does the book give any reason why it should be 480
#help-49
fleet moss
solid island
hm
i think
its a mistake
cos
ive asked everyone esle
everyone getting 360
i think ill leave it at that 😭
the books working out doesnt rly make sense either
but thank u guys for helping
rly
what did u get
fleet moss
ive asked everyone esle
well just because everyone says it's wrong doesnt mean its actually wrong
fleet moss
yeah show that pls
fleet moss
huh
solid island
right
fleet moss
wheres the working 
solid island
im tripping out
😭
RIGHT
its ok im pretty sure
360 is right
theres pretty much nothing else it can be bruh 😭😭
oh wait
did u get
5! * 5c3
solid island
ping helpers on this one
okok
<@&286206848099549185> can u confirm this question for us please
this one
OH
😭😭
solid island
alr thank u both very much for helping tho
😭😭
hopefully we can get another insight
🙏🙏🙏
simple field
is this for part c
fleet moss
yep
fleet moss
the premise is here
choosing five letters from PROBLEM such that both vowels are included and separated by at least two consonants
fleet moss
off by a factor of 2, according to the answer key
fleet moss
5C3 \* 4 \* 3! is what i get
but howd you get this
last slate
1200-360-480
solid island
this was my working out btw
simple field
oops yeah
ok we need both vowels, so then we are choosing 3 letters from the 5 consonants so 5C3
the three arrangements for vowels and consonants are VCCCV, VCCVC, CVCCV
then reordering the specific vowels and consonants is 2! * 3!
so all in all 5C3 * 3 * 2! * 3! = 5!/(2! * 3!) * 3 * 2! * 3! = 5! * 3 = 360
fleet moss
let me share my thought process:
we have 5c3 unique letter combinations. there are two cases, the vowels are separated by two consonants, or by three. in the first case, there are two ways to order the vowels, three ways to pick the consonants in between, two ways to order the consonants in between, and two places left over for the last consonant. this gives us 24. now we consider the case that the vowels are separated by three consonants. we have two ways of ordering the vowels and three ways of ordering the consonants. thats another 12. all in all we have 36 ways of ordering times 10 ways of choosing which gives 360
ok well uh
fleet moss
it seems we have a consensus lol
solid island
thanks for everyones input tho 🙏🙏
fleet moss
yeah. ask your teacher though
fleet moss
np
solid island
.close
midnight plankBOT
fleet moss
lets say we have the following
VCCV
we have a total of 3 consonants, so there are 3c2 = 3 ways to pick which ones go in there
yeah i was going for the more brute force way to get an alternate perspective
nah 3! = 6
oh yeah i meant to write 3! my bad lol
regal barn
how would this be solved?
midnight plankBOT
how would this be solved?
edgy schooner
you know you can find the centre of mass of both of those and then find the centre of mass of the system
regal barn
so for the square itd be (0,2) and the circle would be (0,6) correct?
edgy schooner
yes
regal barn
and just take the average?
regal barn
uhm so the m of square would be 16p and the circle is 4pi(p)
im just not sure how to find the centre of the entire system
edgy schooner
do you know the formula??
now you just have two points
(0,2) where mass is 16p and
(0,6) where mass is 4pi(p)
edgy schooner
$$ \frac{(16\rho)(2)+(4\pi\rho)(6)}{(16\rho+4\pi\rho)}$$
grand pondBOT
Pro_Hecker
edgy schooner
oh would it be the (16p)(2)+(4pi(p))(6)/(16p+4pi(p))
yeah
regal barn
**Pro\_Hecker**
would it just be the simplified form of this?
edgy schooner
no it would be for x
regal barn
oh y is 0
edgy schooner
y would be 0
regal barn
my bad
grand pondBOT
Result:
3.7596033859538
thank you! i was stuck on what formula to use because i kept on trying to use the formula for mass that includes integration
but i get it now
.close
twilit field
I'm unable to understand why all ements must be zero
midnight plankBOT
I'm unable to understand why all ements must be zero
twilit field
the fact that all V_ks must be zero
novel herald
when you read through the proof, is there something specific that you aren't understanding?
because the proof is explaining exactly why
twilit field
my bad
kind zealot
I'm unable to understand why all ements must be zero
What is your textbook's definition of a direct sum?
fleet moss
the fact that all V_ks must be zero
a sum of subspaces is a direct sum if any vector in U + V can be written as u + v for some unique u in U and v in V. there should be some geometric intuition here if you consider the simple example of two planes in euclidean 3 space
twilit field
What is your textbook's definition of a direct sum?
twilit field
a sum of subspaces is a direct sum if any vector in U + V can be written as u + ...
wdym
twilit field
a sum of subspaces is a direct sum if any vector in U + V can be written as u + ...
so i+j+k
?
