sorry if i am being slow
#help-23
lean otter
dreamy elk
Because the stones are ordered as 1,2,3,4,...,7, if not, we can label them that way, doesn't matter. If you are at 3, and then hop to 2, then you must've gone left.
dreamy elk
Like imagine drawing the stones on paper, where 1 is leftmost and 7 is rightmost.
lean otter
thank you for your time
lean otter
Like imagine drawing the stones on paper, where 1 is leftmost and 7 is rightmost...
i will try your way
thanks
both of you
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sacred mountain
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sacred mountain
Does anyone know how to do this?
cyan monolith
which question
1st ne height of the entire shape is 5x
semi circle is constant radius there fore height of cone is 4x
radius of cone is x
volume of hemisphere is half of the sphere
so total volume is volume of hemisphere (2/3) * pi * x^3 + (1/3) * pi * x^2 * 4x
cyan monolith
now the cylinders volume will be pi * (2x)^2 * h
equate that to the first result
find h as the terms will cancel out
dont forget to mention units in the final answer
sacred mountain
how i get h
and do i need the area for the cone and the hemispere?
@cyan monolith u there
cyan monolith
h is 4 x
the total height of the shape is 5x
but hemispheres are constant radius
so the height will be = to the radius = x
total height is radius of hemisphere + height of cone = 5x
therefore height of cone = 5x-x
sacred mountain
o i didnt read it properly
cyan monolith
the volumes are equal
so 6pi/3 x^3 = 2pi x^2 h
the height of the cylinder is x
confirm it once
sacred mountain
so i solve (1/3pix^2 4x) + 4/3pix^3 = 2xpi^2*h
so i need h on its own?
i gotta go to school but ty for helping so far š
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cyan monolith
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lean otter
Idk where to start
shy trench
Idk where to start
finding the maxima
if you want to be fancy just take derivative
and = to zero
lean otter
Is it the vertex?
shy trench
Is it the vertex?
ye
that is
i dont remember parabola rules so i always go to calculus methods
lean otter
So Iād have to change it y=a(x-h)^2+k
lean otter
i dont remember parabola rules so i always go to calculus methods
Idk much abt calculus
shy trench
Nvrm I would prefer a different helper
i can but give me 1 sec
lean otter
Aight thanks
shy trench
-3x^2 +24x -36 = a(x-h)^2+k
-3x^2 +24x -36 = ax^2 -2axh +h^2 +k
a = -3
24x - 36 = 6xh + h^2 + k
h = 4
-36 = 16 + k
just throw k
i dont want it
lean otter
What š
shy trench
put 4 into
-3x^2 +24x -36
lean otter
No no, not at all
Thank you for helping
Iām just bad at math
I will try it by myself
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merry crane
Hello, I'm trying to solve this problem, but on my code, the files are not working.
The exercize consists in the implementation of a minimum-cost multi-commodity flow model
and in the analysis of its results on classic instances related to urban transportation.
The model must be implemented using the Python language and Gurobi as MILP solver. The
model must be run on data from the classic SiouxFalls network and from the Berlin-Mitte-
Center network. The data concerning both cases can be retrieved from:
https://github.com/bstabler/TransportationNetworks
The model can be developed according to existing examples, like the following:
https://github.com/wurmen/Gurobi-Python/blob/master/python-
gurobi%20%20model/Netflow_problem.py
However, input must be read directly from the data files downloadable from the Github
repository. Moreover, at least for the Sioux-Falls example, the output must includes a
representation of the transportation network and the total flow assigned to each link.
safe radishBOT
Hello, I'm trying to solve this problem, but on my code, the files are not worki...
@merry crane Has your question been resolved?
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spice furnace
Hello, I'm trying to solve this problem, but on my code, the files are not worki...
The first thing to do is figure out what is the bug
merry crane
I can show you my code:
It simply does not work, since I got this as an answer: CPU model: AMD Ryzen 5 5600U with Radeon Graphics, instruction set [SSE2|AVX|AVX2]
Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
Optimize a model with 76 rows, 76 columns and 76 nonzeros
Model fingerprint: 0xa410545d
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [0e+00, 0e+00]
Bounds range [5e+03, 3e+04]
RHS range [5e+03, 3e+04]
Presolve removed 76 rows and 76 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Iteration Objective Primal Inf. Dual Inf. Time
0 0.0000000e+00 0.000000e+00 0.000000e+00 0s
Solved in 0 iterations and 0.02 seconds (0.00 work units)
Optimal objective 0.000000000e+00
Soluzione ottimale trovata! (found)
spice furnace
I thought you were having some issue reading the file. Unfortunately I am unable to help you. What I would recommend is using a debugger and hand tracing your code if possible
merry crane
the problem is that I am using jupyter, and the debugging is not working properly
do you know how to do it?
mellow cypress
Start by checking the data has actually been read correctly using print statements
spice furnace
Click the button containing a bug
From there go to the view panel, and open the debug panel
set the breakpoints
The line highlighted indicates the point about to be executed
In case you run into any issues try restarting jupyter notebook
merry crane
Ok, I have printed it, and it shows me nothing
so I guess this is not working
are there any other ways to make my model work by reading these data? I have also create a new data in .txt format, instead of the format it downloaded me
the problem is also what I am getting, so many numbers, so I guess this has been reading
these are my input
merry crane
So, I have no idea what to do!
