.reopen
#help-49
iron escarp
midnight plankBOT
✅
unkempt stratus
I didn't get help with all sections of this last night but I did not see section D.
midnight plankBOT
I didn't get help with all sections of this last night but I did not see section...
unkempt stratus
Can you please help me figure out the equation for section d? Those are the correct answers I just need to know how to find it I know how to do a -c
@ me pls
When u see this
summer terrace
@unkempt stratus same way as you did with c)
just this time, you dont want the population to be 8M
you want it to be double the initial population
summer terrace
neither
unkempt stratus
Oof
summer terrace
just translate the words into math 😛
you want the population to be twice the initial population
let me ask you, what is the initial population?
unkempt stratus
6.14
summer terrace
right, so we want the population to be double of 6.14
we want it to be 12.28M
now, the population is modeled using the function you found in a)
so, just set P(t)=12.28
and find out what t has to be
unkempt stratus
12.28=6.14e^0.0238t
summer terrace
yes, now just solve it
isolate the time t
that would be the number of years that have to pass in order for the population of the city to become 12.28
entiendes
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spiral ravine
midnight plankBOT
spiral ravine
I can’t wrap my head around how I would word this
Like 5 times the distance from 2x + 3 ???
The wording is so confusing
odd lagoon
the distance from chenoas school is x?
spiral ravine
i dont know
the wording is throwing me off so much
I dont know how I would write it down
odd lagoon
+3 because 3 times more
spiral ravine
but thats only from the coffee shop to the school
odd lagoon
exactly
spiral ravine
so how do we know what x is referring to
odd lagoon
yes so that is one expression
spiral ravine
its only referring to the distance from the coffee shop to the school
odd lagoon
sorry now it threw me off too 
the second part anyway
you might need multiple variables and do some kind of equation system
odd lagoon
ah alright
hmm
you might need a different helper sry i couldnt assist you further
i wanna see how to solve this as well
<@&286206848099549185>
last slate
Ye?
odd lagoon
yes hi this
i guess for me my personal question is if you would need an equation system or not
last slate
I see
odd lagoon
then if camarozzz wants to ask for more help then by all means he should
last slate
It would be 1 equation
spiral ravine
ofc it would be 1 equation?
last slate
No worries bro
spiral ravine
wait I think I got it
odd lagoon
i just didnt know i am not familiar with what 1 unit of geometry means
language barrier or new concept for me
spiral ravine
this should be right think about it
home to coffee shop is 3 miles more than twice
so that means the coffee shop to school is half minus the 3 miles
and the home to school is 5 times coffee shop to school which is 2 miles
so 10x
6x+3=10x
odd lagoon
sounds like you meet the condition with that yeah
odd lagoon
damn
spiral ravine
I could have used
20x+3 and 10x and 50x
probably not equivelant
so im stuck
OOOOH
I got it
it would be 2x + 3 + x = 5x
odd lagoon
in sorry i just figured out that x is the distance from coffee shop the school 
spiral ravine
lol
odd lagoon
but nice good job man
spiral ravine
the wording is really challenging
I had to get it wrong to see the explanation but I was on the right track :/
odd lagoon
still good job but sad you didnt just logic it all the way
spiral ravine
its only 1 point out of 80 anyways
odd lagoon
at least u have more experience now
odd lagoon
big win have a nice day good luck with the rest
spiral ravine
thanks man
How did I get this wrong
3x+1 is equal to 2x+8
if you solve for x you get 7
then do 3(7)+1+4(7)-6+2(7)+8
and get 22+22+22
so 66
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last slate
midnight plankBOT
last slate
Is this right?
small jasper
Is this right?
Yes
last slate
how about this?
small jasper
how about this?
That’s fine too
midnight plankBOT
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twilit field
could I have a hint?
midnight plankBOT
could I have a hint?
twilit field
So the first thing I did was to find the number of possible combinations, which is c(100,10)
next the possible digits in each places
So The sum of the first 90 natural numbers has 4 digits
small jasper
could I have a hint?
