yeah plug n = 2,3 into the formula for c
#help-17
trim tree
urban zinc
yeah plug n = 2,3 into the formula for c
hmm
so far with n = 2
it equals 1
i will do n=3 rn
urban zinc
not sure if i did it correctly
chatgpt tells me c 6 and 0 equals 1
so that would make both n = 2 and n = 3 equal, 1
vocal sleetBOT
@urban zinc Has your question been resolved?
urban zinc
no
vocal sleetBOT
@urban zinc Has your question been resolved?
urban zinc
.close
bitter pilot
Let $G$ be a group. For $g\in G$ define $P(g) \coloneqq {g^n \mid n = 1,2,3,...}.\$
Declare on the set $G$ the relation $\sim$
[ g_1 \sim g_2 :\Leftrightarrow P(g_1) \cap P(g_2) \neq \emptyset. ]
Show, that this relation is an equivalence relation. $\$
So far I managed to show quickly that it is reflexive and symmetric. However I am failing at the transitivity part and it also feels unintuitive and I would love some help please.
vocal sleetBOT
Let $G$ be a group. For $g\in G$ define $P(g) \coloneqq \{g^n \mid n = 1,2,3,......
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
twin meteorBOT
Axe
lilac pebble
what do you get from the definition of ~?
bitter pilot
P(g1) and P(g2) is non-empty and P(g2) and P(g3) is non-empty
twin meteorBOT
Axe
lilac pebble
we can get g_2 ^ (bc)
bitter pilot
how and why
twin meteorBOT
Axe
bitter pilot
it will connect g1 to g3
I understand now and it was actually simple
but it still feels unintuitive for some reason lol
lilac pebble
i spent like an hour and a half on one problem earlier
bitter pilot
Also I wanted to ask if a ~ b => b ~ a because you can literally do P(a) n P(b) = P(b) n P(a)
bitter pilot
i spent like an hour and a half on one problem earlier
on the same or another?
lilac pebble
Also I wanted to ask if a ~ b => b ~ a because you can literally do P(a) n P(b) ...
yeah that seems right
lilac pebble
on the same or another?
another one involving the definition of ring
and subring
it was just a lot of details to keep track of 
bitter pilot
it was just a lot of details to keep track of <:bleakcat:913340873771716630>
Can you help me with another one lol
Let G be finite, then prove there exists exactly one equivalence class.
quiet echo
i know this is off topic, but we figured out in the other server that it had to satisfy the conditions (for nCk), n>=k and k>0
lilac pebble
Let *G* be finite, then prove there exists exactly one equivalence class.
uh i think they all have to hit 0 at some point but i'm not sure
by the pidgeonhole principle i guess
there must exist a,b such that g^a=g^b
then use the inverse of g on that equation
you'll get either g^(a-b)=e or g^(b-a)=e depending on which of a and b are bigger
sorry i should probably use e instead of 0 (edited the message)
bitter pilot
there must exist a,b such that g^a=g^b
can you explain this pleas
lilac pebble
g can be raised to any positive integer power (that's countably infinitely many)
but all of these powers of g are elements of the finite group g so they cannot all be different
bitter pilot
ok i understand i think
lilac pebble
i think you can also say g generates a cyclic subgroup of G, which must be finite, and e must be in that cyclic subgroup
hm but how do you know it's not one of the inverses that gets you e...
i'm gonna have dinner
bitter pilot
ty
desert plume
2\sin x \sin 2x = 3 - \sqrt{3} \sin x
vocal sleetBOT
2\sin x \sin 2x = 3 - \sqrt{3} \sin x
desert plume
How can I solve this?
meager shoal
Do u know double angle formula
meager shoal
2\sin x \sin 2x = 3 - \sqrt{3} \sin x
Can u plug that in here
Let u = sinx and cosx = sqrt(1 -u^2)
Dunno whether that approach is right or not
desert plume
Uhh cosx can be negative so should I consider both cases?
Btw the solution should be aπ/b + k2π (find a and b) so I can't just plug it into my calculator
vocal sleetBOT
@desert plume Has your question been resolved?
vocal sleetBOT
@desert plume Has your question been resolved?
tropic brook
vocal sleetBOT
earnest trench
hmm
earnest trench
im confused on how to do this
well first
use the midpoint formula: diagonals of a parallelogram bisect each other.
tropic brook
ok
earnest trench
then you find the midpoint of ac
(-3 + ( -6))/2, (-4 +4) /2 = -9/2,0 = -4.5,0
set this equal to the midpoint of bd
(5 + x) /2, (4 + y) /2
next solve for x and y
earnest trench
bet
vocal sleetBOT
earnest trench
thanks bro i got it
np
vocal sleetBOT
Available help channel!
sick trellis
need some help with significant figures and unit conversion, can anyone help out here?
vocal sleetBOT
need some help with significant figures and unit conversion, can anyone help out...
sick trellis
I need to convert 5 feet and 2.0 inches to meters with the correct amt of sig figs. however, given that the question is asking for 5 feet and 2.0 inches, i am unsure of how to get to the correct number of sig figs
rare granite
Convert it to inches first
sick trellis
convert feet to inches?
rare granite
convert feet to inches?
convert 5 ft and 2 inches to just inches
chrome steppe
Or convert everything to feet... you need everything in terms of one unit
feet, inches, meters, cubits... pick one
sick trellis
ok so now i have 60 inches. when adding to 2.0 inches, how do i consider sig figs into here. 60 inches is one sig fig, and 2.0 inches is two sig figs. with adding and subtracting you use the lowest amount of numbers after the decimal point. so because 60 has no decimal point, does that mean its just 62 inches?
chrome steppe
60 inches is 2 sig figs.. it's screwed up, but on the left side of the decimal, you count all the figures back to the decimal
sick trellis
waat
chrome steppe
on the right side, you don't count all the way to the decimal...
