everg
#help-19
clever fjordBOT
pastel dew
?
tired crystal
yeah
pastel dew
so -1 maps to 1
tired crystal
oh wait
pastel dew
i.e. f(-1)=1
pastel dew
😉
tired crystal
oh so it becomes surjective
pastel dew
yes
pastel dew
odd edgeBOT
odd edgeBOT
Available help channel!
autumn shard
so I have a linear algebra question set as shown below
i've found the answer to (a): $\textbf{r} = \langle 3, -2, -6 \rangle + \mu \langle cos \theta - sin \theta , sin \theta , cos \theta \rangle$
i've also found the answer to (b) (it's very long and probably not relevant)
however, while working on (c) i've hit a roadblock. I understand that I can use the dot product of two vectors to find the angle between them, so i evaluated $\frac{\langle sin \theta , cos \theta, sin \theta + cos \theta \rangle \cdot \langle cos \theta - sin \theta , sin \theta , cos \rangle}{\sqrt{sin^2 \theta + cos^2 \theta + sin^2 \theta + 2 sin \theta cos \theta + cos^2 \theta} \sqrt{cos^2 \theta - 2 sin \theta cos \theta + sin^2 \theta + sin^2 \theta + cos^2 \theta}}$ which gave me $\frac{3 sin \theta cos \theta - sin^2 \theta + cos^2 \theta}{2 \sqrt{1 + sin \theta cos \theta} \sqrt{1 - sin \theta cos \theta}}$. then because $cos(60^{\circ}) = \frac{1}{2}$, $\sqrt{1 + sin \theta cos \theta} \sqrt{1 - sin \theta cos \theta} = 3 sin \theta cos \theta - sin^2 \theta + cos^2 \theta$
clever fjordBOT
haru~
autumn shard
but i'm not too sure where to proceed from here
using wolfram alpha it appears that there is a valid solution but i don't know how it got there
also i'm not actually sure if my process is right
my first instinct is to square both sides of the equation, is that the right way to go?
odd edgeBOT
@autumn shard Has your question been resolved?
autumn shard
okay so i squared both sides of the equation and got the answer $\theta = tan^{-1}(\frac{1+\sqrt{5}}{2}) = 58.3^{\circ}$
clever fjordBOT
haru~
autumn shard
it checks out with what wolfram alpha says are the solutions to the equation but i plotted the lines and it seems to be wrong
my work so far
<@&286206848099549185>
autumn shard
it checks out with what wolfram alpha says are the solutions to the equation but...
wolfram also agrees with me on my original equation (1/2 = the large eqn with the dot product)
i'm not sure if my graphical checking is wrong or if i'm wrong
or both
autumn shard
okay so i squared both sides of the equation and got the answer $\theta = tan^{-...
more specifically i got 0, 58.3 ± nπ, -31.7 ± nπ, but that's the only one in range
odd edgeBOT
@autumn shard Has your question been resolved?
autumn shard
<@&286206848099549185>
odd edgeBOT
@autumn shard Has your question been resolved?
autumn shard
(my answer is correct my geogebra that i was using to check my work was having some bugs)
.close
blazing stirrup
I am wondering if I setup this integral correctly
odd edgeBOT
I am wondering if I setup this integral correctly
blazing stirrup
odd edgeBOT
@blazing stirrup Has your question been resolved?
odd edgeBOT
@blazing stirrup Has your question been resolved?
blazing stirrup
.close
odd edgeBOT
odd edgeBOT
Available help channel!
lean wasp
odd edgeBOT
odd edgeBOT
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
2
south plume
show your process
lean wasp
lean wasp
but in the problem it said that x couldnt = 1?
does that not matter since c is continuous?
south plume
i think you are misreading
$f(x) = \begin{cases}\frac{x^2 - 3x +2 }{x-1} \text{ for } x \neq 1 \ c \text{ for } x=1\end{cases}$
clever fjordBOT
artemetra
south plume
this is how they defined f(x)
south plume
does that not matter since c is continuous?
your task is to pick such value of c that will make f(x) (and not c) continuous
south plume
the mistake is on the third step
okay mb
lean wasp
so would c be (-inf, 1) u (1, inf) ?
south plume
okay mb
what you did there was not incorrect, but it would be better if it was slightly more rigorous
but the final conclusion is wrong
south plume
so would c be (-inf, 1) u (1, inf) ?
i am not sure why you are thinking c is an interval/element of an interval
what your question is asking you to do is fix a removable continuity
here's what the graph looks like
the function behaves exactly the same as the x-2 function except at the point x=1, where it is undefined (because we are dividing by 1)
your task is to fill that hole in with such value c that will make the whole thing continuous
lean wasp
ohh i see, my mistake was entering the equation wrong on desmos so that there would be a vert asymp at 1, and that was why I had a range
so i would just have to plug in 1 for x in x-2?
south plume
yep
lean wasp
Oh ok thank ypu!
south plume
that will be your value of c
lean wasp
-1
lean wasp
thank you sm
south plume
no problem; if you are done, type ".close"
lean wasp
.close
odd edgeBOT
civic yacht
1+1=3
odd edgeBOT
Available help channel!
small sail
odd edgeBOT
odd edgeBOT
@small sail Has your question been resolved?
small sail
.close
odd edgeBOT
ember oak
It gives me the time but nothing else
Do you know the equation for free fall?