This is the same as the number of possible sums for a ten-element subset. How can you bound said sum? Are all values in the range achievable?
twilit field
The sum can be bounded by chosing the 10 largest numbers in the set , for that will give us an upper bound
we then find the summation of the 10 smallet numbers in the set
and that gives us a lower bound
the lower bound is 55
the upper bound is 1045
hard shard
sus
twilit field
,w sum of first 10 natural numbers
grand pondBOT
hard shard
oh that part is fine
twilit field
,w sum of natural numbers from 91 to 100
grand pondBOT
chrome vessel
the upper bound is 1045
it should be 1000-45 not +
hard shard
another way is add 90 to each term
55+90*10=955
how do you get from ten terms summing to 55 to summing to 56
twilit field
I don't follow
hard shard
which part?
twilit field
how do you get from ten terms summing to 55 to summing to 56
twilit field
First 10 elements
hard shard
what ten elements sum to 56?
last plaza
can anyone help me
small jasper
can anyone help me
!occupied
midnight plankBOT
can anyone help me
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
twilit field
elements from 2 to 10 +12
hard shard
check that sum
twilit field
oops
hard shard
note that you only need to add one to one of the elements
twilit field
Yeah, I realise that. I have to add one element and remove one element
so remove say 9, add 11
hard shard
removing 9 is the same as doing what to the total?
chrome vessel
so remove say 9, add 11
yes, however, since the increment is 1 the difference should be 1.
twilit field
removing 9 is the same as doing what to the total?
reducing it by 9
hard shard
and then putting in 11 does what?
twilit field
increases it by 2 units
hard shard
so how can you make the net effect +1?
twilit field
I would add 10, but 10 would be repeated then
hard shard
yes
twilit field
I can remove 10 and add 11
hard shard
yup
twilit field
11
hard shard
what about 55 to 955?
twilit field
901
hard shard
yup
hard shard
youre welcoem
midnight plankBOT
chrome vessel
hmm, so every number between 955 and 55 can be achieved
there is a little bit more care that you need to put to prove this
midnight plankBOT
✅
twilit field
so Induction I would guess?
chrome vessel
specifically, when you reach 1,2,3,4,5,6,7,8,9, 100 what do you do now?
chrome vessel
so Induction I would guess?
yeah!
if you have $a_1,\ldots, a_{10}$ that sums to $k$, then can you create a set of distinct numbers that sum to $k+1$?
suppose the $k$ is not 945
grand pondBOT
qwertytrewq
twilit field
Remove say $a$ and to that add $a+1$
grand pondBOT
(why am i here )= idk
chrome vessel
Remove say $a$ and to that add $a+1$
but what if a+1 is also in the set？
what if a+1 is 101?
twilit field
et the last element be $d$ , then we have $k=d-a$ we we add the number d+k
grand pondBOT
(why am i here )= idk
chrome vessel
>et the last element be $d$ , then we have $k=d-a$ we we add the number d+k
k=d-a?
what is a?
grand pondBOT
qwertytrewq
twilit field
I think I'll come back to this in a bit
Maybe after I become a bit more familiar with induction
sorry
.close
midnight plankBOT
chrome vessel
what did you guys come up with for final answer?
yeah 901
junior flower
cool
junior flower
why the fuck is your name sweatyballs_123
junior flower
bad
last slate
💔 i hope things get better for u soon
junior flower
that would be nice
last slate
🙏
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drifting root
midnight plankBOT
drifting root
this is part of my friends solution
im confused on where the 1 went from the -2a^2k+1
oh nvm she just wrote it wrong
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midnight plankBOT
wary thorn
perhaps your sir divided through by "a"
drifting root
perhaps your sir divided through by "a"
the second term doesnt have an a to be divided
wary thorn
the second term doesnt have an a to be divided
yes it does
it actually had 2k+1 a's to be divided by
😂
drifting root
then there would be inconsistency in the first term tho
drifting root
yea probs
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chilly cobalt
midnight plankBOT
chilly cobalt
is there any manipulation used cause I’m stuck
midnight plankBOT
@chilly cobalt Has your question been resolved?
chilly cobalt
x^11
viral dagger
x isnt real :(
merry pewter
11th root of unity
chilly cobalt
just wondering how 1/1 + x + x^2 would even simplify
uncut cloud
is there any manipulation used cause I’m stuck
what have you tried?
chilly cobalt
what have you tried?
tried simplifying didn’t work
burnt flame
$\f{1-x^{3n}}{1-x^{n}}=1+x^{n}+x^{2n}$
grand pondBOT
🫎 Moosey 🫎
midnight plankBOT
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hoary drift
which set is this?
midnight plankBOT
which set is this?
runic hamlet
natural numbers including 0
hoary drift
why didnt they just write W 💀
runic hamlet
because nearly no one cares about W
midnight plankBOT
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shut canyon
midnight plankBOT
shut canyon
Please help understand this question.
