sublattice
jovial merlin
So if I'm in (1,0) I can't change any points sup or inf and that is the rule ?
jolly ginkgo
So if I'm in (1,0) I can't change any points sup or inf and that is the rule ?
Yeah you can't change
Give me some different example we can go through it
Make a table
jovial merlin
So 0,A,1 is sublattice? All have same sup and inf?
jolly ginkgo
Yeah I think this will be sublattice
jovial merlin
jolly ginkgo
Aren't the points given any letter
jovial merlin
So like here I can't take out yellow if I wanna leave any red point
We have to name it by ourselves
jolly ginkgo
Yeah you can't
jolly ginkgo
So 0,A,1 is sublattice? All have same sup and inf?
Wait here we don't have the middle row right
None of the b,c,d,e is in this set
jovial merlin
So 0ad1is still sublattice here
jolly ginkgo
So 0ad1is still sublattice here
No
jovial merlin
Wait here we don't have the middle row right
Yes
jolly ginkgo
I'm sorry we aren't making much of a progress here
jovial merlin
Why no, none of them changed sup or inf
jolly ginkgo
{0,d,x,a,1} is a sublattice
jolly ginkgo
Why no, none of them changed sup or inf
Is d joined to a by any means?
jovial merlin
But d e c b all have 0 and a
jovial merlin
Is d joined to a by any means?
Yes by going thru c
jolly ginkgo
Then check if we get the same table for the subset
jolly ginkgo
Yes by going thru c
But c isn't in your subset is it?
jovial merlin
No so I can remove it
jolly ginkgo
No no it should be in subset
jovial merlin
Here I skipp one inside and it still works
jolly ginkgo
Just plot the points of your subset and draw the lines in lattice and check if it's connected
jovial merlin
Can u show me what u mean ?
warm shaleBOT
fäf
jolly ginkgo
Yes
jolly ginkgo
But here they said axby is lattice so it's different example ?
That doesn't seem like a sublattice because $a \lor b = c \notin L_1$
warm shaleBOT
fäf
jovial merlin
Fuuck im in the middle of table
Just tell me how to get sublattices from it before u go xd
Btw thank u for help
rocky goblet
,rccw
warm shaleBOT
rocky goblet
"rotate counterclockwise"
your image was sideways, now it's the right way up so it's easier to read
jovial merlin
Oh right 😅
rocky goblet
what's the question here? i scrolled up but couldn't actually work it out
jovial merlin
I don't get when it's sublattice in signature 01
Ehh i don't think I'm gonna get it anyway but still please anyone help me I'm brain-dead 😭 I need to know what all sublattices are and understand why. I get all the easy ones but still don't know if 0a1 would be sublattice
obtuse pebbleBOT
@jovial merlin Has your question been resolved?
jovial merlin
I don't get when it's sublattice in signature 01
obtuse pebbleBOT
I don't get when it's sublattice in signature 01
@jovial merlin Has your question been resolved?
jovial merlin
<@&286206848099549185>
obtuse pebbleBOT
@jovial merlin Has your question been resolved?
obtuse pebbleBOT
@jovial merlin Has your question been resolved?
fallen needle
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@fallen needle Has your question been resolved?
fallen needle
Show your work, and if possible, explain where you are stuck.
1
obtuse pebbleBOT
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jolly ginkgo
Btw thank u for help
I'm sorry I had to go urgently
jolly ginkgo
C(t) is continuous, so it has to be continuous at 16 and 8
What is the definition of continuity?
timid silo
how dyou answer this question?
obtuse pebbleBOT
how dyou answer this question?
marsh geyser
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
marsh geyser
Do you know what's the range of a function?
timid silo
yh like the set of possible values the function can output?
bright geyser
obtuse pebbleBOT
obtuse pebbleBOT
@bright geyser Has your question been resolved?
round frigate
Hi, I have this question:
Given two subspaces of $\mathbb{R}^4$:
$W_1 = { (x_1,x_2,x_3,x_4) \in \mathbb{R}^4 | x_1 + x_3 = x_2 + x_4, x_1 - x_3 = x_2 - x_4 }$.