small sail
No
ember oak
.reopen
odd edgeBOT
✅
clever fjordBOT
SWR
small sail
But how do I calculate the acceleration without anything else
I’m only given the time
dusty badger
But how do I calculate the acceleration without anything else
differentiate the equation of velocity with respect to time
and then substitute the value of t in the equation u get after differentiation
ember oak
But how do I calculate the acceleration without anything else
@small sail, acceleration due to gravity on earth is a known value
$g\approx-9.8 \text{ m s}^{-2}$
clever fjordBOT
SWR
small sail
.close
odd edgeBOT
odd edgeBOT
Available help channel!
snow hemlock
how ould i find the cartesean equation of a line with an angle of 5/6 pi
snow hemlock
if it starts at 0,0
snow hemlock
You can only find the slope.
yeahh thats what im finding difficult to find
ember oak
!xy
odd edgeBOT
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.
snow hemlock
a) arg(z) = 5pi/6
i) display in cartesian form and ii) draw the locus of points represented by the complex number
snow hemlock
a) arg(z) = 5pi/6
i) display in cartesian form and ii) draw the locus of points...
@ember oak
ember oak
Oh so it's complex analysis
That extra context helps a lot
then your extra point is the origin: (0, 0)
snow hemlock
so the equationj would just be y=-(?)x + 0
im just not sure how to find the value of x
is it just trigonometry
snow hemlock
im just not sure how to find the value of x
im just not sure how to find the value of (?)
mb
ember oak
$m=\tan{\theta}$
clever fjordBOT
SWR
odd edgeBOT
Available help channel!
lean wasp
how to find inverse of this? I got to 2^y = 2^x -1 but I don’t understand how to isolate the y
ember oak
how to find inverse of this? I got to 2^y = 2^x -1 but I don’t understand how to...
you take log of both sides
ember oak
how to find inverse of this? I got to 2^y = 2^x -1 but I don’t understand how to...
Inverse of what, btw?
oh
I see. I read it backwards
You are trying to solve for $x$ in $y=\log_2 (2^x-1)$?
clever fjordBOT
SWR
lean wasp
yes
lean wasp
how to find inverse of this? I got to 2^y = 2^x -1 but I don’t understand how to...
I set x in that equation to y and tried to solve for y here
ember oak
Then yes, you take log of both sides
mystic saffron
you're on the right track
mystic saffron
how to find inverse of this? I got to 2^y = 2^x -1 but I don’t understand how to...
btw shouldn't it be 2^y -1 = 2^x?
assuming you switched your y and x (you are solving for y)
silent dust
😭 😭
lean wasp
Is this right 🧍♂️🧍♂️🧍♂️
mystic saffron
uh so
nimble blaze
no
clever fjordBOT
nimble blaze
it supposed to be apply log to each side, not log to each term
mystic saffron
you were right up to 2^x + 1 = 2^y
mystic saffron
like
its best to denote the base of your log operation here
what base is your logarithm?
also that last line is nonsensical
lean wasp
2.. i think…
clever fjordBOT
lean wasp
Oh my god I can’t believe I forgot that rule
AHHH ITS Y TIMES 1 IHHFECIEUFHCFUHEC
thanks 😭
lean wasp
mystic saffron
yeah alrighty
naive hollow
Anyone know how to math a good xp scaling for a game?
odd edgeBOT
Anyone know how to math a good xp scaling for a game?
@naive hollow Has your question been resolved?
vagrant blaze
- How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?
I know the answer is 125, but that doesn't make any sense to me, because that's 5 x 5 x 5 x 1 for each slot, but you can't place a 0 in front of the number and ahve it be distinct from the other combinations.
wise jasper
Why can't the leading number be 0?
nimble blaze
you didn't consider non- 4 digit numbers
vagrant blaze
Why can't the leading number be 0?
0346 is the same number as 346
vagrant blaze
you didn't consider non- 4 digit numbers
OHHHHHHHHH
wise jasper
It says positive odd integers, not positive four-digit integers
wise jasper
0346 is the same number as 346
which is still an answer
vale sand
So does the question mean they want all 4 in one or just for all awnsers to include those numbers
wise jasper
What?
nimble blaze
So does the question mean they want all 4 in one or just for all awnsers to incl...
what?
vagrant blaze
which is still an answer
no it's not lol
i just got the answer, and it's 4x5x5x1 + 4x5x1 + 4x1 + 1 like math symbol guy was saying
ty love
vagrant blaze
😭
odd edgeBOT
odd edgeBOT
Available help channel!
west pond
Made a mistake there, meant help 14
I have some questions about the logic in these messages: #help-14 message
If I set m = lg(n) for convenience, do I need to sub the lg (n) back in at the end?
toxic monolith
If I set `m = lg(n)` for convenience, do I need to sub the `lg (n)` back in at t...
if you get the result, then no need to return to old vairable
m is a helper variable to help you get the result
toxic monolith
too small for me :))
west pond
If you open in browser you can see the full resolution version and scroll through it
toxic monolith
yes i know, , you do that well, due to hints, very well
west pond
Oh whoops
I left that at the bottom
It’s directed towards the math problem, not you:)
toxic monolith
though maybe numbers you calcualted wrong shud i compute it and shwo it to you ?
in my opnion you shud 24 in numerator
have*
ah i see you were cancelling sth ok
west pond
Yup
toxic monolith
i omitted in my demonstration jsut to shwo you the beginning
west pond
The sqrt(2)
toxic monolith
yes
west pond
But my question is, with l’hopital’s rule, I’m supposed to take the derivative of both the numerator and denominator
west pond
Doesn’t that mean I need to treat m as a complex function?