.0000003 is only 1 sig fig
sick trellis
right
chrome steppe
But 30 is 2 sig figs
sick trellis
what about 300
chrome steppe
3 sig figs
sick trellis
tf
sick trellis
most videos ive seen say that 300 is 1 sig fig
drifting jackal
3 sig figs
No it's 1 sig fig
sick trellis
or 60 is 1 sig fig
drifting jackal
- is three
sick trellis
so 60 is one sig fig?
chrome steppe
Now it's going to depend on who you ask... UND's physics department, 300 is 3 sig figs
oh for fuck's sake.. if it depends on whether or not we include the decimal, then there's a problem
if 300 is 1 sig fig
but 300. is 3 sig figs
then no
drifting jackal
That's what I said...
chrome steppe
No.. absolutely not.. there's a total lack of consistency here
drifting jackal
It's common that 300 is 1 sig fig, not 3
sick trellis
im just going to go with no decimal point and ending in zero being one sig fig bc if i remember correctly thats what my prof said is right
chrome steppe
Common in your circles; my experience as a Civil Engineering student at the University of North Dakota suggests otherwise
Granted, Spring 2025 is only my fourth semester here
But hey
drifting jackal
It's just that university.... everywhere else, it's taught that 300 is 1 sig fig
chrome steppe
Ok.. so an ABET certified university is... just different?
drifting jackal
No just that university
drifting jackal
Different
chrome steppe
That's what I asked - thanks
So! Banana.. it depends on what your university teaches
drifting jackal
The way you phrased it made it sound like all ABET certified university is different, but it's just yours that is different
sick trellis
going back to my original question, so 60 + 2.0 would simply be 62, right?
chrome steppe
No one here can help you, since apparently universities teach significant figures differently
drifting jackal
The rest of the ABET are normal
chrome steppe
Yes, 60 + 2 = 62
sick trellis
not 62.0?
chrome steppe
-
- 2 is also 62
drifting jackal
not 62.0?
No because sig fig rules for adding/subtracting is based on decimal places
chrome steppe
Ok, I see where you're going.. 60 = 60.
2 sig figs
2.0 has 2 sig figs
so 60. + 2.0 = 62.
2 sig figs
drifting jackal
going back to my original question, so 60 + 2.0 would simply be 62, right?
Fyi
chrome steppe
Fyi
And this is my gripe with the "sig fig" argument... because if anything on the left of the decimal has to be broken down this way, then there's a problem
600.0 x 2.0
The least certain measurement is apparantly 2.0, based on these rules.. so the answer isn't 1200.0
it's 0
drifting jackal
No it's 1200
chrome steppe
No, the graphic you posted explicitly states that the number of sig figs is based on the least certain measurement, and if 2.0 has only 2 sig figs, then it is the least certain
Based on the graphic YOU posted
drifting jackal
Yes. So 600.0 x 2.0
2.0 has the least amount of sig figs which is 2, so 600.0 x 2.0 = 1200
1200 has 2 sig figs
drifting jackal
.
drifting jackal
1200 is 4 sig figs
That's 2 sig figs
chrome steppe
1200 is 4
drifting jackal
Not 4
chrome steppe
It is 4
drifting jackal
No, there's no decimal point
chrome steppe
You said yourself the decimal doesn't matter
drifting jackal
I never said that
chrome steppe
No because sig fig rules for adding/subtracting is based on decimal places
Here
drifting jackal
You have two different rules for adding/subtracting and multiplying/dividing
Adding/subtracting, you use decimal places
restive tundra
Sig figs are really based on how you'd write it in standard form. 1200 could either be 1.2*10^4 (2 sig figs), 1.20*10^4 (3 sig figs), or 1.200*10^4 (4 sig figs)
chrome steppe
That is not what you said
drifting jackal
Multiplying/divsing is using the least amount of sig fig
chrome steppe
You explicitly told me to exclude the decimal point
chrome steppe
No need for the decimal
No need for the decimal
drifting jackal
so 60. + 2.0 = 62.
If you're referring to this, it's not necessary to have the decimal point because 62 is 2 sig figs and 62. is still 2
There's no need for a decimal point
chrome steppe
There's no need for a decimal point
There is, or there isn't..
drifting jackal
It would be different if you were doing 60 vs 60.
chrome steppe
600.0 * 2.0 = 1200 or it equals 0
Either we include the decimal point or we don't
MAKE UP YOUR GODDAMNED MIND
drifting jackal
You're misunderstanding the concept of sig figs
chrome steppe
You said that sig figs are based on the least certain
drifting jackal
The decimal point matters when there are zeros involved
drifting jackal
Yes
drifting jackal
As I stated, 1200 is 2 sig figs, not 4
chrome steppe
1200 is four sig figs.
drifting jackal
1200 has no decimal point
chrome steppe
Who cares, 12 is not equal to 1200
drifting jackal
1200 is different to 1200.
drifting jackal
- is 4 sig figs
chrome steppe
12 has 2
heavy yoke
the 00 is just necessary to specify the order of magnitude
chrome steppe
No, you said to exclude the decimal
the 00 is REQUIRED to show the magnitude
is the magnitude not significant?
drifting jackal
1200 has 4 sig figs
Trailing zeros don't count unless there is a decimal point
chrome steppe
is 12 the same as 12,000,000?