$W_2 = { (x_1,x_2,x_3,x_4) \in \mathbb{R}^4 | x_1 + x_3 = -x_2 - x_4, x_1 - x_3 = -x_2 + x_4 }$.
We also given the set $Q = { (x_1,x_2,x_3,x_4) \in \mathbb{R}^4 | x_1 x_3 = x_2 x_4 }$, prove that $W_1,W_2 \subseteq Q$, and check if Q is a subspace of $\mathbb{R}^4$.
I proved that there's $W=W_1+W_2=W_1\oplus W_2$ and I proved that $W=\mathbb{R}^4$.
I was thinking on maybe show first that Q is a subspace of $\mathbb{R}^4$ and then since $W_1,W_2,Q$ are all subspaces of $\mathbb{R}^4$ and then get my way to proving $W_1,W_2 \subseteq Q$.
I also was thinking on proving it by showing that $W_1$ can be the same as Q if I use a scalar to transform it to Q, but no idea how to do that, and I have no clue on how to prove $W_2 \subseteq Q$, Can I get a hint?
obtuse pebbleBOT
Hi, I have this question:
Given two subspaces of $\mathbb{R}^4$:
$W_1 = { (x_1,x...
warm shaleBOT
therealcain
royal basin
\{ and \} for braces
also Q isn't a subspace of R^4
(well, spoilers ig)
but even setting out to do it this way is more work than simply proving two set inclusions
round frigate
also Q isn't a subspace of R^4
Was just working on this, and found out it wasn't
round frigate
but even setting out to do it this way is more work than simply proving two set ...
How would I approach showing they're subsets?
royal basin
do you know in general how to prove one set is a subset of another?
round frigate
Suppose $a \in W_1$ ... therefore $a \in Q$
warm shaleBOT
therealcain
round frigate
Or maybe... Showing every vector in $W_1$ is a linear combination of the vectors in Q
warm shaleBOT
therealcain
obtuse pebbleBOT
@round frigate Has your question been resolved?
merry vault
Hey
merry vault
We learned about one-sided limits using a weird definition including sequences
I don't really understand it
thus I don't know how to start with these ones
not sure if the sequence definition must be used here to get the result
or am I missing something else?
(up arrow means coming from the left and down arrow means coming from the right)
Why is this 0?
royal basin
as x approaches 0 from below, what happens to 1/x?
merry vault
1/x becomes very large, my bad
merry vault
and x is negative yeah
hm
the issue is I don't seem to have anything in my script that defines what happens if I input negative variable into the function exp
royal basin
script?
what's important about this is that 1/x in fact approaches negative infinity as x -> 0-.
merry vault
math script from uni
This says "for all x in R" which confuses me. Could I use this here because x is negative?
Or does this also work for negative x
like, exp(-x) = ... does that mean "for any negative x" or is it a normal minus that inverts the sign
royal basin
exp(-x) means exp(-x)
merry vault
ok lol
royal basin
we never prefix a minus sign to a variable as an indication of it being negative.
merry vault
alright
good makes sense
so we basically have exp(-infinity)
which I guess I could turn into 1/exp(infinity)
which is 1/infinity which is 0
royal basin
indeed
merry vault
[ \lim_{x \rightarrow 0^-} \exp\left(\frac{1}{x}\right) = \exp(-\infty) = \frac{1}{\infty} = 0 ]
ok that is broken latex but
my question is can I literally put infinity sign in there
or is this bad
warm shaleBOT
madmike
merry vault
lol
ok hm
thanks a lot
now I need to try from right side
I hope that's straightfoward then
yeah exp(1/x) is just exp(infinity) then which is infinity
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lyric bison
obtuse pebbleBOT
lyric bison
Need help as to why domain becomes less then 0 after converting to b2-4ac
Thanks in advance
Need help as to knowing when to make it less than, equal to, or larger than 0
<@&286206848099549185> 🙏
obtuse pebbleBOT
@lyric bison Has your question been resolved?
stray shoal
Need help as to why domain becomes less then 0 after converting to b2-4ac
It will be because somewhere in the question it says or is implied that there are no real solutions to the polynomial.