toxic monolith
can be considered as a genrral term of certian series
and then you can easily prove
that series is covnmegrent
due to cauchy criterion
hence general term goes to zero
that is more elegant than hopsital
toxic monolith
Doesn’t that mean I need to treat m as a complex function?
m is real
this series is convergent due to Cauchy theorem
in sua you cal it as root test
and then
west pond
Yes
toxic monolith
How is m real?
real but not negative
toxic monolith
of course it is
n is natural
goes to inf
log is real
and you wrote
sqr( log n )
0
west pond
Okay that makes sense
toxic monolith
Okay that makes sense
it is A MUST 🙂
odd edgeBOT
@west pond Has your question been resolved?
toxic monolith
But thank you:)
yvw)
odd edgeBOT
@west pond Has your question been resolved?
light inlet
is this right?
odd edgeBOT
@light inlet Has your question been resolved?
odd edgeBOT
@light inlet Has your question been resolved?
north jasper
Good drawing
odd edgeBOT
@light inlet Has your question been resolved?
edgy stag
KAPOW
zenith tusk
odd edgeBOT
zenith tusk
hi could someone give me a hint on how to start this please
west merlin
ln(ab)=ln(a)+ln(b)
and ln(a/b)=ln(a)-ln(b)
also ln(a^b)=b*ln(a)
those rules should be enough for you to complete this
zenith tusk
and ln(a/b)=ln(a)-ln(b)
Start by ln = pq^2 - root r
edgy stag
Start by ln = pq^2 - root r
Do you know your log rules?
what wumbo stated are the rules you should know to solve these
zenith tusk
Yea the 3 Wumbo sent I have learnt
edgy stag
Yea the 3 Wumbo sent I have learnt
ok well in that case what rule do you think you should use first to simplify a)
zenith tusk
The minus one
edgy stag
correct
zenith tusk
The 2nd
zenith tusk
So I need to make ln p the subject ?
edgy stag
nope, all you need to do is express it in turns of ln p, ln q, and ln r, meaning that things like lnpq^2 should be changed
in a way, detangle the ln pq^2 to something that uses ln p, ln q, or if necessary, ln r
zenith tusk
Do I make pq^2 into pq then move the squared in front of the ln so it becomes 2log 10(pq)?
Hopefully that makes sense what I just said
edgy stag
no, you cannot apply the power rule as of right now, because you have $\ln pq^2$, not $\ln (pq)^2$ remember the power rule only applies when the entire thing being natural log'd has a power
clever fjordBOT
Friska
edgy stag
in this case, you have the ln of the product of two numbers
so you should use ln(ab)=ln(a)+ln(b) rule
THEN you can use the power rule if needed
zenith tusk
Ahh I see
edgy stag
So $\ln pq^2 = $\ln p + \ln q^2$
clever fjordBOT
Friska
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
edgy stag
no
zenith tusk
Yea nvm I saw the msg
edgy stag
Try your best to apply rules like ln(ab)=ln(a)+ln(b) accurately to a situation like these
zenith tusk
Yea
Where would the brackets go then or is this entire equation inside the ln bracket
edgy stag
So now we have $\ln p + \ln q^2 - \ln \sqrt{r}$
clever fjordBOT
Friska
edgy stag
Where would the brackets go then or is this entire equation inside the ln bracke...
wdym?
well we don't need brackets here
zenith tusk
**Friska**
Oh nvm I got it
edgy stag
now if you want, use the power rule and put the 2 in front of ln q
zenith tusk
So when u are multiplying u just add the log in front of both of the variables u are combining together
edgy stag
and same thing for r, except its 1/2
edgy stag
So when u are multiplying u just add the log in front of both of the variables u...
once again, the rule is ln(ab) = ln(a) + ln(b)
that's all you need to know
zenith tusk
I just get confused by ln I just need to tell myself that ln is just log 10
edgy stag
ln is not log 10
zenith tusk
Oh
edgy stag
$\ln x = \log_{e}{x}$
zenith tusk
Isn’t just a simplified version something or am I getting it mixed up with something else
clever fjordBOT
Friska
edgy stag
Isn’t just a simplified version something or am I getting it mixed up with somet...
ln is log with base e, I think you are thinking about when you see log without a base, when you see log without an explicit base, then it is by default base 10
but if you just see ln, that stands for "natural log", which means it is the same as log with a base e
zenith tusk
Ahh ok
edgy stag
yeah
now try to do the rest of the questions yourself
and remember, to look at what's inside ln
and break it up bit by bit
as according to the log rules
zenith tusk
So basically ln = loge x
edgy stag
yes
zenith tusk
Ok ok ty
edgy stag
or in other words $\log_{e}x = \ln x = y \\ \therefore e^y = x $
zenith tusk
So then the final answer I have is ln p + 2*ln q - ln root r
edgy stag
$\log_{e}x = \ln x = y \ \therefore e^y = x$
clever fjordBOT
Friska
edgy stag
So then the final answer I have is ln p + 2*ln q - ln root r
yes, and you can simplify the ln root r too if you like
using the same power rule
incase you don't know, $\sqrt{x} = x^frac{1}{2}$
woops
hang on
incase you don't know, $\sqrt{x} = x^\frac{1}{2}$
clever fjordBOT
Friska
zenith tusk
Ye ye I get that I’ll do it ty
edgy stag
yep, good luck!
zenith tusk
yep, good luck!