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deft surge
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slate drift
u can simplify it first making it a quadratic
and for a soln we know discriminant greater than or equal to zero u get values of m for which eqn have value for x
deft surge
Sorry I still don't get it
So
Am I looking for values of m that gives a discriminant of >= 0?
deft surge
Can you explain what a parameter is?
idle pulsar
Can you explain what a parameter is?
Think of it as another name for variable
slate drift
yeah
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gaunt garnet
Define $f(n)$ as the sum of the squares of the digits of $n$.
For example: $f(12) = 1^2 + 2^2 = 5$\
Prove whether or not the following statement is true: For every integer $n$, there exists a positive integer $m$ such that the $m$th composition of $f$ with itself applied to $n$ results in a single-digit number.
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Define $f(n)$ as the sum of the squares of the digits of $n$.
For example: $f(12...
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OÄuzhan
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karmic hedge
Define $f(n)$ as the sum of the squares of the digits of $n$.
For example: $f(12...
show that it is decreasing for all 2+ digit integers
gaunt garnet
show that it is decreasing for all 2+ digit integers
How do I do that for exactly 2 digit integers
Because for example 29 doesn't decrease
gaunt garnet
Even 199 increases actually
karmic hedge
Even 199 increases actually
no
karmic hedge
but intuitively i feel like the statement is true, because there exist no 2 digit or 3 digit numbers such that f(a)=a
gaunt garnet
ok 4+ is easy
I think you can just say, for 4 or more digits, the maximum value of f is 81*4 = 324 therefore it decreases
karmic hedge
f(a)=a only when a is 1 digit
karmic hedge
I think you can just say, for 4 or more digits, the maximum value of f is 81*4 =...
yeah
i dont think there is any 3 digit number that increases right
karmic hedge
haha
gaunt garnet
If there is no other way I will close
karmic hedge
there is always a solution
gaunt garnet
Maybe
karmic hedge
behavior for 2 digits seems kind of erratic, maybe the statement is false
if we found some 2 digit number that goes in a loop
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gaunt garnet
if we found some 2 digit number that goes in a loop
For some reason they always move on a single-digit number
65 -> 61 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4
Some are long like this
glass coral
there are 36 unique 2 digit numbers
glass coral
**OÄuzhan**
I would guess this function rate of change is:
glass coral
$\Delta y = -\frac{x}{log(x)}$
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clonesolopros
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clonesolopros
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trail otter
How should I determine absolute convergence of this series
[\sum_{n=1}^{\infty}\left(-1\right)^n\tan\left(\frac{1}{\sqrt{n}}\right)\cos n\ln n^2]
I already know that [\lim_{n\to\infty}\left|\left(-1\right)^n\tan\left(\frac{1}{\sqrt{n}}\right)\cos n\ln n^2\right|=0]
but what test should i use or rather how should I alter it before using some test?
safe radishBOT
How should I determine absolute convergence of this series
\[\sum_{n=1}^{\infty}...
flat frigateBOT
Slowaq
sleek plank
since the series is alternating, you could use the alternating series test
light shoal
(assuming you can somehow show that the abs vals of the terms are decreasing)
also, the alternating series test says nothing about absolute convergence
sleek plank
oh ur right i didnāt see that
trail otter
well my task is to determine convergence and absolute convergence so how should i do it such that ill get both with least effort
light shoal
for abs convergence you could try the usual suspects
ratio test etc
or comparison test if you can make it termwise smaller than a known convergent series
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long oracle
Maybe Iām missing something, but how would their distance decrease at that instant?
Yes, thatās the error
Or rather, thatās what it should be
No thatās correct as is, but since youāve decided to have the origin/intersection places like so, then the x coordinate has to be negative too
Theyāve given you the correct distance from that intersection, but you have to decide on the correct orientation
Yeah exactly
Always good to make these types of intuitive checks
This is also why drawing a picture is so crucial
Ur welcome
Even if it seems non rigorous, the intuition is very important
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long oracle
Good luck!
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indigo sail
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indigo sail
which would it be
eternal carbon
is that number greater than or less than 8 1/10 ?
eternal carbon
1/10 is 0.10000
1-bar is 0.1111111
indigo sail
greater
eternal carbon
yes
sturdy barn
so it would be 8 1/10
eternal carbon
then you can figure out which of 1/9 and 1/11 it is
sturdy barn
*11
eternal carbon
- don't give answers without actually helping
- that's wrong
indigo sail
its 1/9?
eternal carbon
it is
indigo sail
but its greater?
eternal carbon
1/9 is greater than 1/10 yes
indigo sail
why 1/10?
flat oar
alternatively you can:
x = 8.1111 ...