stray shoal
Need help as to knowing when to make it less than, equal to, or larger than 0
For 2 discrete solutions it is >0
There are always 2 solutions to a quadratic but if they are the same then b^2-4ac = 0
If there are no real solutions then b^2-4ac < 0
static mason
I tried all methods on both matrices, I get different inverse, but on calculator it says that this is true
obtuse pebbleBOT
I tried all methods on both matrices, I get different inverse, but on calculator...
static mason
How do i solve number 3
ruby path
I think you need to show that B is the inverse of A
Judging from the previous question
obtuse pebbleBOT
@static mason Has your question been resolved?
static mason
Oh sorry i forgot about it
static mason
What’s the instruction
Show that B is inverse of A
grizzled shore
Have you tried multiplying them together
static mason
Does that count
grizzled shore
Well if it’s invertible there’s only 1 unique inverse
static mason
Yes det()>=1
grizzled shore
You just said show, that would adequately show that B is the inverse of A iff AB = I
grizzled shore
I tried all methods on both matrices, I get different inverse, but on calculator...
Also show your working
Maybe you made a mistake and you didn’t see it
grizzled shore
Then organise it
static mason
Then organise it
My brain can’t handle this
Let me multiply them now
I got 1 in a11 and 0 in a12
Then it’s identity matrix
yes it is
but why i couldn't get it
ok
help
static mason
oh
i was using the determinant method to get the cofactors
i'm proud of my brain
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noble kindle
if a mxn matrix has full column rank, then it won't have anything in the null space and will only have 1 or 0 solutions right?
obtuse pebbleBOT
if a mxn matrix has full column rank, then it won't have anything in the null sp...
noble kindle
1 solution iff for Ax=b, b is in the column space of A (so like a combination of the columns)
0 solutions otherwise
Since x = x particular + x nullspace
obtuse pebbleBOT
@noble kindle Has your question been resolved?
trail musk
yes
obtuse pebbleBOT
noble kindle
tyty
obtuse pebbleBOT
Available help channel!
rigid fog
How does the alternating series test work? I thought it was if you have something like $(-1)^n/(n(sqrt(n+1)))$ you could see if $1/(n+1)(sqrt((n+1)+1))$ was less, then take the limit of $1/(n(sqrt(n+1))$ and if it got 0 then the original series converges
obtuse pebbleBOT
How does the alternating series test work? I thought it was if you have somethin...
warm shaleBOT
Meep
native inlet
How does the alternating series test work? I thought it was if you have somethin...
please if you can use \sqrt{} and rewrite your problem, it is very hard to understand
is it $\frac{(-1)^{n}}{n\sqrt{n+1}}$?
warm shaleBOT
XxMrFancyu2xX
gilded needle
How does the alternating series test work? I thought it was if you have somethin...
this is roughly correct... if the absolute values of the terms form a sequence that decreases to zero, and the signs alternate, then the series converges
zinc stump
Hey guys, can anyone help me with this - SET THEORY -
prove that $n \in m$ or $m \in n$ or $n=m$
obtuse pebbleBOT
Hey guys, can anyone help me with this - SET THEORY -
prove that $n \in m$ or $...
warm shaleBOT
meitar5674
zinc stump
for all n,m natural
timid silo
what does n in m mean in this context?
are you using this? https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers?
zinc stump
Yeah they are both natural numbers @timid silo
Yeah indeed
I'm trying induction on m, but not sure this is what I got to do
as well as I'm having trouble showing that n+1 \in m+1
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
obtuse pebbleBOT
@zinc stump Has your question been resolved?
obtuse pebbleBOT
@zinc stump Has your question been resolved?
obtuse pebbleBOT
@zinc stump Has your question been resolved?
obtuse pebbleBOT
@zinc stump Has your question been resolved?
sleek mural
How do I find the lengths of the altitude for #34?
nocturne minnow
How do I find the lengths of the altitude for #34?
This channel is taken meaning you should not post here, you need to open your own
sudden coyote
I need help with transversals in my geometry class
obtuse pebbleBOT
I need help with transversals in my geometry class
sudden coyote
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obtuse pebbleBOT
Available help channel!
timid silo
pls I need help
obtuse pebbleBOT
pls I need help
timid silo
I have a bunch of position vectors, and I want to put them in a matrix P(u,v), and then differentiate that to find the velocity vector
Ive never worked with matrices before
wooden marten
I have a bunch of position vectors, and I want to put them in a matrix P(u,v), a...
wouldn't differentiating a bunch of position vectors get you a bunch of velocity vectors
timid silo
wouldn't differentiating a bunch of position vectors get you a bunch of velocity...