Tysm for helping me and for ur time
edgy stag
no worries
odd edgeBOT
@zenith tusk Has your question been resolved?
quasi tapir
Heyyy Can anyone here help me write the PLDU Decomposition of a matrix in python without using any libraries ?
quasi tapir
def pldu(M):
n = len(M)
P = [[0 if i != j else 1 for j in range(n)] for i in range(n)]
L = [[0 for _ in range(n)] for _ in range(n)]
U = [[0 for _ in range(n)] for _ in range(n)]
D = [[0 for _ in range(n)] for _ in range(n)]
A = [row[:] for row in M] # Copy of M to avoid modifying the original
for i in range(n):
L[i][i] = 1
for k in range(n):
# Find pivot for column k
maxindex = max(range(k, n), key=lambda x: abs(A[x][k]))
if k != maxindex:
P[k], P[maxindex] = P[maxindex], P[k]
A[k], A[maxindex] = A[maxindex], A[k]
# Decompose A into L and U
for i in range(k+1, n):
if A[k][k] == 0:
continue # Skip if pivot is zero
L[i][k] = A[i][k] / A[k][k]
for j in range(k, n):
A[i][j] -= L[i][k] * A[k][j]
# Extract D and set U's diagonal elements to 1
for i in range(n):
D[i][i] = A[i][i]
U[i][i] = 1
for j in range(i+1, n):
U[i][j] = A[i][j] / D[i][i]
return P, L, D, U
This is my current code it is failing for the matrix|
Testing PLDU
non-singular matrix:
Verdict: Incorrect decomposition
A
[[-6. 0. 1. 5.]
[-4. -1. 1. 4.]
[-3. 1. 2. 2.]
[-1. 2. -2. -3.]]
P
[[1. 0. 0. 0.]
[0. 0. 0. 1.]
[0. 0. 1. 0.]
[0. 1. 0. 0.]]
L
[[ 1. 0. 0. 0. ]
[ 0.67 1. 0. 0. ]
[ 0.5 0.5 1. 0. ]
[ 0.17 -0.5 -0.29 1. ]]
D
[[-6. 0. 0. 0. ]
[ 0. 2. 0. 0. ]
[ 0. 0. 2.58 0. ]
[ 0. 0. 0. -0.84]]
U
[[ 1. -0. -0.17 -0.83]
[ 0. 1. -1.08 -1.92]
[ 0. 0. 1. 0.55]
[ 0. 0. 0. 1. ]]
reconstruction
[[-6. 0. 1. 5. ]
[-1. -1. 0.5 1.5]
[-3. 1. 2. 2. ]
[-4. 2. -1.5 -0.5]]
odd edgeBOT
@quasi tapir Has your question been resolved?
odd edgeBOT
quasi tapir
.reopen
odd edgeBOT
✅
quasi tapir
!status
odd edgeBOT
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
1
odd edgeBOT
@quasi tapir Has your question been resolved?
odd edgeBOT
@quasi tapir Has your question been resolved?
odd edgeBOT
@quasi tapir Has your question been resolved?
odd edgeBOT
@quasi tapir Has your question been resolved?
odd edgeBOT
@quasi tapir Has your question been resolved?
edgy stag
Heyyy Can anyone here help me write the PLDU Decomposition of a matrix in python...
Could you like, properly define what you mean by "help", what exactly are you stuck on?
Also you can have code highlighting in discord like this:
def pldu(M):
n = len(M)
P = [[0 if i != j else 1 for j in range(n)] for i in range(n)]
L = [[0 for _ in range(n)] for _ in range(n)]
U = [[0 for _ in range(n)] for _ in range(n)]
D = [[0 for _ in range(n)] for _ in range(n)]
A = [row[:] for row in M] # Copy of M to avoid modifying the original
for i in range(n):
L[i][i] = 1
for k in range(n):
# Find pivot for column k
maxindex = max(range(k, n), key=lambda x: abs(A[x][k]))
if k != maxindex:
P[k], P[maxindex] = P[maxindex], P[k]
A[k], A[maxindex] = A[maxindex], A[k]
# Decompose A into L and U
for i in range(k+1, n):
if A[k][k] == 0:
continue # Skip if pivot is zero
L[i][k] = A[i][k] / A[k][k]
for j in range(k, n):
A[i][j] -= L[i][k] * A[k][j]
# Extract D and set U's diagonal elements to 1
for i in range(n):
D[i][i] = A[i][i]
U[i][i] = 1
for j in range(i+1, n):
U[i][j] = A[i][j] / D[i][i]
return P, L, D, U```Oh I see your code failed
I would recommend telling us exactly what the issue is, or what you think might have caused the problem. I.e, please go more into details
sly barn
odd edgeBOT
sly barn
I have no idea where they get Pr(K=K_2) * 0 from. Specifically the 0. Could someone guide me ?
potent folio
I have no idea where they get Pr(K=K_2) * 0 from. Specifically the 0. Could some...
notice that there is no 1 in the second column of your encryption mapping table, so Pr(x = b) = 0
you only have 2, 3, 4
sly barn
notice that there is no 1 in the second column of your encryption mapping table,...
oh that makes sense. Thank you !! Can't believe I couldn't figure that out myself
potent folio
np!! it happens lol
odd edgeBOT
Available help channel!
tropic swan
We are in a place where we look at the empty boxes from 1 to 5;
- Let its digit appear exactly once in each row and column.