No
So the zeroes aren't significant, even though they dictate the magnitude?
hence 12 = 12,000,000
This is wrong.
This is fundamentally and extraordinarily wrong.
restive tundra
Sig figs is a measure of accuracy, not magnitude
Think about it like this
I go for a run
drifting jackal
is 12 the same as 12,000,000?
You can argue this with the same logic about 0.00001 too. That's 1 sig fig, not 5
heavy yoke
i think you have the wrong idea of what sig figs even are
restive tundra
I run 1.2km
I convert that to metres and I get 1200m
Am I suddenly 100 times as precise?
No
It's just a notational thing
chrome steppe
Argue amongst yourselves. This is wrong.
restive tundra
Write everything in standard form and this is not an issue
Because that's how sig figs are actually defined
drifting jackal
Argue amongst yourselves. This is wrong.
You're just wrong and stubborn about it
chrome steppe
You're just wrong and stubborn about it
Then I've been taught wrong by an ABET certified university. Take it up with the ABET certification board.
I'm not your enemy, they are.
Because they say you're wrong.
So... congrats?
Whatever.
I'm done with you.
.close when you're ready, banana
heavy yoke
ideally all significant figures would be written in scientific notation e.g. we would write
1.2 E3
the significant figures are the number of decimal places we wrote in the mantissa (1.2 is 2 digits). the magnitude is not included. if we wrote 1.20 E3 then that would be 3 sig figures
chrome steppe
Nothing else positive is going to be produced here
restive tundra
How would you round 1200 to two significant figures then?
restive tundra
Nothing else positive is going to be produced here
I totally agree btw
heavy yoke
because significant figures are a measure of relative uncertainty
heavy yoke
ideally all significant figures would be written in scientific notation e.g. we ...
notably the number of significant figures for any notation other than scientific is up to convention, and conventions vary. so in some convention 1200 may be considered to have 4 sig figs, because they count trailing 0s no matter what. this is not because the order of magnitude is included, just a matter of which convention would be more commonly useful (since you do need to go to scientific in edge cases)
vocal sleetBOT
Available help channel!
steep merlin
hello
steep merlin
I understand that the square root with a polynomial argument is considered a composite function
which uses the chain rule that is f'(g(x)) * g'(x)
which would be (1/2)(3+tan^2x)^-1/2 * sec^2
which would be tthe same as 1/2(3+tan^2x) * sec^2
which is the same as sec^2/2(3+tan^2x)
which sec^2/6+2sin^2/2cos^2
which is the same as sec^2/6+2sin*2sec^2
which reduces to 1/6+2sin^2
but
that is not the answer
so im not sure what I did wrong
chrome steppe
steep merlin
im having trouble figuring out what error I made when I was finding the derivative of y = sqrt(2+tan^2x)
I got 1/6+2sin^2 as my answer
chrome steppe
What steps did you take?
steep merlin
first I took the derivative of tthe outer
so I put the square root as a fractional exponent
chrome steppe
Personally, I hate radicals... sqrt(3+tan^2 (x)) = (3+tan^2 (x))^.5 is easier
chrome steppe
What's the derivative of 3?
steady plover
I got 1/2(3+tan^2x)^-1/2 * sec^2
how did you get sec^2
steep merlin
how did you get sec^2
the derivative of the inner function
chrome steppe
Ok, so.. remember this is chain rule followed by a simple sum
steady plover
are you sure the derivative of 3 + tan^2 = sec^2?
steep merlin
tan's derivative is sec, so tan^2's derivative would be sec^2 no?
steep merlin
are you sure the derivative of 3 + tan^2 = sec^2?
I mightt be getting something wrong
what do you think?
steady plover
no haha unfortunately it dosent work like that
chrome steppe
No.. you might want to check that
chrome steppe
Remember, tan isn't just tan.. it's sin/cos
steep merlin
Remember, tan isn't just tan.. it's sin/cos
right
AH
Id have tto use the quotient rule on sin^2/cos^2
chrome steppe
So you've got a quotient rule hidden in there
Work on that and see where it leads you
vocal sleetBOT
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Available help channel!
crude swan
Can someone help me wrap my head around this question?
vocal sleetBOT
Can someone help me wrap my head around this question?
crude swan
For Sequentially closed => closes, could we say, let A* be the set of all monotonically increasing and convergent sequences in A and A' be the set of all the monotonically decreasing and convergent sequences in A.
nvm
mental egret
for sequentially closed => closed, you might want to use A not closed => A' not open => there exists a x in A' such that a ball with radius 1/n centered at x contains at least one point from A, say x_n. Show that lim x_n is not in A thus contradicting our assumption
proof by contradiction
crude swan
what does that ball with 1/n radius part mean?
mental egret
Do you know what a ball is?
we generally use an open ball for analysis proofs so ig that'd be enough hmm
crude swan
is it like eg the ball of x is (x - epsilon , x + epsilon)
mental egret
yes, if your space of concern is R, for R² it's a circle, for R^3, a sphere but with the same idea as (x - epsilon, x + epsilon)
crude swan
ahh ok
mental egret
it's just simpler generalizing the concept into a ball
crude swan
I don't quite get this part: there exists a x in A' such that a ball with radius 1/n centered at x contains at least one point from A
mental egret
I don't quite get this part: there exists a x in A' such that a ball with radius...
you can visualize it as: A' is closed => there exists a point x from the boundary points of A' such that the ball with radius 1/n centered at x will share an intersection with A
for n = 1, 2, 3, 4, ...