Yes but they’re in a row matrice
Im tracking the ISS
wooden marten
but why do you need to put them in a matrix
are you transforming it after that or whatever
timid silo
So I have latitude and longitude
Of the ISS
Here let me show you
This is all real time
I just don’t know what to do to find the velocity vector
wooden marten
well derivative of a matrix is the matrix of the derivatives of the entries
oh ig you don't have du/dt and dv/dt
if you want to calculate it you could just check u, v at 2 close points in time and find the slope of each entry of the matrix
timid silo
Alright I’m going to try that
Thanks
I just evaluated the first entry and I got this crazy huge number
I’m confident that’s not right
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
timid silo
I have no idea how to do this problem
swift adder
It requires a bit of Calculus
fierce lagoon
GD profile picture lol
fierce lagoon
I have no idea how to do this problem
Also don't occupy more than one channel
Either close this one or your other one
swift adder
GD profile picture lol
Nice
nocturne minnow
Either close this one or your other one
Especially when someone was there trying to help you
fierce lagoon
I think they simply just forgot. It happens
swift adder
True
And I got the answer
Write the equation of the price of the fence in terms of one of the sides
nocturne minnow
And I got the answer
And hopefully you aren't going to give out the answer
swift adder
I won't
timid silo
Write the equation of the price of the fence in terms of one of the sides
Im confused on how to get the equation though
swift adder
Say that one of the sides length is x ft
timid silo
And hopefully you aren't going to give out the answer
Well I want to learn how to do it
timid silo
Say that one of the sides length is x ft
Ok im following
timid silo
Im not sure
swift adder
We know the area of the rectangle is 8 square feet, yes?
timid silo
Yeah
swift adder
So the length and width's product must be...
timid silo
Multiplying together to get 8
swift adder
Yep
timid silo
But it also had to minimize the cost
swift adder
This is the first step
timid silo
So cant be 2 and 4
swift adder
The write the equation one
In this situation we want to write the equation of the cost in terms of one side's length
timid silo
How do you do that?
timid silo
Cant you make it any other variable?
swift adder
Yes you can
timid silo
Ok so lets make it z
timid silo
So x and z
swift adder
Should we vc though, the process is long
timid silo
Sure hold on give me around 5-10minutes?
swift adder
Sure
timid silo
Ill add you as a friend and call when ready
swift adder
Yea sure
timid silo
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
uneven otter
Just want to confirm something here but basically if I want to find the volume of this then I would do something like pi integrate from a to b for (volume of whole shape)^2 - (area between y = x and y = x^2)^2
obtuse pebbleBOT
Just want to confirm something here but basically if I want to find the volume o...
@uneven otter Has your question been resolved?
velvet lodge
obtuse pebbleBOT
velvet lodge
I tried doing this using math summation
But this is incorrect
Then by observation I got the answer
Anything wrong with my steps
Why it depends on n's parity
python program I use for getting sample data:
def con(n):
r=0
for i in range(1,n+1):
for j in range(i+1,n+1):
for k in range(i+j-1,n+1):
r+=1
return r
<@&286206848099549185>
Verification program:
def con2(n):
if n%2==0:
n/=2
return n*(n+1)*(4*n-1)/6
else:
n-=1
n/=2
return n*(n+1)*(4*n+5)/6
azure anchor
python program I use for getting sample data:
```python
def con(n):
r=0
...
why do you have n+1 in all the ranges? problem clearly states to n in each loop
its been a while since i read up on big o but im pretty sure it's always worst case, so considering n can be any number, each for loop is n^1 operations
3 loops means n^3 operation time if im not mistaken
velvet lodge
gilded needle
why do you have n+1 in all the ranges? problem clearly states `to n` in each loo...
python's range statement takes an interval of the form [i,j) , it stops at one less than j
azure anchor
ah, python
gilded needle
your formula on the third line looks wrong, i checked it with n=4, i=1, then the sum on the previous line is 2+3 = 5, but your (n-i)(i+1+n)/2 formula gives (3)(6)/2 = 9
velvet lodge
I think I made an error here. The top number is meant the number of steps. j's value range is from i+1 to n
gilded needle
oh right, i didn't even notice that
obtuse pebbleBOT
@velvet lodge Has your question been resolved?
velvet lodge
<@&286206848099549185>
vernal musk
I tried doing this using math summation
the first step, should j from i+1 to n?
velvet lodge
the first step, should j from i+1 to n?