10x - x = 81.1 ... - 8.1 ... = 9x = 73
x = 73/9 = 8 + 1/9
flat oar
why 1/10?
1/10 is between 1/9 and 1/11 so comparing if it's larger or bigger than 8 + 1/10 will show you if it's 8 + 1/9 or 8+ 1/11
if the options were 1/13 and 1/17, it would be 1/15 to do the comparison
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slate basalt
could someone explain and teach logarithms? This is less of a question im just asking for free tutoringš
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could someone explain and teach logarithms? This is less of a question im just a...
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light shoal
could someone explain and teach logarithms? This is less of a question im just a...
try khan academy
light shoal
nw, it's just that this server isn't really set up for tutoring
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fathom plume
whats the range of x when (n+1)/(n-1) = tanx, 0=<x=<360
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whats the range of x when (n+1)/(n-1) = tanx, 0=<x=<360
eternal carbon
how?
eternal carbon
but its not?
no
an easy way to see why is say n = -1, then 0 = tanx and x = 0 is in the range, though it's not included in your interval
eternal carbon
ah ok cool
this question makes a bit more sense now with that restriction
tan(x) is periodic with period 180 degrees, so your answer should be periodic as well
it helps to first consider the range of (n + 1)/(n - 1) when n > 1, then compare that with the range of tan(x) for x between 0 and 180
pure grail
given the matrix A and question is to find for which value a, the matrix A is diagonalizable. So the matrix is diagonalizable when its eigenvectors are linearly independent right?
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given the matrix A and question is to find for which value a, the matrix A is di...
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long oracle
Oh
pure grail
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ā
pure grail
@long oraclego on
pure grail
i assumed what i said is true
long oracle
Well yes itās true, itās even an iff statement, a well known theorem
pure grail
so all i need to do is to find eigenvectors, and then see for what value of a they are linearly independen
pure grail
Well yes itās true, itās even an iff statement, a well known theorem
ok, gotcha
long oracle
Yep
pure grail
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narrow quail
P or Q ~P or Q
Q ~Q
-----------------------------
empty
Could this also be done?
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P or Q ~P or Q
------------------------------
...
narrow quail
<@&286206848099549185> (I tag because I already made a previous channel where I got no helper <3)
paper flume
P or Q ~P or Q
------------------------------
...
i think so yeah
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rustic grail
Heyo!
rustic grail
Can anyone help me solicit answers for these two?
'800 crore' is 8000000000.
And I did get as far as calculating that the disease-burden being 10% must mean the total being 800000000.
So all the subsequent calculations must be made by way of that number. I have got this far.
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rustic grail
No.
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teal kite
Hello, I saw this while reviewing and the answer I got is 143 degrees, simply because
<ADC = 180 - 85 = 95
Since BD is the diameter, <DAB = 90
180 - 42 - 90 = 48
< between the tangent and side of the triangle is = interior opp <
So, <ACB = 48
Sum of angles
95 + 48 = 143
May I know if this approach is wrong and there is something I've overlooked or right and that the reviewer had none of the answers?
safe radishBOT
Hello, I saw this while reviewing and the answer I got is 143 degrees, simply be...
vague slate
Hello, I saw this while reviewing and the answer I got is 143 degrees, simply be...
Can you please elaborate how you found the value of angle ACB
fresh forum
Can you please elaborate how you found the value of angle ACB
its given in the exercise
glacial cairn
Hello, I saw this while reviewing and the answer I got is 143 degrees, simply be...
It would seem you are correct
Might be a typo from 143 to 153
teal kite
It would seem you are correct
Oh I see, Thanks for the illustration!!
May I know what application did you use that for?
glacial cairn
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cursive tapir
why do they times by (2-sqrt(3))/(2-sqrt(3)) on the 5th line?
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why do they times by (2-sqrt(3))/(2-sqrt(3)) on the 5th line?
blazing sail
that equal sign is wrong
ruby bolt
why do they times by (2-sqrt(3))/(2-sqrt(3)) on the 5th line?
rationalization
to remove the sqrt terms from denominator
cursive tapir
rationalization
how did they know to do that
ruby bolt
how did they know to do that
we need to remove 2+sqroot3 from denominator so we just take conjugate of term in denominator and multiply and divide the fraction with the conjugate
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sleek vessel
could sum1 help me with part c? feel stupid afš
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could sum1 help me with part c? feel stupid afš
sleek vessel
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trail otter
How to determine convergence and absolute convergence of this series in $\mathbb{C}$
[\sum_{n=1}^{\infty}\frac{z^n}{n2^n+(-1)^n}.]
I alreaady found out that radius of convergence is 2 thus this series converges for $z<2$ and diverges for $z>2$. How should i determine convergence in $z=2$ and alsolute convergence for all three possibilities?\
I know I can rewrite it into this form but what should I do next?