basically, the point is to show that the sequence thus formed (x_n) lies entirely in A, but the limit point lies in A'
crude swan
basically, the point is to show that the sequence thus formed `(x_n)` lies entir...
the first A has to be A' right?
crude swan
basically, the point is to show that the sequence thus formed `(x_n)` lies entir...
in this sentence
mental egret
it's A
crude swan
both are A
mental egret
second is A', mb
mental egret
because the ball is centered at "x" the limit point is x
which by construction, lies in A'
crude swan
so is this right: Let A be set and x_n an arbitrary convergent sequence in A ,which its limit x is not in A.
mental egret
Are you trying to show closed => sequentially closed?
crude swan
based on the definition of convergence, there exists an n>N_x such that |x_n - x| < e regardless of how small e gets
mental egret
Then perhaps you might want to add, Let A be a closed set. Let (x_n) be a convergent sequence with x_n in A for all n and let lim x_n = x
crude swan
Are you trying to show closed => sequentially closed?
no I just want to know if this thought process is correct.
mental egret
no I just want to know if this thought process is correct.
I want to know which direction of the proof you're working on to say whether you're correct or not. Is it (=>) or (<=)
crude swan
the one you already showed me
crude swan
```for sequentially closed => closed, you might want to use A not closed => A' n...
this one
Not sequentially closed => Not closed
mental egret
so is this right: Let A be set and x_n an arbitrary convergent sequence in A ,wh...
For sequentially closed => closed, your assumption is that for any convergent sequence in A, the limit points lie in A. So this fails
mental egret
so because the "ball" of every element of x_n lies within A, this fails
No, because A sequentially closed implies every convergent sequence in R, whose elements lie in A, has a limit in A. So by definition the limit of your constructed sequence cannot lie outside of A
I'm saying you created a false pretext, so you cannot build your proof on that
crude swan
No, because A sequentially closed implies every convergent sequence in R, whose ...
But i was trying to go from Not Sequentially Closed => Not Closed
if the limit lies outside of A, that means it's not sequentially closed right?
mental egret
That's not how logic works. $p \implies q \neq \neg p \implies \neg q$
twin meteorBOT
crude swan
🤦♂️
mental egret
You have to assume either of p or q and work for the other direction
crude swan
I saw this in my script and thought it does
mental egret
XD
crude swan
number 7)
mental egret
Yeah no, it has neg B => neg A :p
so you can show not closed => not sequentially closed, which is what we're esssentially doing in our proof by contradiction
vocal sleetBOT
@crude swan Has your question been resolved?
vocal sleetBOT
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Available help channel!
leaden ingot
I came across a problem that goes like this:
2 people A and B plays a game. Person A is given 9 numbers from 1 to 9. Person B is given 8 numbers from 1 to 8. For each person, here's how it goes:
- From the given numbers, pick 3 of them
- Arrange the chosen numbers in a descending order
- Combine the numbers to create a 3-digit number
The person creating the bigger number than the other is the winner.
Calculate the probability that A wins.
leaden ingot
It is easy to count the sample space, it's simply 9C3 * 8C3, because there's only 1 way to arrange the numbers
Next I find n(E) as follows:
Case 1: Suppose one of 3 numbers A picks is always a 9
- Because 9 is already picked, we only need 2 more numbers.
- Note that when arranging A's number, the number 9 is always the largest, so A's number is always larger than B's number. So any 3 digits he chooses will always result in a loss.
Hence, the number of ways for E to happen is n(E1) = 8C2 * 8C3
(I can also find the probability directly from this case, it's 8C2 / 9C3 = 1/3)
Case 2: Both A and B have to make a number from digits from 1 to 8
- This is where I got stuck.
vocal sleetBOT
@leaden ingot Has your question been resolved?
dark kiln
1/8c3 that they pick the same number
otherwise it's equal chance that A wins
1/3 + (2/3)(0.5)(55/56)
so we just skip the calculation
what did we skip idk
solemn sonnet
vocal sleetBOT
sinful heron
I would say now just calculate the determinant in the ordinary way (using cofactors or using rule of Sarrus)
vocal sleetBOT
@solemn sonnet Has your question been resolved?
random nexus
Quick question, if my substituent is in the middle where should the numbering be (left or right?)
vocal sleetBOT
Quick question, if my substituent is in the middle where should the numbering be...
sullen wigeon
Quick question, if my substituent is in the middle where should the numbering be...
doesn't matter
visual marsh
result wud be same
random nexus
But what if it's like this
Oh
I'm dumb
It doesn't matter too😭
Thank you!
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
minor pewter
This where to send question?
vocal sleetBOT
This where to send question?
mental egret
!original
vocal sleetBOT
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.
mental egret
Hello keii
minor pewter
I need help on 12, and 15, I'm unsure of 12, in 12, the x = 1 but I don't know how to get the angle K and on 15 I'm completely stuck and don't know how to solve it pls help
mental egret
Did a good job finding x, to find K note that the trapezoid is an isosceles trapezoid, and you're given the base angles.
J and K are co-interior, thus supplementary
minor pewter
So j and m is 26⁰ , so angle j + angle k = 180?
mental egret
yes because J and K are cointerior angles
minor pewter
Thx but how about 15?, I can't seem to find the measure of y
mental egret
For 15 you have two equations, can you tell me what they are?
minor pewter
Wait, nvm I solved it thx
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
@minor pewter Has your question been resolved?
weak heath
how do i ask for help im a bit lost
vocal sleetBOT
how do i ask for help im a bit lost
mental egret
!status
vocal sleetBOT
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
Rule of thumb: If you dont know what to do, try doing the steps that you think is useful
For me, the very long requirement can be shortened to "simplify g(x)"
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
Can someone help me with vector impulse
vocal sleetBOT
Can someone help me with vector impulse
vast shale
mental egret
Now v = u + I/m => v = (4i + 4j) + [(5cos t)i + (5sin t)j]
=> v = (4 + 5cos t)i + (4 + 5sin t)j```That's the gist of it ig 
What condition makes v on a 45° from u
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
```Let \lambda = (2.5cos t), \mu = (2.5sin t).