Yes
velvet lodge
I think I made an error here. The top number is meant the number of steps. `j`'s...
This explains that
velvet lodge
what about changing it correct and do it again?
I think it's small, and didn't continue to the third line
velvet lodge
o, it's from i+1 to n-i+1 i guess.
This is the original problem
velvet lodge
.
vernal musk
no, the first line j should be from i+1 to n-i+1.
b/c you need to make sure i+j-1 <= n, which means j <= n-i+1.
velvet lodge
I got n*(n-1)*(n+1)/6, this gives the result f(5)=20, but con(5)=22, still not work
vernal musk
yes, and im not sure. but i guess the problem is we didn't make sure i+1 <= n-i+1.
i didn't prove that will influence the answer. but i guess this is the only part to be wrong.
(con(5)=13 though.
so my conclusion is that for odd number. we let i from 1 to (n-1)/2, then for j from i+1 to n-i+1.
for even number. we let i from 1 to n/2-1, then fro j from i+1 to n-i+1.
and i suppose that's the reason that answer relies on the parity of n.
velvet lodge
Yes. This explains it. I'll think it for a bit longer.
Thank you very much for your help.
vernal musk
np
velvet lodge
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mystic blade
obtuse pebbleBOT
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!15mins
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
fathom flicker
The question is asking which statement is true
since your "answer" doesn't even pick one
your answer is wrong
and you didn't provide any work
so no one can check you work
did you even read the question before sending it here?
mystic blade
as in lime,i picked the first one
it made the most sence to me
there rlly isnt anyhing to show
fathom flicker
Picked the first what?
Read your question
before asking for help here
none of what you are saying makes sense, and it doesn't help that you don't spell anything properly either
unkempt marlin
How would I go about solving this question. First I let the polynomials multiplied by scalars a,b,c = 0 and then solve for a,b,c but once I get a,b,c what do I do next?
obtuse pebbleBOT
How would I go about solving this question. First I let the polynomials multipli...
unkempt marlin
your solution is right no?
I am not sure if it is right. I am just checking it multiple times to make sure it is not incorrect.
unkempt marlin
get a rref then look if there are less pivots than columns
Also for the rref, put coefficients into rows or columns. Like, 6,-10,-6 horizontally or vertically?
unkempt marlin
get a rref then look if there are less pivots than columns
Also, if there are less pivots than columns what exactly does that mean, that it is linearly dependent.
pure tusk
Also for the rref, put coefficients into rows or columns. Like, 6,-10,-6 horizon...
Vertically
unkempt marlin
This is the rref
pure tusk
Also, if there are less pivots than columns what exactly does that mean, that it...
That means it's linearly independent cuz of free variable
Ok that means it's linearly independent
Lemme check tho hold on
unkempt marlin
Please, it would mean a lot if you are able to check it for me, thank you kind sir.
unkempt marlin
oh, include the zeroes?
pure tusk
This is the rref
Does it give this?
unkempt marlin
Does it give this?
yes just with extra zeros at the end
pure tusk
Aight then it's L.I.
unkempt marlin
But how do I get the coefficients now?
pure tusk
You can set the c to be equal to a variable t
Then you solve for a and b
Set t to be anything and you get a set of numbers
Your question asks for you to leave it blank tho
unkempt marlin
so can a = 3/2, b = -3/4?, oh yeah you're right, if it's L.I. then I leave it blank lol
pure tusk
Wait lemme make sure I'm not saying wrong things
unkempt marlin
Your question asks for you to leave it blank tho
It said it was wrong,
Fuck i stuffed up
So, because it said it was wrong, I'm guessing that it is linearly dependent.