@delicate helm Thank you for your help yesterday!
I would like to show how it works, but I am a bit confused, if it works at all.
We have the usual propositions:
φ, ψ, θ in {false, true}
So one way of composition of logical and operators, or functions would be:
(φ ∧ ψ) ∧ θ
Here the result of (φ ∧ ψ) is used as input in another and function … ∧ θ
A proposition is a subset P ⊆ X of subsets of X, for which P holds.
The logical and operation is an intersection of such subsets P ⋂ Q ⊆ X
For instance, if X is all the possible states of a potato, and P means boiled, while Q means cooked, then P ⋂ Q are all the states of a potato when it is both boiled and cooked.
⋂: A → B
⋂: (P, Q) ↦ ⋂(P, Q)
and: Boolean × Boolean → Boolean
Boolean is the set {false, true}:
and: {false,true} × {false,true} → {false,true}
∩: P(X) × P(X) → P(X)
and seems to be analogous to multiplication in integers modulo 2.
from sympy import symbols, And
# Define abstract Boolean variables
a, b, c = symbols('a b c')
# Compose the logical AND function using symbolic variables
result = And(And(a, b), c)
print(result) # Output: And(a, b, c)
So can we do the following:
$and \circ and$
grand pondBOT
kytsu
shut canyon
I think and(a, b) could be composed like this: and(and(a,b), c)
midnight plankBOT
@shut canyon Has your question been resolved?
midnight plankBOT
shut canyon
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midnight plankBOT
✅
shut canyon
We can compose two functions if they have the same codomain and domain:
dom g = cod f, so dom f = dom(g ∘ f) and cod(g ∘ f) = cod g
dom ∧ = {false, true} × {false, true}
cod ∧ = {false, true}
Perhaps this is why we can't compose, because the domain of and has a different form, than codomain of and.
shut canyon
<https://en.wikipedia.org/wiki/Function_composition#Multivariate_functions>
Thanks @shell wigeon
midnight plankBOT
@shut canyon Has your question been resolved?
pearl idol
**kytsu**
Yeah I wouldn't use this notation for it, as it's ambiguous if the right AND is occurring in the first or second argument of the left AND
elfin fox
I am stuck on this proof. I don't know where to begin
If 10^x = 2 then x is irrational
midnight plankBOT
I am stuck on this proof. I don't know where to begin
If 10^x = 2 then x is irra...
exotic pelican
a simple proof by contradiction should work. Assume that x = p/q for integers p and q
elfin fox
a simple proof by contradiction should work. Assume that x = p/q for integers p ...
The furthest I know how to get from this is then by saying p/q = ln(2)/ln(10)
exotic pelican
oh no dont use any logs
novel lion
try taking log with base 10 instead, if log
exotic pelican
$10^{\frac{p}{q}}=2$
grand pondBOT
rbit
exotic pelican
theres one simple thing you can do from here
elfin fox
Raise both sides to q/p is the only other thing I can think of
exotic pelican
raising both sides is good, try to just get rid of the fraction
elfin fox
Raise both sides by q?
exotic pelican
yeah
elfin fox
Lhs and rhs are both integers now
exotic pelican
$10^p = 2^q$ and just think about whether this is possible or not
grand pondBOT
rbit
exotic pelican
right (unless ofc p is zero but that can be excluded)
elfin fox
Oh true yeah thank you
exotic pelican
also negatives
elfin fox
.close
last slate
midnight plankBOT
last slate
Why only when it converges?
When it converges the limit will have a finite value
I am guessing that's the reason
Even if it is I don't understand why
Help?
shadow schooner
Help?
take point 1. the limit is a real number with a special property, then if either the limit of the a_n or b_n does not exist as a real number then adding these limit will not make sense.
last slate
Oh
Yeah
Makes sense
A lot
Same with the rest of the properties too right?
Division with infinity as denominator won't make sense
Okay
Thanks!