- Allow “greater than” or “less than” changes between the two boxes.
fallow wolf
We are in a place where we look at the empty boxes from 1 to 5;
- Let its digit ...
i don't understand
what is the question?
tropic swan
we fill the gaps
odd edgeBOT
@tropic swan Has your question been resolved?
ocean hamlet
How many binary strings exist that are 16 bits long and contain exactly 5 bits "1" such that between every "1" and the next "1" there are atleast 2 bits "0"?
ocean hamlet
I figured we can arrange the 1's and 0's like this 100100100100100 + a 0 that we can put in 6 places
Then what?
north crow
Actually, there are 3 0s you can move freely
ocean hamlet
Oh right
north crow
Imagine 5/6 boxes and 3 values you can put into boxes, in how many ways you can put those values?
5/6 depending on if you can put 0 at the start of binary string
ocean hamlet
(5 choose 3) and (6 choose 3) ?
north crow
Can you put 0s at the start?
And it's not choose, as you can put multiple values(0s) in the "boxes"
Rather 6^3 or 5^3
ocean hamlet
Oh yea right
Wait isn't this a multiset?
There are 5 repeating "100" and 3 free 0s
So {5 x "100", 3 x "0"}
north crow
Sounds right
ocean hamlet
8 elements total, it's a combination with repetitions
8! / 5! 3!
I don't have the solution so i don't know if its right
ocean hamlet
8! / 5! 3!
56
north crow
Rather 6^3 or 5^3
Nope, this one
odd edgeBOT
@ocean hamlet Has your question been resolved?
north crow
Find by what it is multiplied each time
Yes
Nope
It is some form of..
Do you know the formula of geometric progression?
Or you can just divide the whole sum by 3 and get 1+2+4+..+512
Yes, in this case
north crow
Or you can just divide the whole sum by 3 and get 1+2+4+..+512
Here
odd edgeBOT
@gleaming basalt Has your question been resolved?
gusty ridge
i didnt understand how to this at all
odd edgeBOT
i didnt understand how to this at all
cursive field
sqrt 27 = sqrt (9 times 3) = sqrt 9 times sqrt 3 = 3 sqrt 3
dusty badger
i didnt understand how to this at all
seperating the perfect squares from the imperfect squares
If Im not wrong
cursive field
basically, yes
dusty badger
inside the root btw
cursive field
same with 3 sqrt 12. that turns into 3 times sqrt (4 times 3) = 3 times sqrt 4 times sqrt 3 = 6 times sqrt 3
$\sqrt{27}=\sqrt{9}\cdot\sqrt{3}=3\sqrt{3}$ and $3\sqrt{12}=3\cdot\sqrt{4}\cdot\sqrt{3}=6\sqrt{3}$, basically
clever fjordBOT
ren
cursive field
you get it?
gusty ridge
wow that bot is handy ah
cursive field
ikr
gusty ridge
you get it?
gimma a sec i need to process it
clever fjordBOT
ren
cursive field
for all n
odd edgeBOT
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plucky fjord
hi
gusty ridge
.close
odd edgeBOT
cursive field
!occupied
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cursive field
(idk how to get to the how to get help channel w/o factoids)
gusty ridge
(idk how to get to the how to get help channel w/o factoids)
should i reopen this channel
cursive field
no...?
gusty ridge
HOW DID YOU DO THAT
ull get the channels
odd edgeBOT
Available help channel!
gusty ridge
Question : Rationalize the denominators
Doubt : the demonitor is postive?
dusty badger
Question : Rationalize the denominators
Doubt : the demonitor is postive?
it is positive
ur supposed to multiply and divide the ratio by the conjugate pair of the denominator
conjugate is just the opposite middle sign
its denominator is root3 + root2 then multiply and divide by root3 - root2
gusty ridge
its denominator is root3 + root2 then multiply and divide by root3 - root2
then why isnt it negative here
dusty badger
then why isnt it negative here
thats just 1 digit
multiplying by conjugate for 2 pairs is to get the formula (a+b)(a-b) = a^2 - b^2
to remove the roots
u dont need negative when it just 1 term
gusty ridge
right shit why do i find the easiest chapter the hardest
dusty badger
its fine
gusty ridge
multiplying by conjugate for 2 pairs is to get the formula (a+b)(a-b) = a^2 - b^...
are these all expansions?
dusty badger
u will get a hang on it slowly
dusty badger
are these all expansions?
what all these
dusty badger
(a+b)(a-b) = a^2 - b^2 is an expansion yeah
gusty ridge
these are expansions rights
dusty badger
yes
dusty badger
yea thanks a lot (snowflake)
Np!
gusty ridge
wait i didnt understand how (root 3 - root 2)square became 3+2 - 2 root6
nimble blaze
definition of squaring/distributive property
binomial expansion/multiplication
dusty badger
isnt it supposed to become 3 -2 as the root cancels out?
the whole expansion
its a different formula
gusty ridge
oh shit 2ab one
nimble blaze
you don't just square individual terms like that
dusty badger
(a+b)^2 = a^2 + b^2 + 2ab
gusty ridge
yea gotcha thanks
gusty ridge
<@1133427150129725560> btw close the channel if ur done
ah i was just about to
but before that
same sum
one more doubt
why can i simplify this more
dusty badger
u cant
gusty ridge
like 3+2-2
and the 3-2
gusty ridge
i can make the answer just 3 root 6 right
nimble blaze
consider whether actions would violate the order of operations
gusty ridge
right okay
nimble blaze
e.g.