[\sum_{n=1}^{\infty}\frac{2^ne^{i\phi n}}{n2^n+(-1)^n}; \ \phi\in [0,2\pi )]
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How to determine convergence and absolute convergence of this series in $\mathbb...
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Slowaq
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trail otter
<@&286206848099549185>
flat frigateBOT
Cpt. Zeph
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
safe radishBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
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gentle burrow
simple ahj question
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simple ahj question
paper flume
du/2x is the same as 1/2x*du right
if its (du/2)x then yes
gentle burrow
no its (du)/(2x)
paper flume
no its (du)/(2x)
then its (1/2x)du
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solemn terrace
Hello
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solemn terrace
<@&286206848099549185>
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warm crest
I feel like i did something wrong when integrating but I cant seem to figure out what?
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I feel like i did something wrong when integrating but I cant seem to figure out...
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stoic dune
You win the record. You are the furthest student I've ever seen that still writes their algebraic steps on the line. It's very hard to read that.
I'm not certain what you've done in the integration
pure agate
Algebraic mistake from the 3rd to 4th line.
warm crest
Algebraic mistake from the 3rd to 4th line.
is it the Q?
pure agate
(2t^3 - 1)/t^2 = 2t - 1/t^2
warm crest
(2t^3 - 1)/t^2 = 2t - 1/t^2
I feel like im missing something, how would that even work?
theres nothing factoring out the t^2?
pure agate
1/Q dQ = (2t - 1/t^2) dt?
warm crest
1/Q dQ = (2t - 1/t^2) dt?
why are you factorying out t^2?
pure agate
Because it's divided by t^2?
warm crest
Because it's divided by t^2?
why is the denominator still t^2 then?
pure agate
warm crest
OH
yea forgot that happens when u subing
sry im really tired š¤£
ok i think i got it this time
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fervent hatch
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fervent hatch
How do I start here
fervent hatch
How does that help
lean otter
Did you expand it?
flat frigateBOT
Nathan
fervent hatch
Thatās all I canāt simplify
lean otter
Of the 3 terms you can directly integrate 2 of them
fervent hatch
Ok
lean otter
Tanx=u
lean otter
Why so?
fervent hatch
We would have du/secx
lean otter
You have sec^2
lean otter
ā
still charm
fervent hatch
š¤Æ
lean otter
Did I need to expand it?
Expand what?
lean otter
I didn't get you
lean otter
Ofcourse
sweet trout
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frozen marlin
!status
safe radishBOT
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
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rough bobcat
Ooh can I jump in on this question?
The question demands using special triangles i.e. the following right triangles:
- (30Ā°, 60Ā°, 90Ā°)
- (45Ā°, 45Ā°, 90Ā°)
Check the table of trigonometric ratios corresponding to these triangles, substitute the values and simplify the expression @sweet trout
For e.g. sin(45Ā°) = 1/ā2
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sweet trout
Preciate it
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narrow quail
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narrow quail
how did they get to this step?
obsidian oracle
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toxic yacht
how do i do this question
ik to use the intersecting coords theorem but that just gives y in terms of x how do i find x?
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how do i do this question
ik to use the intersecting coords theorem but that jus...
toxic yacht
finding the value of y btw
thin bridge
there are other power of point theorems applicable here
note that you also have two secants originating from point A
and secant-secant theorem would also be applicable
toxic yacht
oh im unfamiliar with those
thin bridge
(that'll give you an equation with only x)
look up secant secant theorem
or power of a point
hearty shoal
Is anyone German here? because I really need help
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warm crest
am i supposed to do integration by parts here?
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am i supposed to do integration by parts here?
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patent shore
so i have the geomatry regents tommorow, and have only slightly been paying attention all year, what's the best way for me to study and pass?
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so i have the geomatry regents tommorow, and have only slightly been paying atte...
brave wolf
proud belfry
Prove that a linear diophantine equation with relatively prime coefficients in the form
ax + by + cz + dw + ā¦ = n
Always has integer solutions
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Prove that a linear diophantine equation with relatively prime coefficients in t...
proud belfry
Im stumped, dont know where to start
Someone mentioned something about something called bezouts, dont know what that is
fallen oriole
Actually I don't know what I'm doing lmao, but this might be the correct track.
proud belfry
Ah thanks
How do you generalize to N integers
Also, how would i have discovered this on my own
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wet pecan
Also, how would i have discovered this on my own
Why don't you use Bezout on two variables, and then just set the others to0
Integer solution
If you want to derive Bezout, look at the Euclidean algorithm
fallen oriole
How do you generalize to N integers
Wdym, ax_1, ax_2, ā¦, ax_N, this?
The expression ax + by + cz + dw + ā¦ = 1 already takes the generalization into account, given the ellipsis, no?
wet pecan
Wdym, ax_1, ax_2, ā¦, ax_N, this?
The expression ax + by + cz + dw + ā¦ = 1 alrea...