Now v = u + I/m => v = (4i + 4j) ...
Ok thanksss
vast shale
That's the gist of it ig <:holothink:595992719633940482> What condition makes v ...
I = 0
Or j = 0
mental egret
Yes
fossil oak
What is up with my text book
vocal sleetBOT
What is up with my text book
mental egret
perhaps you're watering them too much they're overgrowing, try watering them appropriately
crude yoke
What is up with my text book
Is this math?
vast shale
What is up with my text book
clean you laptop 
vocal sleetBOT
@fossil oak Has your question been resolved?
fossil oak
Is this math?
No it’s geography
fossil oak
clean you laptop <:blobwg:1130147597428998184>
U got a wipe I can use
languid basalt
{ -2x + ay = 7
{ bx - 3y = -6
system of equations, infinite solutions, find a + b
shut canyon
do you know the condition for infinite solutions using the cramers rule?
languid basalt
whats cramers rule
ruby slate
is the book telling you that there are infinite solutions?
languid basalt
is the book telling you that there are infinite solutions?
yes
ruby slate
ok, nothing more?
languid basalt
mhm
ruby slate
you didn't study determinants, did you?
languid basalt
no
ruby slate
ok don't worry ahaha, I'm thinking about something else
languid basalt
i could only find a but not b
ruby slate
how did you find it
languid basalt
coefficient -7/6
ruby slate
could you show your work here please?
languid basalt
subbing it in to line 1
wait lemme check again
wait thats a diff equation i think
languid basalt
could you show your work here please?
so im at square 1
ruby slate
ok
I think I got it
when you have a system in the form
{ a1x + b1y + c1 = 0
{ a2x + b2y + c2 = 0
to have infinite solutions, as you said, you need one to be a scalar multiple of the other
this can be translated in the condition
a1/a2 = b1/b2 = c1/c2
so c1/c2 = -7/6
this means that a1/a2 must be -7/6 too, so -2/a2 = -7/6, so a2 = 12/7
and following the same reasoning b1 = 7/2
translating these results back to our system means that a = 7/2 and b = 12/7
so a + b = 73/14
languid basalt
uhh what
ruby slate
indeed
{ -2x + 7/2y = 7
{ 12/7x - 3y = -6
has infinite solutions
ruby slate
the system has infinite solutions
to have infinite solutions the system has 2 have the 2 rows, one multiple of the other
example: x + y = 1 and 2x + 2y = 2
ok?
languid basalt
ok
ruby slate
now
a row, if translated to canonical form (implicit form) can be written as
ax + by + c = 0
a and b are the coefficients of x and y and c is the constant
so in our example it becomes x + y - 1 = 0
and 2x + 2y - 2 = 0
ok?
languid basalt
ok
ruby slate
now this condition, if you look closely can be translated in an equality of fractions
a1/a2 = b1/b2 = c1/c2
because, taking the example, 1/2 = 1/2 = -1/-2
languid basalt
a1/a2 = b1/b2 = c1/c2
wait wdym by this
ruby slate
wait wdym by this
a1 is the coefficient of x of the first row and a2 is the coefficient of x of the second row
same for the other letters
ruby slate
a1/a2 = b1/b2 = c1/c2
.
languid basalt
ah ok
ruby slate
ax + by + c = 0
.
as you can see if one is the multiple of the other, the coefficients must have some relation
so every ratio must be equal to the others
now read again what I wrote the first time and you should get it
ruby slate
=> b/-2 = 6/-7
=> b = (6*(-2))/-7
=> b = -12/-7
=> b = 12/7
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warm blade
How can I go about solving this? I don't even know how to start lol, BUT I was thinking that I should somehow use BD = DC.
vocal sleetBOT
How can I go about solving this? I don't even know how to start lol, BUT I was t...
warm blade
yes, i'm familar with it
warm blade
Have you solved it?
nope
wait
could i
do cosine law for idk like C, and then just solve BC
copper root
Im going for a different route but okay
warm blade
then i'd just have to rearrange the equation a bit
warm blade
Im going for a different route but okay
wut were u thinking of?
copper root
That problem is actually an application of stewarts but here it is
warm blade
ya i've heard of it, but i haven't been taught it yet, and the formula won't be available during my test
copper root
Let ADB = A°, and ADC = B°
warm blade
oke
copper root
That meant AB² = AD² + BD² - 2(AD)(BD) cosA
and AC² = AD² + DC² - 2(AD)(DC) cosB
Do you get it?
copper root
Nope
copper root
That meant AB² = AD² + BD² - 2(AD)(BD) cosA
and AC² = AD² + DC² - 2(AD)(DC) cosB
But you get this okay?
copper root
That meant AB² = AD² + BD² - 2(AD)(BD) cosA
and AC² = AD² + DC² - 2(AD)(DC) cosB
Next is, the cosine of supplementary angles states that cos(180-theta) = -costheta
That meant CosB = -cosA
Substituting that from the 2nd equation, you will get AC² = AD² + DC² +2(AD)(DC) cosA
Adding both equations
You would get AB² + AC² = 2(AD² + BD²)
Since BD = DC, you would easily get BC
You have all three variables there
AB = 4, AC = 7, AD = 7/2
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vital latch
Hey!