2 (just the number 2 clearly not apples) + 2🍎 won't result in 4🍎
odd edgeBOT
gusty ridge
.reopen
odd edgeBOT
✅
gusty ridge
why is it not simplified in the first question and simplified in the second question given here
nimble blaze
nfi. the numerator and denominator of the first one can be simplfied
just not the way you initially proposed
plucky fjord
why is it not simplified in the first question and simplified in the second ques...
kenn
gusty ridge
nfi. the numerator and denominator of the first one can be simplfied
just not th...
right
keen tartan
Why does adding 2 functions together, f(x) and g(x), give another function a(x) where the y-value of a(x) is always the average y-value of f(x) and g(x)?
I'm searching for a more intuitive answer if that's possible.
keen tartan
I'm not too familiar with operations on functions like adding them or making a composite function.
keen tartan
Wdym? Take x=1 for example.
The red function gives out y = 1
The blue function gives out y = 6
The addition of the functions, the green function, gives out y = 3.5
nimble blaze
you divided by the sum by 2
keen tartan
Oh I didn't add the 2 functions, but I added the left side with the left, and the right side with the right.
nimble blaze
which literally gives the average
low locust
well adding the functions means y=f(x)+g(x)
what you did is 2y=f(x)+g(x)
so your option does give you the average but its not what is meant when we say adding the functions
keen tartan
Yup, things are connecting now. Lemme process things.
I can see how the green function is the average of the y's above. But why does adding the 2 equations give me their average? That's unintuitive to me.
I.e., is there an intuitive way to think about what happens when I add 2 equations together?
.
y=f(x)
y=g(x)
2y = f(x) + g(x)
Mathematically, adding 2 equations of 2 functions will give me their average instead of their addition. I'm struggling to digest that.
What exactly happens when I add 2 equations?
They all intersect at 1 point too
.close
odd edgeBOT
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buoyant narwhal
odd edgeBOT
buoyant narwhal
Can someone help me check the above calculations?
Can you also apply the Leibniz Criteria for sequences?
spark cargo
Isn’t it converging to zero?
for all even index it will be in the positive reals axis and for all odd indices it will be in the negative axis
and sort of narrows into zero
@buoyant narwhal
buoyant narwhal
<@699697139810566304>
Yes, I was just confused if the rule is also applicable for a Sequence instead of a series?
spark cargo
are you able to see the sequence in your head?
calculate the terms a1, a2, a3, …, and see what happens to the sequence
Think of the terms moving in the real number line
buoyant narwhal
The entire exercise is only a sequence and not a series
But I only know the Leibniz-Criteria from Series applications
spark cargo
Series is really and application of sequences
spark cargo
You can see that the absolute value of the terms gets smaller and smaller as you move away toward infinity
buoyant narwhal
Yes
spark cargo
which is exactly you are looking for
buoyant narwhal
So even though we get positive and negative values, they both get smaller and smaller
Does that mean that we still have a Limit of 0?
buoyant narwhal
I have it somewhere yes
spark cargo
the idea is, if you claim 0 is the limit of the sequence
then for any distance from c, there is some stage in sequence after which all of the terms fall with in the given distance
long story short, you can get ** however** close to zero
Sort of like, how much closer can you get the sequence to zero? However close.
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fringe magnet
Guys can anyone help with this weird question
odd edgeBOT
Guys can anyone help with this weird question
@fringe magnet Has your question been resolved?
fringe magnet
No
fringe magnet
Done!
pastel dew
Has your question been resolved?
fringe magnet
Has your question been resolved?
It wasn’t but I will find a way later
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Available help channel!
languid gorge
patent swallow
what is this?
languid gorge
There is a step in the proof of the rigidity lemma in Gortz-Wedhorn that I don't understand.
patent swallow
wait give 1 min to write
here the proof is saying that since the map from U × k(y') to U × k(y') is affine and since k(y') is a field the global sections of U × k(y') can be identified with k(y').
for some point s from U × k(y'), the map also factors through Spec(k(y')), and since Spec(k(y'))) is reduced, the point can be written as p then, the proof is stating that p is also contained in eq(f, g), which is the set where f = g.
did u understand?
if u still cant understand tell me
languid gorge
Why the global sections of $U \times k(y')$ can be identified with $k(y')$? Since $U$ is affine , the global sections would be $\Gamma(U, O_U) \otimes k(y')$.
clever fjordBOT
DavidL1450
patent swallow
wait
you're correct, the proof should state specifically that the global sections are identified with Spec(k(y')). In this case, since Spec(k(y')) is a reduced scheme and its global sections are identified with the field k(y'), this means the global sections only consist of a single point corresponding to the identity element of the field.
languid gorge
$X \times_k Spec(k(y')) \rightarrow^{id_X, y, id_{Spec(k(y'))}} X \times_k Y \times_k Spec(k(y')) \rightarrow U \times_k Spec(k(y'))$ must be constant , but I don't understand why, when I put in $f$ and $g$ for the map $X \times Y \rightarrow U$, it must be the same constant?
clever fjordBOT
DavidL1450
patent swallow
wait a min
the map from X × Spec(k(y')) to U × Spec(k(y')), which is given by the identity on X and y on Spec(k(y')), is constant.
now, if u substitute this map for g in the original expression g = f∘(tx, idSpec(k(y')))∘π2, this gives the composite map
fx = idX, y, idSpec(k(y')), where f is the original map f: X × Y → U.
languid gorge
I think I understand, if we choose a point $p \in X \times_k Spec(k(y'))$ such that $\pi_1(p) = x$, and let $q \in X \times_k Y \times_k Spec(k(y'))$ be the image of $p$, then $(f, id_{Spec(k(y')})(q) = (g, id_{Spec(k(y')})(q)$, so the two constants are the same, right?
clever fjordBOT
DavidL1450
patent swallow
YOUR RIGHT
languid gorge
Also, can you please make an answer on the linked question so I can accept it.
odd edgeBOT
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spiral blade
find domain and range?
odd edgeBOT
find domain and range?
pastel dew
what have you found so far ?
odd edgeBOT
@spiral blade Has your question been resolved?
spiral blade
what have you found so far ?
ive found the inverse (cos thats the question), but idk how to find the zero value for the denominator
since i need to find the domain for the inverse
odd edgeBOT
@spiral blade Has your question been resolved?