fleet moss
uh hold on
kind zealot
The uniqueness secures that you can't do something like v1 = -v2, because then there would be 2 ways of representing the sum
That is, if v1 = 1 and v2 = -1, then since V1 and V2 are vector spaces, V1 will also contain -1 and V2 also 1
So you could write 0 as a sum in a way that isn't unique
twilit field
I get that, but in the proof for uniquness the only thing i get is $v_1=u_1$
grand pondBOT
ƒ(Why am. I here)=I don't Know
grand pondBOT
ƒ(Why am. I here)=I don't Know
novel herald
you're talking about this part right?
twilit field
yes
novel herald
it's not that the vk's are zero, it's that vk - uk is zero by the assumption, the conclusion is that v is able to be expressed uniquely
fleet moss
so i+j+k
sorry i meant two lines not two planes. pretty clearly there is only one way to get u + v here
runic hamlet
0 = (v_1-u_1) + ... + (v_m - u_m) is one way of writing zero. but you are only allowed to have 0 = 0+..+0, so this also has to be that form. so v_1-u_1=0, v_2-u_2=0 and so on
fleet moss
essentially this asserts that there is no v_k im V_k that can be written in terms of vectors in the other spaces
twilit field
sorry i meant two lines not two planes. pretty clearly there is only one way to ...
hmm, makes sense
twilit field
0 = (v_1-u_1) + ... + (v_m - u_m) is one way of writing zero. but you are only a...
why though
why all 0s
runic hamlet
why though what
novel herald
it's the assumption
twilit field
I could assume they're all one then
steep knoll
I don't know if I'm right, but it seems to me that the definition of direct sum is being confused with what it seeks to demonstrate...
novel herald
twilit field
that's what we want to prove
tribal temple
"Now suppose that the only way to write 0 as a sum..."
twilit field
ah
twilit field
why though what
why are all the elements 0
novel herald
we are trying to prove for V1, ..., Vm subspaces of V,
- if V1 + ... + Vm is a direct sum, then the only way to write 0 = v1 + ... vm is by taking each vk = 0
- if the only way to write 0 = v1 + ... + vm is by taking each vk = 0, then V1 + ... + Vm is a direct sum
twilit field
ah
novel herald
you're talking about this part right?
this part here boxed in red is working on part 2
midnight plankBOT
twilit field
.reopen
midnight plankBOT
✅
twilit field
sorry i meant two lines not two planes. pretty clearly there is only one way to ...
thanks
fleet moss
hmm, makes sense
building off this consider an additional subspace W where U + V + W is not a direct sum
twilit field
why isn't it a direct sum here
fleet moss
because you can write the vector w as u + v, which contradicts the definition
fleet moss
the defn of direct sum is that each vector in the subspace can be written as the sum of vectors in each addend subspace in only one way. if we tak $\hat{u},\hat{v},\hat{w}$ to be basis vectors for U, V, and W respectively, we have $0\hat{u} + 0\hat{v} +\hat{w} = \hat{u} + \hat{v} + 0\hat{w}$
grand pondBOT
esca (@ with reply)
fleet moss
yep
midnight plankBOT
midnight plankBOT
Available help channel!
last slate
int log(x+1)/x^2+1
midnight plankBOT
int log(x+1)/x^2+1
errant swan
Try using partial integration
midnight plankBOT
@last slate Has your question been resolved?
midnight plankBOT
Available help channel!
dawn prism
If this is true, then f(x) = 1?
midnight plankBOT
If this is true, then f(x) = 1?
subtle blaze
Let’s see, FTC says then F(b) - F(a) = b - a
zealous schooner
ahh yes
subtle blaze
That’s all you should know
zealous schooner
||first principle|| nice
subtle blaze
Differentiating both sides then f(b) - f(a) = 0
strong stump
If this is true, then f(x) = 1?
Mm no
subtle blaze
,w int -1 to 1 of x^2
grand pondBOT
subtle blaze
Differentiating both sides then f(b) - f(a) = 0
That’s not rigjt..?
Oh because it doesn’t satisfy b - a
sharp coral
Differentiating both sides then f(b) - f(a) = 0
differentiating with respect to what?
heavy falcon
Differentiating both sides then f(b) - f(a) = 0
what are you differentiating wrt
zealous schooner
Let’s see, FTC says then F(b) - F(a) = b - a
first principle from here directly gives you f'(x)=1, or f(x)=x+c
subtle blaze
what are you differentiating wrt
Lmao good point
zealous schooner
substituting that into the integral gives c=0
wait
im tripping hold on
ahhh it gives me F'(x)=1, or f(x)=1
zealous schooner
how?
dawn prism
I have a curve Г and it's length is 2pi.
It is defined on [a,b] = [-pi, pi]
So can I conclude from this formula that x'(t)^2 + y'(t)^2 = 1?
zealous schooner
non integrable?
zealous schooner
I have a curve Г and it's length is 2pi.