vital latch
Is there a shortcut to tell in which quadrant the following complex numbers are?
wasn't the greatest fan of 5*180 / 7 etc
vital latch
could you show me an example of one?
not sure im following
like for the first one i just thought 7*x = 900, x ~ 130
so second quadrant
but for e^2000pi*i / 13 that approach is a bit worse
vital latch
so you're free to multiply 13 with 100?
i mean what quadrant would you get it to be in with your logic?
serene needle
4th
vital latch
yes
serene needle
Yes
vital latch
so how did you go from that to 2000-1300?
serene needle
You know you can write 50/13 as 3 11/13
vital latch
uhh sure
serene needle
My cancelling is just taking 2pi on side
In first step I wrote 2000-1300=700
I simply did
2000pi/13 = 100pi 700pi/13
Got it?
vital latch
ah think i see what you mean
serene needle
Yeah just asimple way
vital latch
and then?
like we can remove the left term since 100pi is just 50 cycles
so you have 700pi / 13
serene needle
Repeat until you get numerator less than 2 times denominator
Or simply divide of that's convenient to you
serene needle
50pi * 50 pi / 13?
Yeah
serene needle
It's 2pi + 24pi/13
vital latch
uhhh
serene needle
I think you did odd multiple
vital latch
2000pi/13
100pi 700pi/13
40pi 180pi/13
10pi 50pi/13
2pi 24pi/13
yeah
and then we can see that it's less than 26, more than 19,5 so 4th quadrant
aight that's a neat method, thank you!
have a nice day 
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timid leaf
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timid leaf
is my explanation accurate? anything i could add?
question is basically- is it a function?
lavish dock
Looks good to me
One thing tho: "no repeated x value"
I belive that {(1, 1), (1, 1)} is also function
reef agate
I belive that {(1, 1), (1, 1)} is also function
I thought sets couldnt have repeated values. Correct me if im wrong
lavish dock
I thought sets couldnt have repeated values. Correct me if im wrong
Multisets?
reef agate
Multisets?
Idk what that is 😦
lavish dock
But for relations it probably doesnt matter
So @timid leaf it seams clear and correct
timid leaf
So <@1132371071975309322> it seams clear and correct
neat, thanks!
learned something new too
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gaunt crown
how do you do this
vocal sleetBOT
how do you do this
gaunt crown
I have labelled all the angles around the pentagon but no matter what i try to do i only get x+y+z+w=160
quiet echo
I have labelled all the angles around the pentagon but no matter what i try to d...
how so?
quiet echo
how do you do this
note here the inscribed angle theorem
gaunt crown
CED is w
BDC is y
ACE is 20 degrees etc
gaunt crown
note here the inscribed angle theorem
how though none of the angles are on the centre
quiet echo
how though none of the angles are on the centre
inscribed angle
gaunt crown
*inscribed* angle
isn't that the one where the angle at the centre is double the angle on the circumference?
gaunt crown
how does that help
quiet echo
how does that help
you can find arc measures now.
gaunt crown
how
gaunt crown
a whole bunch of the angles must be equal
yeah i've labelled them but i don't know what to do next
lilac pebble
now EAB = ABC
gaunt crown
angle ABC is half of the arc measure of AC
what's an arc measure
quiet echo
oh.
lilac pebble
so you have angle EAB=green + orange + purple ?
gaunt crown
so you have angle EAB=green + orange + purple ?
yep
lilac pebble
and ABC = ?
lilac pebble
so equate those
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vast shale
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flat whale
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gray fox
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gray fox
im having a hard time getting the function in terms of y. how do i do that for e^(4x)?
mighty nacelle
why do you need the function in terms of y?
gray fox
because its revolving around the x axis
lilac pebble
the function is already in terms of y
you can use the disk method, integrating with respect to x
gray fox
you can use the disk method, integrating with respect to x
but im in the section that is supposed to be cylindrical shells
should i still use disks?
gray fox
okay cool
gray fox
no i haven't sketched it yet but im pretty sure that i need to solve the function for x since its revovling around the x axiis
lilac pebble
y=e^(4x)+3
y-3=e^(4x)
from here use the natural log
lilac pebble
now i think you'll want to sketch it
gray fox
now i set that to 0 to get the bounds right
lilac pebble
yeah you'll want to set it to 0
gray fox
so i got y=4
lilac pebble
what's next?
gray fox
but shouldn't there be an upper and lower bound?
lilac pebble
for the integral bounds?
i think you'll need 2 integrals
so you'll need an upper and lower bound for each integral
gray fox
wait why would i need two integrals?
lilac pebble
you'll see if you sketch it
the left bound is different for y<4 and for y>4
when y<4 it's bounded on the left by x=0
when y>4 it's bounded on the left by x=ln(y-3)/4
are you sure you can't use the disk method?
gray fox
i mean it doesn't say what method i have to use im just in section 6.3 which is the cylindrical shells section 6.2 was the disk method
also here is the graph that i got
lilac pebble
yeah that looks right
gray fox
okay so the graph this i also need to set this to 0.3
lilac pebble
this integral is really hard
gray fox
so u did two cylindrical integrals
gray fox
can you explain why you have (0.3) in the first integral
gray fox
why is it not just the second integral? what does the 0 to 4 integral do? because isnt that outside of the overlap?
lilac pebble
isn't this the area we need to rotate?