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@spiral blade Has your question been resolved?
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@spiral blade Has your question been resolved?
quasi sparrow
ive found the inverse (cos thats the question), but idk how to find the zero val...
For any nonzero p, if a^p = 0 then that implies a = 0
odd edgeBOT
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deep prawn
odd edgeBOT
deep prawn
thats sorta my thought process so far
im guessing we're looking for the change in x from 50 to 0
dark gulch
odd edgeBOT
dark gulch
Bob calculator
odd edgeBOT
Bob calculator
dark gulch
I got this as my answer but not sure if it is right ?
And could I simplify could I simplify my answer ?
odd edgeBOT
@dark gulch Has your question been resolved?
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@dark gulch Has your question been resolved?
dark gulch
I did 42w -12w
thorn palm
what about wy term?
dark gulch
what about wy term?
2wy ?
thorn palm
why 2wy?
clever fjordBOT
high tusk
not bad
dark gulch
Would the answer be y = 30w/6-21w
mystic nest
(2w+y)6 = (7w)(3y+6)
12w + 6y = 21wy + 42w
12w +6y -21wy -42w =0
-30w +6y -21wy = 0
6y - 21wy = 30w
y(6-21w) = 30w
y = (30w) / (6-21w)
odd edgeBOT
@dark gulch Has your question been resolved?
dark gulch
(2w+y)*6 = (7w)*(3y+6)
12w + 6y = 21wy + 42w
12w +6y -21wy -42w =0
-30w +6y ...
It can’t be 21y it is 21yw
dark gulch
(2w+y)*6 = (7w)*(3y+6)
12w + 6y = 21wy + 42w
12w +6y -21wy -42w =0
-30w +6y ...
How did u get a number if everything is timed by letters
mystic nest
It can’t be 21y it is 21yw
it is 21y
(7*w)(3y+6)
So in order
7•3y + 7•6
21y + 42
then 3wy + 6w
dark gulch
It’s a multiplication
Times 7w by 3y gives 21wy and then times 7w by 6 which gives 42y
mystic nest
Would the answer be y = 30w/6-21w
that would be the final solution for the question
you are indeed correct
mystic nest
you can close the channel
odd edgeBOT
odd edgeBOT
Available help channel!
fathom sable
odd edgeBOT
fathom sable
Help
manic jungle
!status
odd edgeBOT
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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
frigid canopy
Try finding f(0) to start
manic jungle
First of all notice that f(n) = f(n - 1 + 1) = f(n-1) + f(1) = .... = n*f(1) for every natural n
fathom sable
First of all notice that f(n) = f(n - 1 + 1) = f(n-1) + f(1) = .... = n*f(1) for...
Yes
fathom sable
Ah
odd edgeBOT
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iron grotto
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@fathom sable Has your question been resolved?
fathom sable
<@899968077192642580> Has your question been resolved?
Tor maa ke chudi
shell stirrup
odd edgeBOT
shell stirrup
g was given, i needed to find tbe extremes and visuelizd them
I only got 1 solution, the answers show two
let me show you
the drawing shows the extremes, they found -2 & 3
mystic saffron
thats the roots of g(x)
shell stirrup
what do you mean
mystic saffron
-2 and 3
shell stirrup
I dont understand, apologies, how is this related?
mystic saffron
the drawing shows the extremes, they found -2 & 3
you said -2, 3
those are the roots of g(x)
nothing related to g'(x)
shell stirrup
I found g'(x) and solved for g'(0) to find the extremes, thats how I find them no?
mystic saffron
you mean g'(x) = 0?
mystic saffron
thats how you find the extrema
shell stirrup
yes
and I think I did that correctly
yet the extremes they found is -2 and 3 and not 1/2
shell stirrup
then the question has a mistake in it as they mention extremes... Let me solve it for g(x) then 1sec
somber prawn
I am trying to solve this differential equation. But I think I might have messed up an order of operations. For my y prime of -1. Do I go with +C1 and -C2. Or do I use -C1 and +C2? The example I was given for this had a positive X and not a negative one. So I dont really know how to deal with the negative being in the exponent of e with regards to when its plugged in.
odd edgeBOT
I am trying to solve this differential equation. But I think I might have messed...
@somber prawn Has your question been resolved?
odd edgeBOT
@somber prawn Has your question been resolved?
odd edgeBOT
@somber prawn Has your question been resolved?
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@somber prawn Has your question been resolved?
somber prawn
<@&286206848099549185>
somber prawn
.close
odd edgeBOT
signal sluice
Finding area of shaded region. I integrated with respect to x in the first line, but how do I integrate with respect to y now?
odd edgeBOT
signal sluice
.