It is defined on [a,b] = [-pi, pi]
So c...
oh, no, definitely not
zealous schooner
If this is true, then f(x) = 1?
this only tells you something if this is true for all a, b
subtle blaze
Let $f(x) = \begin{cases}-x& -1<x<0\ 2-x & 0\leq x \leq 1\ 0&\text{otherwise}\end{cases}$
grand pondBOT
Frosst
heavy falcon
If this is true, then f(x) = 1?
ig f(x)=1 is the only possible solution here
heavy falcon
It’s 1 at x=-1 and 1 at x=1
isnt it 0 at x=-1
heavy falcon
ah yes
dawn prism
I have a curve Г and it's length is 2pi.
It is defined on [a,b] = [-pi, pi]
So c...
A curve has a unit speed if this is true. How can I change variables so that this is true for Г?
subtle blaze
Let $f(x) = \begin{cases}-x& -1\leq x<0\ 2-x & 0\leq x \leq 1\ 0&\text{otherwise}\end{cases}$
Then $\int_{-1}^1 f(x), dx= 0.5 + 1.5 = 2 = 1 - (-1)$
grand pondBOT
Frosst
hard umbra
what's even happening
subtle blaze
f is clearly not 1
subtle blaze
If this is true, then f(x) = 1?
Does this imply f(x) = 1
And I think it’s only true if it holds for all a, b, not just particular ones
zealous schooner
Yeah
If it holds true for all a, b we can use FTC and first principle
Clearly that’s not what OP is asking at all
junior flower
hard umbra
junior flower
doesn't that also hold when f(x) = 1 for nonzero x and f(0) = 0
hard umbra
oh no
midnight plankBOT
junior flower
i have no idea what just happened
hard umbra
<a:sky_wannadateOwO:1045725107903017070>
junior flower
you know i've tried a lot on you
hard umbra
true
surreal moon
<a:sky_wannadateOwO:1045725107903017070>
,w date
grand pondBOT
Requested by spelwerdzrite
midnight plankBOT
Available help channel!
slate ferry
So f(x) = x^n
midnight plankBOT
So f(x) = x^n
slate ferry
Im learning deritvatives
And im taught that the derivative of that is nx^n-1
Correct?
nova yoke
sure
slate ferry
But i remember smth that was like x^(n-1)/(n-1)
nova yoke
that emoji looks sus
nova yoke
But i remember smth that was like x^(n-1)/(n-1)
perhaps you are thinking of integration
surreal moon
But i remember smth that was like x^(n-1)/(n-1)
Nah this ain't it
slate ferry
Oh someone ❌’ed me
knotty forge
And the operator is backwards
surreal moon
If you change - with +, then yea it would be integral
slate ferry
Oh
Damn
I was about to say how does derivative of x equal log(x) and 1 at the same time
knotty forge
$\int x^n dx = \frac{1}{n+1}x^{n+1} + C $
slate ferry
So theres nothing called x^n-1/n-1 it only works with integration and its + not -
knotty forge
$\int x^n dx = \frac{1}{n+1}x^{n+1} + C $
Latex is dead for me rn
Or I got a bad connection
nova yoke
well i mean certainly there's a function whose derivative is x^(n-1)/(n-1), but that function is not x^n
slate ferry
$\int x^n dx = \frac{1}{n+1}x^{n+1} + C $
Why u talkin in- quantum physics
slate ferry
well i mean certainly there's a function whose derivative is x^(n-1)/(n-1), but ...
Oh ok
knotty forge
Why u talkin in- quantum physics
It's LaTeX. It is the markup language used to make the equations in textbooks
But it's not rendering rn for some reason
This happens sometimes on this server
slate ferry
Oh i see
robust isle
$12345$
grand pondBOT
aPlatypus
slate ferry
Ok tysm everyone
robust isle
hmm
grand pondBOT
Melvin Eugene Punymier
knotty forge
Hmmm
robust isle
$ \int x^n dx = \frac{1}{n+1}x^{n+1} + C $
slate ferry
Oh you wrote the thimg wrong
grand pondBOT
aPlatypus
knotty forge
What did I miss
robust isle
yeah idk it didn't like the spaces before and after your math
knotty forge
Lol
midnight plankBOT
knotty forge
Guess so
midnight plankBOT
Available help channel!
simple heron
The question I have is as follows:
midnight plankBOT
The question I have is as follows:
simple heron
This is a question from my practice, but I don't really know how to begin.
livid wasp
x is an angle in radians, so the first inequality just clarifies which of the equivalent angles to give. Start by isolating x in the second inequality
simple heron
.close
midnight plankBOT
simple heron
.reopen
midnight plankBOT
✅
livid wasp
First factor is correct
sin^-1(1/3) is approx 0.3398 and a valid solution
to the second factor
So is pi - sin^-1(1/3)
midnight plankBOT
Available help channel!
limpid shore
Stuck on this problem:
midnight plankBOT
Stuck on this problem:
limpid shore
Sec taking photo
Its number 3. The first part of the problem
These are the two avenues ive tried to go at this
(just the green)
On the second attempt im stuck in the weeds in the lower right hand corner
I tried the professor's suggestion and turned the -1/2 - 1/2√5 into the variable f
And in the lower right hand corner of my second attempt im trying to turn f back into -1/2 - 1/2√5
So 1 minus 1/2 is 1/2, but what do i do with 1/2√5
Or am i way off the mark?