gray fox
ya
lilac pebble
the first integral is for rotating this part
gray fox
why would the rotation around the x axis split the integral
lilac pebble
to do it in one integral, you need an equation for the left bound. it will need to be piecewise
this is the left bound
$g(y)=\begin{cases}0 & 0\leq y<4\\frac{\ln{y-3}}{4} & 4\leq y < e^{6/5}+3\end{cases}$
twin meteorBOT
Axe
gray fox
i feel like this is way harder than it should be
gray fox
are we sure that we are doing this right?
lilac pebble
no i think it should be disk method
gray fox
okay then lets try that way
lilac pebble
sorry i have to go
i'm back
yeah the disk method will be integrating with respect to x
from 0 to 0.3
the integrand is pi*f(x)^2
gray fox
like this?
lilac pebble
yeah
gray fox
what did i do wrong?
lilac pebble
the 0 bound doesn't completely go to 0
gray fox
oh wait its because e^0 is 1 so i actually need to do the other side!
lilac pebble
yeah
gray fox
i think im going crazy! this is still wrong
gray fox
okay finally! thank u
lilac pebble
nice 👍
vast shale
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copper root
Hi, I'm solving this problem about recursion, but I can't find how they got the answer which is 18213, One thing I did was to factor the recursion which will yield as (x_n - x_(n+1))(x_n*x_(n+1) - 27) = 0, Given that x_20 = x_25 = 3, the only possible I could see is when x_n = x_(n+1), but that would only yield 6075, the other case is not possible since it has satisfy x_20 = 3 and x_25 = 9, since its alternating, and it will not yield 18213 regardless, are there any other ways?
vocal sleetBOT
Hi, I'm solving this problem about recursion, but I can't find how they got the ...
copper root
Yuh from the recent PMO Area Stage
copper root
I hate geometry ones more
copper root
I agree
deft vapor
there are obviously a lot of cases
and the easiest one that I found is x_n = 3
for all n
it works
but its not the maximum
since when you plug in x_n = 3
you get 3 or 9
bro good luck i cant help you im too dumb for this shit
😢
copper root
I can't find the reasoning too
deft vapor
you might wanna ping helpers
copper root
I think I got it
copper root
we know that x_n = x_(n+1) or x_n*x_(n+1) = 27
That meants to find the maximum, we need to set x_1 to x_19 as 9, then follow the second condition for x_20 to yield 27, then x_21 to x_24 is 9, x_25 is 3, Then all the rest till 2025 is 9, there are 2023*9 + 3(2) = 18213?
copper root
I'm not familiar with recursion but can be it be like erratic or smth
little cedar
Except x_20 and x_25
copper root
Like for some reason x_20 and x_25 is 3
little cedar
So let x_21 be a for easier typing
.
rancid kelp
I don’t understand their definition of M as a maximum. M is perfectly defined as a sum, no ?
little cedar
A/3 = (a^2+27)/(3^2 + 27) @copper root
We get a^2-12a+27
We get the root 3 or 9
If we insert 3 again it will be the same for each therm
Term*
X_20 = 3
X_21 = 3
copper root
Hmmm
little cedar
But if we set x_21 to be 9
See what happen
Try doing it
So let x_22 be B
We get b^2 -12b + 27
little cedar
We get a^2-12a+27
Same as .
So the maximum value will be when all of the x_N value is 9 except x_20 and x_25
Because it is specified
copper root
Oh I see, you meant to say for every sequence of two terms like x_n and x_n+1, then theres always two possibilities
little cedar
So we choose the biggest one
Because it ask for maximum
So if I ask you
What is the minimum value
copper root
6075 when its all 3?
little cedar
Yeah
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weak terrace
is my new computation correct or nah
vocal sleetBOT
is my new computation correct or nah
weak terrace
.
sharp lynx
is my new computation correct or nah
as written your computations line up, but are you 100% certain you've done all of the required computations?
vocal sleetBOT
@weak terrace Has your question been resolved?
weak terrace
as written your computations line up, but are you 100% certain you've done *all*...
yeah
i got the mean
sharp lynx
you do got the mean
fleet hemlock
u canot put "=" back to back to back they create false equation keep that in mind if u need to hand the sheet
fleet hemlock
is my new computation correct or nah
cz this equation for example isnt valid amd if u hand that it will be mark as wrong
i understand what u did just keep in mind to not hand work like that
grizzled breach
A locus is |z-1-i|=1. How do I find the max and min value of |z|
sly sierra
do you know what this equation represents geometrically?
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grizzled breach
do you know what this equation represents geometrically?
a circle a 1,1 with radius 1
so the max |z| is 2 + x where x is the distance from the orgiin to the circle but idk how to find that
sly sierra
well geometrically it's clear that the min and max should be along the same line that connects the origin and the center of the circle
so (1,1) plus or minus a unit vector in the same direction as (1,1)
grizzled breach
how do I find that tho
sly sierra
well a unit vector in the same direction is (1,1)/sqrt(2)
so the max should be at (1,1) + (1,1)/sqrt(2)
and the min at (1,1) - (1,1)/sqrt(2)
now just find the magnitudes of those numbers
grizzled breach
what is a unit vector and how do u know its sqrt 2
grizzled breach
where did u get root 2
sly sierra
sqrt(1^2 + 1^2)
grizzled breach
but don't u have to find the distance from the origin to the circle then add 2 for the diameter
sly sierra
should be equivalent
grizzled breach
what
sly sierra
you'll get the same answer either way
(you add or subtract 1 for the radius though, not 2 for the diameter)
oh wait
grizzled breach
idk what you mean with the whole subtracting and adding
sly sierra
you meant to the edge of the circle
no it's easier to find the distance to the center of the circle
and then add or subtract 1 to get the min and max distances
grizzled breach
well the max mod is from the origin to the furthest point isn't it?