Wait what are you trying to do
fallen oriole
Wait what are you trying to do
Iām not trying to do anything, Iām asking for clarification on what heās looking for
wet pecan
The question is asking to show there exists an integer solution
What part would you like to clarify?
fallen oriole
The question is asking to show there exists an integer solution
I tried to show it here #help-23 message
wet pecan
Oh
Yh so you have Bezout, just apply it to ax +by = n. Then you have a solution (x, y, 0, 0, 0...) for ax + by + cz + ... = n
fallen oriole
**dghf**
From here, we know x, y, ā¦, are integers. So if we multiply both sides by n, we get nx, ny, etc. and these will all compose integers, which later is multiplied by the coefficients (a, b, ā¦)
wet pecan
ok
wet pecan
Yh so you have Bezout, just apply it to ax +by = n. Then you have a solution (x,...
But you can just do this
fallen oriole
āDo thisā thereās no doing there, youāre just stating the obvious lmao. I gave him the steps.
wet pecan
..but you said you didn't know what you're doing..
I mean I never said the problem wasn't obvious
Was just trying to help
fallen oriole
I just checked with a friend whoās a math major and he confirmed itās correct, but thanks for your input.
Your method looks good, generalization of BĆ©zout's identity holds.
The conclusion you draw from the last equation is that there are integers such that the equation is true.
Note that without the assumption of relatively prime coefficients, the theorem holds if and only if n is a multiple of gcd(a,b,...,). In this case, gcd(a,b,...)=1, which means that the theorem applies trivially for all integers n (except 0).
wet pecan
I have a degree in maths, thanks.
Thought you wanted to not use the general version. It's just a way to do it with two variable Bezout
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onyx lantern
quick question, I don't get what's the difference between a split characteristic polynomial and one that isn't (in matrix)
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quick question, I don't get what's the difference between a split characteristic...
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wispy vortex
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wispy vortex
the video my teacher gave me was garbage and didn't explain anything
so 28 is the pre image length
OA = 28
so k = 28?
so y is OA'?
wtf
garbage example
if y is OA'
then 28*19/19
wtf
that is fucking 28
the scale factor is not fucking 28
maybe it is 28/19
still doesn't make any sense
because the dialation is a reduction
not enlargment
hoary wind
Is ky/y the standard notation for this stuff? I hate it if so
Scale factor = New Length / Original Length
wispy vortex
Scale factor = New Length / Original Length
thanks
jeez
my notes and the video my teacher gave make no sense with weird examples
.close
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karmic lantern
Im trying to use direct proof for the question and the way my TA helped me was kinda confusing so help would be appreciated!
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Im trying to use direct proof for the question and the way my TA helped me was k...
karmic lantern
tbh im stuck right now in why Span{a1, ..., ai-1, c, ai+1, ..., am} is a subset of R^n
i remembered the TA saying that we only really need to prove that span{a1, .., am} is a subset of span{a1, ..., ai-1, c, ai+1, ..., am} but i dont really remember why
<@&286206848099549185>
rough bobcat
Hi @karmic lantern
karmic lantern
hello
rough bobcat
Do you still need help?
karmic lantern
yes
rough bobcat
Okay, I'll pitch in
Essentially, you need to prove that we can shift the blame for a list of vectors to be linearly dependent on a single vector
And why so? Because it can be represented as a linear combination of the vectors preceding it
Oh wait, i think we don't need to prove that
Sure, let's proceed
Essentially, we need $m \geq n$ otherwise it would be wrong
flat frigateBOT
Uta
rough bobcat
With that done, our spanning list is mostly going to be linearly dependent
If m = n, our spanning list is linearly independent
Can you make out why?
Not that it's something we need for this question
karmic lantern
because there are the same numbers of members in the vector and R^n so there would be a linera combination of it?
rough bobcat
Or you might as well say that tje length equals the basis of R^n, and there's a probable result that shows that if a list of vectors has the same length as the basis, and is linearly independent, then the list is a basis too
Anyways, not the point
It's true that since the list of a's span R^n, we can represent any nonzero c in R^n as a linear combination, right?
karmic lantern
yes
rough bobcat
So we can write c as a linear combination of the a's
karmic lantern
i understand that yes
rough bobcat
Now, since c is nonzero, there has to be some term in the combination having a nonzero coefficient
Do you agree?
karmic lantern
yep
rough bobcat
Perfect!
Let this term be the ith term
Then we can represent the ith term in terms of the remaining a's and c?
karmic lantern
yeah
rough bobcat
So the next time we're spanning R^n using the a's, we can reduce the ith vector to a linear combination of the remaining a's and the c vector
And that means, we have done away with the ith vector by introducing the vector c in the spanning list
This list still spans R^n
karmic lantern
OK thanks for the help
karmic lantern
.close
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radiant spade
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radiant spade
i just need help on how that left part became the right part
forest gust
what's -sin(theta) + sin(theta)
radiant spade
what's -sin(theta) + sin(theta)
is that a gen question ur asking me? orr, if so 0 no?
forest gust
or know that $\left(a-b\right)\left(a+b\right)\ =\ a^{2}-b^{2}$
flat frigateBOT
Combustion
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grave ridge
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grave ridge
Where did I go wrong?