<@&286206848099549185>
midnight plankBOT
@limpid shore Has your question been resolved?
limpid shore
It has not
thin crater
limpid shore
?
Can you please be more specific
This assignment will be due by the time someone tries to help lol
midnight plankBOT
@limpid shore Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
keen rock
midnight plankBOT
keen rock
i have to select the option that doesnt fit the pattern of other options
not sure what the pattern is
kindred wraith
what all have you checked?
keen rock
well the pattern can be anything really? difference, multiply, add, divide idk
kindred wraith
well the pattern can be anything really? difference, multiply, add, divide idk
can you tell me which grade this from
caus if it from higher grade then log might also be there
keen rock
can you tell me which grade this from
err its for an entrance exam. but it falls under the logic section, not maths section
so use anything really
keen rock
<@297297632093667328> idk if this it but all of the number are prime except 81
thanks, im pretty sure thats correct
kindred wraith
thanks, im pretty sure thats correct
yw
but that still dont make much sence
but if it works then it works
keen rock
.close
midnight plankBOT
midnight plankBOT
Available help channel!
regal violet
Assuming the average distance of the earth from the sun to be 149700000 km and the angle subtended by the sun at the eye of a person on the earth to be 32', find the sun's diameter.
How do I solve this, I searched on the net but the diagram they represented made me confused
midnight plankBOT
Assuming the average distance of the earth from the sun to be 149700000 km and t...
dark obsidian
well that basic trigonometry
we know the distance and the angle
its a triangle
|sun
|—————distance———> angle
|
regal violet
I want to add one more thing
dark obsidian
there are two same right angle triangles where we know one side of the triangle and the degree
dark obsidian
so what this question says is that the diameter of the sun is almost the same as if we drew a circle with the center in the observer and a diameter of the distance between the observer and the sun
observer ————distance———) sun
regal violet
Still not get it
dark obsidian
they essentially calculate it by calculating whats the diamater of this circle then divide it by the angle that the observer sees as the sun 32’
i will draw it better gimme a sec
regal violet
Ok
regal violet
I did not understand this as well
Explain this also
dark obsidian
the angle 32’ is how much of the big circle is the sun
thats is approximately the lenght of that arc is the diameter of the sun
regal violet
Ya got it but the distance is between the earth/observer and the surface of the sun, why are we taking to the centre of the sun
@dark obsidian ?
Or is it because of approximation
dark obsidian
it is because of approximation
midnight plankBOT
@regal violet Has your question been resolved?
Available help channel!
@last slate Has your question been resolved?
rancid jungle
can someone explain how it goes from the top line to the second line? how does it make sense
midnight plankBOT
can someone explain how it goes from the top line to the second line? how does i...
grand pondBOT
faiyrose
rancid jungle
im back, aint no way you can do this
midnight plankBOT
im back, aint no way you can do this
last slate
Check by multiplying 8 again
unreal fjord
you kinda can but that is a bit wrong
if the last term is 3^(k+1) then this is correct
unreal fjord
Hint: 5N is divisible by 5 for all integer N
or you can do it differently with what you did
which should give you two terms where both are divisible by 5
rancid jungle
i remember also trying to sub in 8^k = 5a-3^k
from p(k)
but then i got stuck on the algebra part again
:(
rancid jungle
yeah
last slate
What will be the first case then
rancid jungle
i just get stuck on the algebraic proving
p(1)
and then assuming p(k) is true
i have to prove
k+1
rancid jungle
yeah
rancid jungle
that p(k) is divisble by 5
last slate
So
rancid jungle
so p(k) = 5 * a where a is an integer
rancid jungle
ye
last slate
Now what do we do?
last slate
Yea
last slate
Wait
last slate
Do you know the formula for a^n - b^n
rancid jungle
no
rancid jungle
bro what is that B( ive never seen it in my life
this is the solutions that were given
are they like incorrect or something
do i need to know the a^n-b^n formula to do this solution
last slate
the power of 3 in the 2nd exp. Should be (k+1)
last slate
do i need to know the a^n-b^n formula to do this solution
No
last slate
rancid jungle
o
rancid jungle
i still dont know
how it got from this
to the next line
how did the 8 come infront of the brackets
where did 8^k-3^k come frojm
rancid jungle
hmmmmm
last slate
What did you get
last slate
Yeah
rancid jungle
oh
wait i redid it
and now i have
8(8^k-3^k) + 5 * 3^k+1
which means i have 8(5a) + 5*3^k+1
so 40a
which is 5 (8a+3^K+1)
last slate
How did you got 5 * 3^k+1
rancid jungle
wait im gonna draw out my working out
last slate
Yea
rancid jungle
welp i mean i got the answer eventually
but like
how was i supposed to think about adding and subtracting those specific things
especially on a test
like shit i wouldnt think of that
rancid jungle
nice. alr thanks a lot bro
last slate
Yea
midnight plankBOT
midnight plankBOT
Available help channel!