Finding area of shaded region. I integrated with respect to x in the first line, but how do I integrate with respect to y now?
No I have to integrate with respect to y
halcyon parrot
find x as a function of y
signal sluice
The question is; given y=2 and y=sqrtx integrate with respect to x and then y. It
It’s like a try it both ways problem
signal sluice
Massive cringe
halcyon parrot
The question is; given y=2 and y=sqrtx integrate with respect to x and then y. I...
and thenintegrate with repect to dy from 0 to 2
signal sluice
??????
Tell me what to plug in on the second line
I have 0 and 2 as the limits of integration, this is correct ye?
mystic saffron
yeah
halcyon parrot
I have 0 and 2 as the limits of integration, this is correct ye?
yea
mystic saffron
so now
signal sluice
But then how do I get the right side line? I ended up with
mystic saffron
solve for x in y = sqrt(x)
halcyon parrot
Tell me what to plug in on the second line
y^2 dy
signal sluice
A = int_0^2 (4 - x^2)dy
odd edgeBOT
y^2 dy
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
signal sluice
$\int_0^2 4-y^2 dy$
clever fjordBOT
🌸 Katsune
halcyon parrot
$\int_0^2 4-y^2 dy$
why 4-y^2
mystic saffron
that is not the solution lol
it pretty much is like the whole thing except for the integration
signal sluice
I think I have to somehow translate this graph when solving it with respect to y so like I noticed y=2 with limits of integration at 0 to 4 is kind of the same as x=4 with limits of integration at 0 to 2
If that makes sense
Idk how to explain it but everything shifted slightly including how i look at the given equations
The trouble is
When I plug in in_0^2 4-y^2 dy it gives me
The area of the graph that is NOT what I shaded in
It gives me the bottom larger half.
Is the answer simply 2(4) - [the answer that i got] = Area
How do you directly get to the Area of this shaded region when integrating with respect to y?
mystic saffron
well like
mystic saffron
the common way is to draw lines (radii) from the y axis to the function
and use that to determine the region
like
signal sluice
what do you mean
I did x=4
is that not it??
actually just tell me what goes after this: A = \int_0^2
this is so close!! wtf is missing
mystic saffron
https://cdn.discordapp.com/attachments/903463355619110912/1206508291732148254/IM...
odd edgeBOT
Available help channel!
signal sluice
.
mystic saffron
like imagine if this was like a normal function alright
mystic saffron
ok amazing
signal sluice
LOL
mystic saffron
just open a new channel 
mystic saffron
.close
odd edgeBOT
odd edgeBOT
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If you are done with this channel, please mark your problem as solved by typing .close
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lilac gate
need help
lilac gate
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eternal ravine
how would i find PR? and is K=the major axis length?
urban escarp
yo
eternal ravine
hi
urban escarp
do you know by definition the relation between pr and pq?
eternal ravine
pr-pq = k and k is the constant
urban escarp
yea ig
eternal ravine
how would i find pr though
is k = length of major axis? bc it’s like that for ellipses i think
urban escarp
pq is given and
eternal ravine
yes
eternal ravine
yeah?
urban escarp
you have pq and you might have studied how to find the distace from origin to vertex
urban escarp
yeah
eternal ravine
then what do i doV?
i missed the part of class talking about hyperbolas so i might’ve missed some basic stuff the teacher covered
urban escarp
ok 1 min
eternal ravine
thanks
urban escarp
sry i am not able to send pic
eternal ravine
oh it’s ok
urban escarp
but i can explain
eternal ravine
yay okk
eternal ravine
yeah
urban escarp
2pr = 10 +k
eternal ravine
i got it now tyy
urban escarp
i got it now tyy
welcome
eternal ravine
.close
odd edgeBOT
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Available help channel!
desert marlin
odd edgeBOT
desert marlin
I don't understand this notation
if it is notation
it's just saying like the cogruence class [x] will always be a root in F[x]/p(x) ? because p([x])=p(x)=0 mod p(x)?
what's up with the distinction
buoyant solstice
Instead of the congruence class, are we sure it’s not the ideal generated by [x]? Apologies if I’m way off base, I took abstract like two semesters ago
buoyant solstice
Does that mean you haven’t gone over rings yet?
buoyant solstice
Oh my god that’s really weird lol
desert marlin
So I've been told XD
buoyant solstice
I Guess maybe you’ll have an easier time with groups if you’re doing rings first? Lol but when did you learn about rings? What textbook are you following?
desert marlin
We're using Hungerford
Rings came first in the course
Groups will be next quarter
we're maybe 6-8 weeks in? I don't keep good track of time
buoyant solstice
Hmm I just feel like ideals should come quickly after the introduction of rings. Like I would think you need ideals to talk about extension fields and polynomial rings, and that’s what that notation screams to me. Can you see where ideals get mentioned in the textbook beyond what you’ve covered?
desert marlin
yea we are doing extension fields and polynomial rings
we'll do Ideals this friday it looks like
buoyant solstice
If it really isn’t the notation for the ideal generated by x, I’d guess it has to be congruence classes? Maybe somewhere else in here would be better suited to help ya
buoyant solstice
Well then there ya go
desert marlin
I guess I just am confused why they are like
saying
let alpha=[x]
then...
alpha is a root because...
like why not just say [x] is a roto
root*
dense patrol
Need help with the integration
odd edgeBOT
Need help with the integration
desert marlin
!status
odd edgeBOT
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
1
desert marlin
What have you tried
dense patrol
completing square in the denominator
desert marlin
no need