pure tusk
Nevermind yeah I think I got the two mixed up my bad
A set of vectors is linearly dependent if there is a nontrivial linear combination of the vectors that equals 0.
unkempt marlin
so it is dependent but how to obtain the coefficients is my issue.
pure tusk
So if there's no free variable, its linearly dependent
No
Ok yeah so
Just let the free variable c to be equal to t
And solve for a and b
pure tusk
This is the rref
c = t
b = 3/4t
a = -3/2t
Then you can set t to be any number
And that would be a particular solution
unkempt marlin
Then you can set t to be any number
can you please check if t can equal 1 and if it is a right answer for the question, please kind sir.
pure tusk
can you please check if t can equal 1 and if it is a right answer for the questi...
Yes, it can be 1
But it can also be 4
Which is what you have on your screenshot
Any value of T would work
unkempt marlin
So -6,3,4 can work
Yes, it does, thank you so very much bubble, your knowledge knows no bounds
obtuse pebbleBOT
Available help channel!
solar sluice
5 students shared 3 cakes equally. What fraction of a cake did each student get?
solar sluice
<@&286206848099549185>
rotund ledge
5 students shared 3 cakes equally. What fraction of a cake did each student get?
3 would be the numerator and 5 would be the denominator
so you get the number $\frac{3}{5}$
warm shaleBOT
Bumbie
solar sluice
.close
burnt vector
So, about this question. It made me question the definition of continuity, which goes around the lines of "f(x) is continuous at a point c iff lim f(x) as x approaches c = f(c)".
But I began to wonder: what exactly does it mean by "continuous at a point?" Like, ngl, it feels a bit... vague? also, tbh how would you prove from this definition that every polynomial is continuous within it's domain? It's not like you're gonna prove it for every number 
Would this perhaps be worked around by showing that within it's domain, a function is defined at every point, so it must be continuous? Idk if that counts as a proper proof tho.
Back to the question however, I feel like the answer is that there is no such value, since we would be able to find an irrational number in between any rational number to create a discontinuity. But.... how am I to prove that, if that even is true?
obtuse pebbleBOT
So, about this question. It made me question the definition of continuity, which...
haughty coyote
clearly the only possible value where it could be continuous is if x can't be much different from 0
when x approaches c
so intuitively, c has to be 0
then you can prove by smt like the sandwich theorem that it is indeed continuous at 0
also we often prove polynomials are continuous by proving that
constant functions and the identity (f(x) = x) are continuous
continuity is preserved by addition, multiplication
which constructs every polynomial so every polynomial is continuous
burnt vector
also we often prove polynomials are continuous by proving that
constant function...
I should be leaving such proofs for intro to anal tbh
drifting badger
So, about this question. It made me question the definition of continuity, which...
Continuity means exactly what its definition says. If you want an interpreration though, you could think of a function being continuous at x = c if f(c) has the value that its neighboring points thinks it naturally should have.
burnt vector
hm yeah zero seems to be the only answer.... But... Eh, if the neighboring points of 0 are not continuous (or is it?) how am I to take a limit of f(x) as x approaches 0?
haughty coyote
So, about this question. It made me question the definition of continuity, which...
sequential characterisation/definition of continuity:
f is C0 at c iff for all sequences (xn) converging to c, the sequence (f(xn)) converges to f(c)
drifting badger
Continuity means exactly what its definition says. If you want an interpreration...
There are different interprerations that can help (some more rigorous in nature than others), but this one is what I find the most intuitive.
burnt vector
sequential characterisation/definition of continuity:
f is C0 at c iff for all s...
oh damn never knew that.
haughty coyote
hm yeah zero seems to be the only answer.... But... Eh, if the neighboring point...
why split cases when you can have one inequality that always holds (hence my mentioning of the squeeze theorem)
burnt vector
squeeze theorem to prove this? Mmmm...
haughty coyote
sequential characterisation/definition of continuity:
f is C0 at c iff for all s...
this makes it easy to prove it's discontinuous at every nonzero point
burnt vector
.... I still can't think of functions which I can use to "bind" the values of g(x)
well, best I can think of is f(x) = x tbh 💀
haughty coyote
.... I still can't think of functions which I can use to "bind" the values of g(...