steel peak
BC is BC is a diameter
GA = AC
ABC is blocked in the circle
Triangle GAB=Triangle CAB
** I need to find that there is 2 Degrees that equal to each other in GBC and GAD**
i already found that Degree BGC of triangle GDA is equal to Degree BGC of triangle GCB
midnight plankBOT
BC is BC is a diameter
GA = AC
ABC is blocked in the circle
Triangle GAB=Tria...
midnight plankBOT
@steel peak Has your question been resolved?
lofty summit
wait im anaylising
steel peak
Okt hnaks
lofty summit
jst gimme 2 or 3 mins i have to do smth rlly quickly
steel peak
alr
lofty summit
BC is BC is a diameter
GA = AC
ABC is blocked in the circle
Triangle GAB=Tria...
so what are you trying to find?
steel peak
so what are you trying to find?
I need to find that there is 2 Degrees that equal to each other in GBC and GAD
lofty summit
ok i can help but it might take a while cuz i am also revising for a big test on friday
is it alright if i dm u
simple frost
$\int \frac{3}{ (t(t^3 + 1))}$
midnight plankBOT
$\int \frac{3}{ (t(t^3 + 1))}$
grand pondBOT
Pogram
oblique ocean
That's good
simple frost
so
oblique ocean
so what
simple frost
how to do this
.
oblique ocean
idk
simple frost
since there are no dt
bro just assume its there 🤦♂️
proud island
ok
proud island
I will turn dt to d(t^3+1)
oblique ocean
why
oblique ocean
or using partial fraction
agree this
proud island
partial fraction worked
oblique ocean
it always works.
proud island
it always works.
no, not always
simple frost
partial fraction worked
share
proud island
have you learnt parital fraction?
oblique ocean
yeah partital fraction will work
simple frost
have you learnt parital fraction?
yeah tell me how u did it
proud island
so first you do partial fraction in 3/(the thing)
you can separate three terms
after that do integration
ye
shut canyon
"Solve the equation on the set of real numbers."
midnight plankBOT
"Solve the equation on the set of real numbers."
shut canyon
is this an iff statement a iff b?
how to think meaningfully about this task with logic?
is $log_a{b}$ a function $f$ such that $f(a, a^c)=c$?
grand pondBOT
kytsu
dull yoke
@shut canyon what have you tried
midnight plankBOT
@shut canyon Has your question been resolved?
grand pondBOT
kytsu
dull yoke
$2^{x-3} = 2^x - 7$
grand pondBOT
shut canyon
wait this is for
$$
\begin{aligned}
& f: \mathbf{R} \rightarrow \mathbf{R}, f(x)=2^{x-3} \
& g: \mathbf{R} \rightarrow \mathbf{R}, g(x)=2^x-7
\end{aligned}
$$
dull yoke
This is ur problem?
grand pondBOT
kytsu
shut canyon
This is ur problem?
yes!
dull yoke
Ok now what did u do
shut canyon
to find solution where f(x) = g(x)
dull yoke
Yes, what did u do
grand pondBOT
kytsu
dull yoke
Just show me ur solution and I’ll help
shut canyon
this
shut canyon
Just show me ur solution and I’ll help
thanks
dull yoke
I don’t think that’s a proper solution
grand pondBOT
kytsu
shut canyon
$a^{x-b} = a^x - c$
grand pondBOT
kytsu
dull yoke
Expand the left sidee
shut canyon
Expand the left sidee
$\frac{a^x}{a^b} = a^{x} - c$
grand pondBOT
kytsu
shut canyon
$a^x = (a^b)(a^{x} - c)$
grand pondBOT
kytsu
shut canyon
$\frac{a^x}{a^{x} - c} = a^b$
grand pondBOT
kytsu
dull yoke
**kytsu**
Now get all terms with an x to one side, and all terms without an x to the other sized
dull yoke
$\frac{a^x}{a^b} = a^{x} - c \newline \newline a^x - \frac{a^x}{a^b} = c \newline \newline a^x \left (1- \frac 1{a^b} \right ) = c \newline \newline a^x = \frac c{1 - a^{-b}} \newline \newline x = \log_a {\frac c{1 - a^{-b}}}$
grand pondBOT
dull yoke
@shut canyon
midnight plankBOT
@shut canyon Has your question been resolved?
midnight plankBOT
shut canyon
.reopen
midnight plankBOT
✅
shut canyon
$\frac{a^x}{a^b} = a^{x} - c \newline \newline a^x - \frac{a^x}{a^b} = c \newlin...
oh thanks so much!
midnight plankBOT
@shut canyon Has your question been resolved?