The bounds and initial formulas are right without a shred of a doubt, but my answer is wrong.
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@grave ridge Has your question been resolved?
quiet plume
What result are you expecting? You get something like 8/3 - pi/2 in the last step right?
grave ridge
What result are you expecting? You get something like 8/3 - pi/2 in the last ste...
I honestly have no idea
It just said its wrong
let me get a similar practice problem
quiet plume
What is the actual question though? Are you 100% the initial integrand is right?
grave ridge
Their solution
See, they used the reduction formula for cos^4 (theta). So did I.
Here is mine
quiet plume
Why do you still have thetas in there though?
This is a definite integral, the result is a constant
That's what I meant earlier, if you plug in the bounds you get 8/3 - pi/2
grave ridge
because im an idiot i guess lmfao
i didnt see that
š
hol up let me try
dont go nowhere
lol yeah its right
FML
rip 1 hour
š«”
thanks @quiet plume
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violet spear
Iām stuck on question f
violet spear
4 j please
@helpe
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
viscid rover
Hello
violet spear
Hello
viscid rover
This is the math room
violet spear
4 j please
.
viscid rover
?
violet spear
R u a helper
viscid rover
Idk noo
violet spear
<@&286206848099549185>
violet spear
Can u help with 4 j
viscid rover
4j
violet spear
Yah
violet spear
<@&286206848099549185>
viscid rover
That's a like
violet spear
?
violet spear
Alr
high cedar
Can u help with 4 j
multiply both sides of the equation by $1+x$ to eliminate the denominator
$$ n(1+x) = x + 3 $$
if you have any other issue please let me know, in the meantime try to go on by yourself
flat frigateBOT
Adversing
rugged cargo
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rugged cargo
I tried to solve it with chinese remainder and got no values
lean otter
You can get the number by guessing
toxic stratus
well seeing as it's 1 mod 2 but 2 mod 4, i don't think you can
rugged cargo
well seeing as it's 1 mod 2 but 2 mod 4, i don't think you can
How?
rugged cargo
I have read it that is why i applied chinese remainder no?
@toxic stratus
x=6 mod 7
x=1 mod 2
x= 2 mod 4
x=13 mod 14
x=2 mod 4 no solution
toxic stratus
i mean
rugged cargo
What u mean
toxic stratus
does x = 1 mod 2 and x = 2 mod 4 not already throw up red flags for you
rugged cargo
Yes
toxic stratus
it should be clear that there is no solution from that alone
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fathom jewel
Given $f(x) = \sum_{n=0}^{\infty} \left ( \frac{1}{3} \right )^n \sin(2^nx) \quad \forall x \in \mathbb{R}.\$
Show that $f$ is continuous.$\$
How do I do this again?
safe radishBOT
Given $f(x) = \sum_{n=0}^{\infty} \left ( \frac{1}{3} \right )^n \sin(2^nx) \qua...
flat frigateBOT
šødĻnš²Ā²s
fathom jewel
Do I have to show that it converges pointwise?
I actually proved that it converges uniformly
using weierstraĆ
fathom jewel
**šødĻnš²Ā²s**
Does this imply continuity
solar hazel
yea, a uniform limit of continuous functions is continuous
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fathom jewel
yea, a uniform limit of continuous functions is continuous
f you
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solar hazel
wtf
fathom jewel
that'S what I thought 2
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rugged ruin
hello, how to get the answer in the red box. This is a physics collision problem.
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hello, how to get the answer in the red box. This is a physics collision problem...
sonic sierra
Where are you stuck?
rugged ruin
i know everything upto the red box
so i understand how to get eq 1 and 2
but then what
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raw ledge
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raw ledge
I need help understanding how to determine the global maximum I solved the problem but I keep getting the wrong maxium values
eternal carbon
looks like you eliminated a case
raw ledge
(3,1) ?
eternal carbon
it was right after here
raw ledge
by eliminated do you mean I didnt solve properly ?
eternal carbon
there was an extra case that you needed to consider
raw ledge
would it be when y= 1/6-2 lambda ? when x= 0
x^2+6y-1 - 2lambda =0 and then plug it into constraint ?
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lone arch
We discussed this earlier and noticed that there will be 40 cases if you do it by brute-force cases. Can we use a case-wise approach that's also brute-forcy but reduce the amount of cases?
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We discussed this earlier and noticed that there will be 40 cases if you do it b...
low vector
maybe try proof by contradiction?
lone arch
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lone arch
Got it
low vector
whats the proof?
lone arch
whats the proof?