"bound"
and yes that works
|g(x)| <= |x| -> 0 when x -> 0
since g(0) = 0, g is continuous at 0
haughty coyote
oh damn never knew that.
just noticed your pre-uni role
Yeah it's normal then
burnt vector
"book binding"
reminds me of the totally-not-pirated books which I'm having custom printed anw, so that'll be our first function and our 2nd function would be... -|x|...?
haughty coyote
idk in what country you'd actually see a proper real anal class in HS
burnt vector
idk in what country you'd actually see a proper real anal class in HS
FR THO
burnt vector
"For real"
obtuse pebbleBOT
Available help channel!
harsh salmon
obtuse pebbleBOT
harsh salmon
do we use nPr or nCr?
I though about using nPr
N is 6 and r is 2
so it'll be
6!/4!
harsh salmon
there are also two fives
mhmm
jolly ginkgo
6!/4!
Nope
Fix 5 on both sides then see how many arrangements you get for middle part
Wdym each side?
tepid nacelle
if you fixe the position of 5s then you have 4 numbers --> 4!
from all cases 6! ---> 4!/6!
jolly ginkgo
if you fixe the position of 5s then you have 4 numbers --> 4!
from all cases 6! ...
There's more to it
1 is repeated twice
tepid nacelle
so is 2*(4!/6!) = 1/15?
obtuse pebbleBOT
@harsh salmon Has your question been resolved?
jolly ginkgo
so is 2*(4!/6!) = 1/15?
That is right but idk how you got that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gaunt idol
Hello, i needed help with this question:
obtuse pebbleBOT
Hello, i needed help with this question:
gaunt idol
The table shows the ages of the passengers on an airplane. Calculate the average age of the passengers.
fierce siren
Take the midpoints (middle value between the intervals, e.g. 0 <= x < 10 gives 5 for the midpoint) and multiply them by the frequency
Then you need to divide that by the total frequency like you would with any other average
gaunt idol
do you I should multiply 5* 4+ 15 * 10 + 2516+3518+45*20
and then divide the sum with 68
am I right?
2100/68
which gives me :30.88
thanks
.solved
.close
sage geyser
a particle has an initial position vector of (5i-6j) metres with respect to an origin O. If the particle moves at a constant velocity of (i+6j) m/s, after how many seconds will the particle be 50 m away from the origin?
obtuse pebbleBOT
a particle has an initial position vector of (5i-6j) metres with respect to an o...
sage geyser
50 = 5i-6j + t(i+6j)
where t = seconds
i tried collecting both i and j terms together
50 = |(t+5)i + (6t-6)j|
|magnitude|, shouldve clarified
i dont really know wha tto do from here
slow maple
50 = 5i-6j + t(i+6j)
Be careful; that calculates how much distance it's travelled, not how far it is from a given point
you'll need to use the distance formula to find out how far two points are from eachother
sage geyser
isnt 50 the resultantof the two vectors?
slow maple
slow maple
isnt 50 the resultantof the two vectors?
oh I see how you're doing it
I think that'll work then
the distance formula would still be helpful in calculating the magnitude of the vector though
sage geyser
ive never used the formula before
ill stick to my current method for now
50 = |(t+5)i + (6t-6)j|
2500 = (t+5)i^2 + (6t-6)j^2
does that line of working out look a bit dodgy?
|(t+5)i + (6t-6)j| is the same as sqrt((t+5)i^2 + (6t-6)j^2) so I moved the sqrt to the other side by doing the oppposite
expand brackets on lhs
2500 = t^2 + 10t + 25 + 36t^2 - 72t + 36
collect
2500 = 37t^2 - 62t + 61
37t^2 - 62t - 2439 = 0
quadratic formula
obtuse pebbleBOT
Available help channel!
hard whale
obtuse pebbleBOT
hard whale
Stuck on the second half of the question
Determining the rank of A
For all possible values x1, x2, x3
I tried verifing that the vectors that span the the row space is a basis but got stuck because I can't verify if they're linearly I dependant
obtuse pebbleBOT
@hard whale Has your question been resolved?
scenic fjord
obtuse pebbleBOT
obtuse pebbleBOT
@scenic fjord Has your question been resolved?
scenic fjord
<@&286206848099549185>