twilit field
midnight plankBOT
twilit field
so to start
the zero vector is a common element of both sets by definition and thus is an element of the intersection
next let $v+u\in V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
where $v,u \in V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
so as $v+u$ belongs to this set, the set is closed under addition
grand pondBOT
ƒ(Why am. I here)=lin-alg
misty gorge
you can’t just say let v+u be in both
you have to prove that
otherwise your reasoning is circular
misty gorge
if i ask you “why is v+u in the intersection whenever v and u are” your reason cannot be “because i defined it that way”
the definition of intersection will be useful to you. you are also allowed to define u and v to each be in the intersection individually
grand pondBOT
ƒ(Why am. I here)=lin-alg
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
twilit field
okay, let $v,u \in V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
then $v +u \in V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
misty gorge
why
twilit field
because $v,u \in V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
misty gorge
yeah but that’s what we’re trying to show, that if v,u in V1 cap V2 that v+u is
like how do i show that anything is in V1 cap V2 (because we do not yet know a priori that V1 cap V2 is closed under addition)
twilit field
yeah, I'm lost
hard umbra
it would be good to consider why the proof would be wrong if you said
[ v, u \in V_1 \union V_2 \textss{so} v + u \in V_1 \union V_2 ]
grand pondBOT
prime hornet
hello mayday
misty gorge
yeah, I'm lost
what is the definition of intersection
prime hornet
🙂
twilit field
what is the definition of intersection
the elements common to both the sets belong in the intersection
misty gorge
the elements common to both the sets belong in the intersection
okay. so we have to show that this is true for u+v
so all that we have to do is show that u+v is in V1, and then show that u+v is in V2
twilit field
yes
||I have no idea how to do that || but as I'm doing this just for fun, I would love a hint
misty gorge
okay, so why is u+v in V1? (now we actually know a priori that V1 is closed under addition)
because V1 is a vector space.
grand pondBOT
ƒ(Why am. I here)=lin-alg
misty gorge
yes, so that’s it then. if i take u, v both in the intersection, then we know two facts:
- they’re both in V1
- they’re both in V2
and then we can use the fact that V1 and V2 are vector spaces to achieve all the desired properties of the intersection of the two
thats the general outline for this stuff
misty gorge
you should also consider why it doesn’t work for the union
misty gorge
and what about being disjoint makes the statement untrue?
can you give me a specific counterexample?
in fact, the subspaces don’t have to be disjoint for the union to fail!
twilit field
in that case how is this statement true
twilit field
yes
misty gorge
because once you know that both u and v are in V1 you know that u+v is, which the intersection guarantees that u and v are, and same for V2
but if you only say “or”
well then you can be clever
by taking u in V1 but not V2
and v in V2 but not V1
then it’s a tossup where u+v could POSSIBLY be you know?
but certainly outside both spaces
so we managed to leave the union
twilit field
yeah, makes sense
misty gorge
What's with the disjoint subspace?
we don’t need disjointness actually
misty gorge
Shouldn't "0" be in all subspaces?
i was taking disjoint to mean the intersection only contains the 0 vector
last slate
Ic
twilit field
so we managed to leave the union
now what
misty gorge
now the union can’t be a subspace
because it’s not closed under the induced operation
but the intersection didn’t allow us to do funny business
twilit field
ok, makes sense
let me try to sketch something similar for closure under multiplication
last slate
Meanwhile
last slate
now the union can’t be a subspace
Can think how to prove this. But can't really think of any examples
misty gorge
Can think how to prove this. But can't really think of any examples
do you have any examples of a vector space in mind?
try R^3
twilit field
so we have a common element $t$ belonging to $V_1 \cap V_2$
misty gorge
think about some subspaces
last slate
Real
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
then $\lambda t \in V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
misty gorge
then $\lambda t \in V_1 \cap V_2$
why
again, you don’t a priori get that V1 cap V2 is closed under scalar multiplication
since we are trying to prove that
twilit field
but $\lambda t \in V_1$
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
and $\lambda t \in V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
as it belongs to both $V_1$ and $V_2$, it must belong to $V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
misty gorge
okay, and now we have proved that the intersection is closed under scalar multiplication
it’s good if you’re slightly annoyed at my insistence that we do this
misty gorge
what book are you using?
twilit field
Linea algebra done right, though @prime hornet has suggested FIS too, planning to use that after I finish LADR
prime hornet
wait what
misty gorge
ic
robust isle
\int Why am I here = LADR
misty gorge
is there a reason for the linear algebra? do you wanna do geometry after?
not that there has to be a reason, linear algebra is fulfilling in its own right
prime hornet
mayday with the diff geo propaganda again 
twilit field
is there a reason for the linear algebra? do you wanna do geometry after?
planning to major in maths , so trying to get a head start
prime hornet
please convince physicsrocks to do DG 
hard umbra
do representation theory instead
subtle blaze
Represent deez nuts 🥜
hard umbra
rep theory has all the linalg
twilit field
do representation theory instead
it's not mentioned in my college's prospectus
for now I just need to get a head start
subtle blaze
please convince physicsrocks to do DG <:awoo:586078682985267211>
You could convince him
Take him under your wing!!
twilit field
as it's a private uni, I need a perfect GPA
subtle blaze
I personally think chasing grades don’t get you anywhere but I’m nowhere so what do I know
twilit field
I personally think chasing grades don’t get you anywhere but I’m nowhere so what...