sly sierra
that's what i thought you meant
sly sierra
well the max mod is from the origin to the furthest point isn't it?
sure, but do you know the distance to the closest point? that's the min you're trying to find
so sure, if you have that you can add 2
vocal sleetBOT
sly sierra
to get the max
grizzled breach
oh so ur saying make a triangle at the centre?
sly sierra
well find the distance from the origin to the center of the circle
then you add 1 to that to get the max
or subtract 1 to get the min
grizzled breach
oh ok thanks
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crude scaffold
Find the volume of the solid whose base is bound by the circle whose center is the origin and whose radius is 8 with the indicated cross sections perpendicular to the X-axis
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Find the volume of the solid whose base is bound by the circle whose center is t...
crude scaffold
A. Squares
So I set up an integral and my answer is half the correct one
And I can’t tell where I went wrong
civic yacht
would there be anybody that could help me study for my math test next week?
crude scaffold
Get out of my channel bro
lilac sluice
lol
civic yacht
dog u sent me here
crude scaffold
Anyways
I put 2 times( -8 and 8 as my bounds then I integrated [sqrt(64-x^2)]^2)
Because the function only gives positive so I have to double the volume obviously
And I got 1365.333 repeating
When the answer is
2730.6666 repeating
And the dumbass answer key just immediately sets it up like 8 on the outside then integrated the function from 0 to 8 like WTF
So I need help with the process
outer warren
be careful of your dimensions
you can't just multiply by 2 at the end like that
did you draw a diagram of the cross section
what's the length of square for each one?
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nimble dune
What is the integral from -∞ to ∞ of (1/[1−x^2]) dx?
vocal sleetBOT
What is the integral from -∞ to ∞ of (1/[1−x^2]) dx?
flat whale
What is the integral from -∞ to ∞ of (1/[1−x^2]) dx?
Have you learned partial fractions
quiet echo
as the problem has an asymptope in +- 1
then split it up
and calculate left and right hand limits
reef agate
Isnt this a standard derivative
quiet echo
no?
twin meteorBOT
quiet echo
+ cant you use trig sub rather than pfd
its a - not a +
reef agate
Whoops
sly sierra
then split it up
i don't think this will help
quiet echo
and calculate left and right hand limits
then you can determine convergence/divergence
nimble dune
the integral is 1/2 (ln abs ( 1+x / 1-x ) ) + C
quiet echo
i don't think this will help
its a standard method if you're going to go ahead and evaluate it
sly sierra
gl making it converge
nimble dune
it does not converge
sly sierra
its a standard method if you're going to go ahead and evaluate it
yea i meant it's not gonna help it converge
sly sierra
well you can potentially get misled if you end up with something of the form infinity-infinity, that doesn't automatically imply divergence
nimble dune
Okay, one question, is integral from -inf to 0 and 0 to inf fine to do?
mental egret
No
quiet echo
you want to split up at asymptotes
mental egret
also, why did you pick 0?
quiet echo
if you're going to
leaden ingot
you have to specifically split the integral to: -inf to -1-, -1+ to 1-, 1+ to inf
nimble dune
I was thinking of that
sly sierra
as soon as you find that the integral on any of those three intervals diverges, you can stop
so it's less work than it sounds like
nimble dune
but I was stressing on writing it because it would be lim x - > -inf lim -> -1
mental egret
Given it's an even function, you can just do I equals twice integral from 0 to inf
nimble dune
as soon as you find that the integral on any of those three intervals diverges, ...
I mean, if I get a inf - inf it will be a problem
that is undefined
mental egret
so you don have to split in 3 intervals
quiet echo
the integral is 1/2 (ln abs ( 1+x / 1-x ) ) + C
but we know this
sly sierra
I mean, if I get a inf - inf it will be a problem
well you can see from the graph that it doesn't change signs on any of those intervals so each one will just be infinity or -infinity, then you know the whole thing can't converge
mental egret
$\frac{I}{2} = \int_0^{1^-} \frac{1}{1 - x^2} , \dd x + \int_{1^+}^{\infty} \frac{1}{1 - x^2} , \dd x$
nimble dune
yeah but it misses -1 to 1
twin meteorBOT
mental egret
for the asymptotes, you wanna write in terms of limit
nimble dune
I guess that makes sense because the equation mirrors
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nimble dune
Ill try that out, I need to close the channel?
leaden ingot
if you want, sure
you can still come back at any time
nimble dune
ok
leaden ingot
!done
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timid leaf
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timid leaf
is my math correct? mostly concerned about prediction of phone users and whatever reliability is
timid leaf
i did 2004 because that's what made sense to me
there was some extra context I didn't add cuz it was mostly fluff
but basically the premise was: you are trying to convince your friend to invest in the mobile phone industry
timid leaf
Og it means 2027
the data ends at 2002 so i took it as like "most recent data" and did 2 years ahead
if I did 2 years from 2025 then my prediction would be nonsense because everyone has a phone now
vocal sleetBOT
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lavish dock
if I did 2 years from 2025 then my prediction would be nonsense because everyone...
Exactly, that's the solution lol
lavish dock
but basically the premise was: you are trying to convince your friend to invest ...
Then it makes perfect sense. Your solution is good
vast shale
Can anyone explain me what the hell is this. I found this equation in a document .
vocal sleetBOT
Can anyone explain me what the hell is this. I found this equation in a document...
@vast shale Has your question been resolved?
manic copper