Nvm, I thought I can just brute force it without getting 40 cases because N starts at 1 in this course but that doesn't help
We can still have 0 numbers in a drawer
.reopen
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ā
swift hare
it might be helpful to first prove that if there are only 3 distinct mods mod 4, there is a set of 4 that are divisible by 4
lone arch
Preferably I want something that I can use on similar problems too (not ad-hoc)
gilded vault
i feel like there is no set in stone method for these types of problems
its just "use whichever casework reduction seems the most convenient"
lone arch
@kind tinsel did you find a proof or were you not typing for this?
lone arch
its just "use whichever casework reduction seems the most convenient"
Oh, ok
Well which one is that, in this case?
kind tinsel
<@316739634405048331> did you find a proof or were you not typing for this?
i was typing to try to find something pigeonholey
gilded vault
Well which one is that, in this case?
there aren't really a set of defined casework reductions
kind tinsel
i bet thereās a way to use pigeonhole for something like this
lone arch
i bet thereās a way to use pigeonhole for something like this
There is, https://math.stackexchange.com/a/2566076
But we didn't officially cover the pigeonhole principle
So maybe we can find something else?
gilded vault
um i mean not using something pigenholey would be quite dumb
and honestly if you are being given this problem surely they expect you to know the pigeonhole principle
lone arch
and honestly if you are being given this problem surely they expect you to know ...
As if I remember my teacher made a table with this and ended up with 15 cases or so
gilded vault
As if I remember my teacher made a table with this and ended up with 15 cases or...
ok well the teacher seems to be brute forcing it
lone arch
For some reason we can't replicate that now, I don't have his solution anymore either
It turns out to be 40 cases for us
gilded vault
lowkey your teacher is doing it the bad way then
kind tinsel
So maybe we can find something else?
wait but if you donāt wanna use pigeonhole why are you hesitant to use brute force?
lone arch
wait but if you donāt wanna use pigeonhole why are you hesitant to use brute for...
I want to use brute force
But we get 40 cases
kind tinsel
oh
lone arch
My teacher did brute force too but got 15
gilded vault
I want to use brute force
you can probably make some cases equivalent to each other
here are some reductions
- we can assume that the mode of the numbers is 0
lone arch
lowkey your teacher is doing it the bad way then
Idk if it's a "bad way". He can use it to all sorts of problems like this without having to think too much
kind tinsel
you can do cases where you split into getting n 0ās to make it easier
lone arch
Idk if it's a "bad way". He can use it to all sorts of problems like this withou...
That sounds pretty good
kind tinsel
if you get more than 3 youāre done immediately
gilded vault
if we add 2 to every number for example, the sum of all 4 would be 8 more, which means its the same mod 4. thus we can add anything to each number (mod 4)
kind tinsel
if you get more than one 2 youāre also done immediately
lone arch
you can do cases where you split into getting n 0ās to make it easier
Wdym
So a table?
gilded vault
okay so what reductions we can do:
- 0 is mode (not unique neccesarily)
- number of 1s>=number of 3s
- not more than 3 of any number
i think these combined will get you close to 15 cases
lone arch
okay so what reductions we can do:
- 0 is mode (not unique neccesarily)
- numb...
Ok maybe the official solution is more attractive then, they get 4 cases:
They look at when each of the drawers have at most 3
And then, they do two cases:
left side (0, 2) has atleast 5 numbers
Right side (0, 2) has atleast 5
And then another two; none of them have atleast 5
So four and three
gilded vault
yeah i can see that working
lone arch
Or three and four
lone arch
yeah i can see that working
But yeah, written out, it's still over a page
lone arch
yeah i can see that working
Can we always use this method? 
gilded vault
Can we always use this method? <:hmmcat:831508801646755850>
well i mean idk how to generalize this method
just play around and try what works really
lone arch
well i mean idk how to generalize this method
Oh, true
lone arch
just play around and try what works really
I think just doing the 40 cases brute-force is quicker 
gilded vault
I think just doing the 40 cases brute-force is quicker <:opencry:586078614865444...
no running a computer program will always be the quickest
lone arch
no running a computer program will always be the quickest
Probably this is the most elegant
gilded vault
here i will write a python program quickly
lone arch
@kind tinsel this was probably your idea?
gilded vault
red delta
We discussed this earlier and noticed that there will be 40 cases if you do it b...
The only thing I thought of is splitting it into different cases
peak estuary
zinc berry
I can't wait to see your code to print prime numbers.
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@lone arch Has your question been resolved?
lone arch
Let me try writing up the pigeonhole proof "in my words" from scratch
Generally, given (2n + 1) natural numbers, we can choose (n + 1) so that the sum is divisible by (n + 1) (this is some sort of hypothesis because it seems to agree with everything I've seen up until now.) Now, first break this down into "When given 3 natural numbers, you can always choose 2 so that the sum is divisible by 2". Proof: mod 2, either two of these are 0 or 1. Pick that pair, then the sum is 0 mod 2. Now, from the 7 random naturals, we can pick 3 pairs so that the sum is divisible by 2. Now mod 4, two of these 3 pairs are 2 mod 4 or 0 mod 4. In each case, adding them gives 0 mod 4. Thus, we got two pairs with their sum = 0 mod 4. Thus 4 numbers. QED
lone arch
I can't wait to see your code to print prime numbers.