I want to study at an oxbridge college eventually so I need those good grades
and researdch papers
I do love maths
misty gorge
I do love maths
epic
subtle blaze
Be ambitious but don’t beat yourself up if you don’t hit goals that aren’t realistic for everyone
twilit field
👍
so to summarise the proof
a) the zero element belongs in the intersection by definition
subtle blaze
By definition of what
twilit field
subspaces
subtle blaze
Yep
twilit field
b) $\lambda t \in V_1$ and $\lambda t \in V_2$ as it belongs to both $V_1$ and $V_2$, it must belong to $V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
subtle blaze
Where does t come from
twilit field
t is an element of $V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
subtle blaze
Yes
subtle blaze
Remember you want to show $t\in V_1\cap V_2 \implies \lambda t\in V_1\cap V_2 ,\forall \lambda \in K$
twilit field
**Frosst**
I showed that
hard umbra
frosst using K for the field
subtle blaze
K-vector space
subtle blaze
I showed that
Yeah but remember to start on the left side
subtle blaze
**ƒ(Why am. I here)=lin\-alg**
You didn’t say this until I asked
twilit field
**ƒ(Why am. I here)=lin\-alg**
then we have $v+u \in V_1$ and $v+u \in V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
twilit field
as it belongs to both $V_1$ and $V_2$, it must belong to $V_1 \cap V_2$
grand pondBOT
ƒ(Why am. I here)=lin-alg
subtle blaze
Yep
twilit field
thanks so much everyone!
subtle blaze
If $v, u\in V_1 \cap V_2\subseteq V_1$ then $v, u \in V_1$ and $v + u \in V_1$ since $V_1$ is a subspace
grand pondBOT
Frosst
subtle blaze
You could write it like that as well
midnight plankBOT
midnight plankBOT
Available help channel!
analog perch
if i move the ball on the left of the beam "x" meters over to the right, how would i calculate how much i need to move the fulcrum over to balance out the system?
midnight plankBOT
if i move the ball on the left of the beam "x" meters over to the right, how wou...
sharp coral
you need the moment/torque due to the weights of each ball to balance out
analog perch
you need the moment/torque due to the weights of each ball to balance out
the first part of the problem asked me to find W and i found it
by using this equation
but im confused because now that the fulcrum needs to move, dont i have 2 unknowns and cant solve the problem?
or i guess 3 unknowns?
since i dont know any of the d's anymore
sharp coral
if the fulcrum moves "y" distance, then the distance of each force from the fulcrum will increase or decrease by "y"
analog perch
oh and i can solve for y
i see i see
@sharp coral something like this look right?
the question says the weight on the left (W_1) moves 27.5 cm to the right
which is why i have the -0.275
there has to be an easier way
than solving that long ass equation
midnight plankBOT
@analog perch Has your question been resolved?
midnight plankBOT
ornate fable
i did working out it wasnt correctg
gilded turtle
Show your work
gilded turtle
Tan is opp over adj
ornate fable
is it not the same tho?
abstract iron
the q says east then north ur calculating if something went 54 south then 38 east
gilded turtle
Wait is x your angle ?
ornate fable
yh
ornate fable
Wait is x your angle ?
yeha and i need to work it out
i did the working out i was thought it didnt work
ornate fable
Tan is opp over adj
i did both ways it doesnt work
abstract iron
ur drawing is off, pay attention to the directions given
midnight plankBOT
midnight plankBOT
Available help channel!
molten rune
I'm following along and working through a pre-recorded review tutor session to study for an upcoming test and something isn't sitting right with me about this one...did this skip the chain rule? Shouldn't the 3x get derived out too?
midnight plankBOT
I'm following along and working through a pre-recorded review tutor session to s...
molten rune
Not my work, it's the tutor's work, but it's not a live tutor session so I can't ask directly and I want to make sure I understand how to approach this correctly
molten rune
Ohhh--it got solved first. I was under the impression that chain rule works from the outside in--is that not always the case?
sharp coral
what do you mean by "solved first"?
molten rune
derived first, i mean.
sharp coral
they first took the derivative of the outside function
cos(3x) -> -sin(3x)
then multiplied by the derivative of the inside, which is 3
molten rune
ahhh, okay. for some reason i thought the product rule was supposted to happen first. i misremembered.
Thanks for clearing that up!
.close
midnight plankBOT
midnight plankBOT
Available help channel!
austere rose
<@&286206848099549185>
austere rose
<@&286206848099549185>
midnight plankBOT
@austere rose Has your question been resolved?
austere rose
<@&286206848099549185>
midnight plankBOT
@austere rose Has your question been resolved?
austere rose
<@&286206848099549185>
weak cairn
In parametric surface you have 2 variable
weak cairn
<@&286206848099549185>
x=u
y=v
z=√(9-u^2)
austere rose
Thanks!
brisk canyon
How do I use Moore-Penrose pseudoinverse to find the orthogonal projection of a velocity matrix?
Hi all, I have a set of (196, 196, 40, 10) images where the first 3 axes are x, y, z and the last are measurements with weightings in different directions. I am trying to follow the paper https://onlinelibrary.wiley.com/doi/full/10.1002/mrm.24390 which claims that "If all velocity estimates v̂i are correctly unwrapped, then the reconstructed velocity vector is equation 9". The paper then goes on to use this as a basis for a phase unwrapping technique, but I was wondering if I could use that equation to find orthogonal projections (along x, y, z) of my 10 velocity contributions if I have already unwrapped the phase? If so, I am struggling to understand how to achieve that. I have a 10x3 matrix that shows the weighting in x, y, z directions for each of the 10 measurements. If I use numpy.linalg.pinv I get a 3x10 matrix of some numbers. Doing a dot product of the 3x10 and 196x196x40x10x3 results in a 3x196x196x40x3 matrix and I'm lost. Any guidace would be appreciated.
midnight plankBOT
How do I use Moore-Penrose pseudoinverse to find the orthogonal projection of a ...
pastel spoke
That’s one of my favorite games
midnight plankBOT
@brisk canyon Has your question been resolved?
midnight plankBOT
@brisk canyon Has your question been resolved?
midnight plankBOT
@brisk canyon Has your question been resolved?
midnight plankBOT
@brisk canyon Has your question been resolved?
midnight plankBOT
@brisk canyon Has your question been resolved?
midnight plankBOT
@brisk canyon Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
oblique forum
I think it's 4-sin(3)
midnight plankBOT
I think it's 4-sin(3)
@oblique forum Has your question been resolved?
Available help channel!
twilit field
$\frac{\lim_{x\rightarrow0}4x\left(\tan\left(x\right)-2x\tan\left(x\right)\right)}{\left(1-\cos\left(2x\right)\right)}$
midnight plankBOT
$\frac{\lim_{x\rightarrow0}4x\left(\tan\left(x\right)-2x\tan\left(x\right)\right...
grand pondBOT
ƒ(Why am. I here)=I don't know
slender walrus
is lim supposed to be for the whole thing?
twilit field
yes
stone kernel
u fcked up the formatting m8
twilit field
can you l'hopital that shit?
I was thinking of using series expansions
stone kernel
its piss easy
twilit field
I'll re format it
stone kernel
if you remove a single bracked
slender walrus
looks loke you can do double angle identity
twilit field
just a minute
slender walrus
then limit identity for sin(x)/x
twilit field
I know, I just like working in channels
twilit field
$\frac{\lim_{x\rightarrow0}\left(4x\left(x-2x^2\right)\right)}{\left(2x^2\right)}$
grand pondBOT
ƒ(Why am. I here)=I don't know
twilit field
which is 2, I think
slender walrus
take that lim outta the frac
twilit field
$\ \lim_{x\rightarrow0}\left(\frac{\left(4x\left(x-2x^2\right)\right)}{2x^2}\right)$
grand pondBOT
ƒ(Why am. I here)=I don't know
slender walrus
yeh, looks like 2
twilit field
which is 2
yeah
thanks
Can I use this channel for rough work for the next few hours?
If I need help I'll ping helpers
twilit field
okay
slender walrus
would probably be better and ask clarifying question when required
twilit field
I'll create my own server and use it there perhaps?
how do I invite texit to my server ?
.close
midnight plankBOT
midnight plankBOT
Available help channel!
twilit field
$\int_0^{\frac{\pi}{4}} ln(1+tan(x))dx$
midnight plankBOT
$\int_0^{\frac{\pi}{4}} ln(1+tan(x))dx$
grand pondBOT
ƒ(Why am. I here)=I don't know
twilit field
which is the same as
$\int_0^{\frac{\pi}{4}}\ln\left(1+\tan\left(\frac{\pi}{4}-x\right)\right)$
grand pondBOT
ƒ(Why am. I here)=I don't know
twilit field
$\int_0^{\frac{\pi}{4}}\ln\left(1+\frac{\left(1-\tan\left(x\right)\right)}{1+\tan\left(x\right)}\right)$
grand pondBOT
ƒ(Why am. I here)=I don't know
twilit field
$\int_0^{\frac{\pi}{4}}\ln\left(\frac{2}{1+\tan\left(x\right)}\right)$
grand pondBOT
ƒ(Why am. I here)=I don't know
twilit field
which is
$\int_0^{\frac{\pi}{4}}\ln\left(2\right)-\ln\left(1+\tan\left(x\right)\right)$
grand pondBOT
ƒ(Why am. I here)=I don't know
grand pondBOT
ƒ(Why am. I here)=I don't know
grand pondBOT
midnight plankBOT
midnight plankBOT
Available help channel!
night flint
midnight plankBOT
night flint
Is this proof valid?
rare pine
yes
midnight plankBOT
@night flint Has your question been resolved?
midnight plankBOT