Do you know if
Generally, given (2n + 1) natural numbers, we can choose (n + 1) so that the sum is divisible by (n + 1) (this is some sort of hypothesis because it seems to agree with everything I've seen up until now.)
Generally holds?
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soft trail
Hi I need assistance dividing up a Airbnb of a total of 1,857.55 amongst four people but not all are staying the same amount of time. So it may be fair
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Hi I need assistance dividing up a Airbnb of a total of 1,857.55 amongst four pe...
soft trail
Maur and Erik are staying at a airbnb from Wednesday to Sunday
Dyl is staying Thursday to Sunday
Ant is staying Friday to Sunday
hardy lion
are we assuming its wednesday full day or like wednesday noon to saturday noon
soft trail
Wednesday 3pm is usually the check in for airbnbs
hardy lion
and then you will check out before saturday 3pm?
soft trail
Checkout is Sunday 3pm
soft trail
4 days Maur & Erik
3 Days Dyl
2 Days Ant
soft trail
Yes
soft trail
Erik and I check in Wednesday 3pm
We arrive a day earlier
Airbnb has a per night system but after taxes and other fees on airbnb
it added up to 1857.55
hardy lion
im asking you to add up how many days each person stays
soft trail
9
hardy lion
did you count you and erik separately?
hardy lion
maybe
soft trail
13
hardy lion
divide the total price to get the price per day
soft trail
142.888462
hardy lion
then you multiply by how many days each person is staying to get their price
hardy lion
youll be off a couple cents here or there because of rounding probably, so you secretly give those to your friend
hardy lion
youre welcome
soft trail
you're a lifesaver. saved my friend group
do you have zelle or something?
i can send a tip
hardy lion
youre welcome, have a fun trip
little flare
im back with troubles on basic math. regarding the numerator here, how is it able to come out such a nice number? why, in this case, can FOIL not be used since the square root is effectively one term? and are you really able to multiply the square roots together if they're seperated by a term (in this case, the -1)?
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im back with troubles on basic math. regarding the numerator here, how is it abl...
lean otter
You do indeed use foil or you can also notice the two numerators are of the forms
(a-b) and (a+b)
And when you multiply: (a-b)(a+b)= a^2 - b^2
Which is how they simplified without foiling
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violet spear
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violet spear
1a Iām not sure how to start
I was thinking P=4l but sides could be different
A=lb
hollow knot
I was thinking P=4l but sides could be different
well, is it possible for sides to be different in a square?
violet spear
Ok thought it said rectangle mb
So p=4l
A=lb
O so 4.2x4.2
L and b r the same
Am I supposed to form am equation for 1b
hollow knot
the answer would be a number but yeah you have to form an equation to solve for it
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opaque pasture
opaque pasture
I've found these interval values , how do I find the domain and range ?
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ornate osprey
How would I be able to do this problem?
safe radishBOT
How would I be able to do this problem?
ornate osprey
using the divergence test, the limit is 0, so we have to use geometric series
.solved
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heavy flint
I believe the derivative would be -14*square root of two/ x^8 but it says it is wrong, am i solving this incorrectly?
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I believe the derivative would be -14*square root of two/ x^8 but it says it is ...
mortal arrow
Uhh
Ok so sqrt(8) times the derivative of t^-7
that would be -7t^-8 * 2*sqrt(2)
So -14*sqrt(2)*(4)^-8
heavy flint
oh so the t^8 isnt in the denominator in the derivative?
heavy flint
OH
mortal arrow
remember the exponent rules
heavy flint
right right
mortal arrow
So ` -14*sqrt(2)*(4)^-8`
Is this not your answer
heavy flint
let me try it
heavy flint
the derivative is correct but i think im getting the significant digits wrong
let me try it one more time
mortal arrow
What are you inputting
heavy flint
i got it i was just assuming the significant digits incorrectly! thank you! i forgot to move the denominator to the numerator with the exponent rule!
mortal arrow
np glad you got it right
heavy flint
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hard gale
How do I do part b and c
safe radishBOT
How do I do part b and c
hard gale
In the diagram O is center, TS is perpendicular to FOF and angle FTM = angle FTP=a Idk how to do B and C
<@&286206848099549185>
glass coral
What is part b asking?
hard gale
What is part b asking?
prove OT and TP are perpendicular
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dreamy elk
Maybe prove that TP is tangent to circle with center O and radius OT.
rugged cargo
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rugged cargo
Hints
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shadow glade
kinda confused, what are X and Y supposed to be in relation to A?
is there more context to this?
rugged cargo
Actually no further information
gray tulip
maybe hint: what is this matrix's characteristic polynomial?
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rugged cargo
maybe hint: what is this matrix's characteristic polynomial?
a-lambdai