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midnight plankBOT
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naive sleet
midnight plankBOT
cinder basin
I think "start with y = r sinθ" is typo, should be start with r = sinθ ,this is a circle
midnight plankBOT
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twilit field
${(x,x+y) : x \in R, y\in \Z}$
midnight plankBOT
$\{(x,x+y) : x \in R, y\in \Z\}$
grand pondBOT
(why am i here )= idk
grand pondBOT
(why am i here )= idk
runic hamlet
why do you think so
polar mortar
hmmm, doubt it.
twilit field
I mean say x=2, it maps to (2,3),(2,4),(2,5) \dots (2,2+y)
polar mortar
what about when x = 0?
twilit field
it maps to (0,1),(0,2).....(0,n)
polar mortar
so, how would you get something like (0, pi)?
twilit field
hmm, you can't
I mean it isn't R^2
But It surely isn't a standard curve either, is it
modern sapphire
can you try a small plot for a constant y?
twilit field
Y/N
modern sapphire
Put y = 0 and see what you get
twilit field
For a constant y , it'x x=k
modern sapphire
you mean (k,k)?
modern sapphire
and is that a standard curve?
modern sapphire
and so on for all y
modern sapphire
if you see a countable set, try enumerating the set element by element if you dont get a clear idea immediately
twilit field
so It's the family of curves parallel to x=y
pearl idol
Wouldn't that just be all of R^2?
All of R^2 is contained on some line that's parallel to the line x=y
modern sapphire
so, how would you get something like (0, pi)?
.
polar mortar
yeah, it's a family of curves. Saying the is a little strong
or you need more qualifiers on that set
last slate
midnight plankBOT
last slate
Could someone please give an example opposite to the case shown here.
grim vector
Could someone please give an example opposite to the case shown here.
The first or second ?
last slate
Both are not the same?
I thought since they both were proving that the limit exists,they are the same
tribal temple
Hmmm, "the same" how?
grim vector
So you want an example where the limit doesn't exist ?
grim vector
You can try with (-1)^n
last slate
Okay I will try
last slate
You can try with (-1)^n
Lt n tends infinity (-1)^n = ?
No
Like
What shpuldni take the value of L as ?
Should*
I
@grim vector ?
Funny
The next example
Is the one you gave
grim vector
Is the one you gave
Famous one dealing with sequences
south seal
Yes it is alternating sequence
last slate
@grim vector
grim vector
?
last slate
The ending would have been true
grim vector
Can you show the whole ?
summer ravine
last slate
last slate
Can you show the whole ?
^,Is this what you meant ?
grim vector
Ye
midnight plankBOT
@last slate Has your question been resolved?
last slate
Is it because the definition says "for every epsilon >0"?
So we have to take every case
Just taking some epsilon >1 won't do
Am I right?
@grim vector ?
grim vector
If epsilon is greater than 1 that would work indeed
But making it tends to zero
It became wrong
Moreover this is true cuz all value of (-1)^n are between -1 and 1 so the abs value is < 1
last slate
But making it tends to zero
Making what tend to zero?
grim vector
Epsilon
last slate
I didn't get you
grim vector
Epsilon, in the meaning iirc has to tends to zero, with that, at a certain point you have all the values of the sequence/function close to the limit, but since epsilon tends to zero and has to be greater than 1 its not logical so limit does not exist
grim vector
I didn't know that epsilon should tend to zero
Its a little positive number in the meaning
Thats how i see it
last slate
Okay so 0<epsilon<1 ?
grim vector
Okay so 0<epsilon<1 ?
I took value in it indeed
Since you need counterexample
Ig it works
last slate
Okay so 0<epsilon<1 ?
So it's just for this example that we had to take the above range unordered to prove that the limit doesn't exist
Am I wrong again?
grim vector
(That will probably works the same with cos(n) and sin(n) as well)
grim vector
Am I wrong again?
Soz bad internet
Epsilon has to be little cuz otherwise we cant figure the limit out ( imagine it being like epsilon = 3, it means that all the terms are around the limit with a max distance of 3 at a certain step. So its better to have a little distance rather than a big one, its more precise
midnight plankBOT
@last slate Has your question been resolved?
last slate
Epsilon has to be little cuz otherwise we cant figure the limit out ( imagine it...
Okay
Thanks a lot!
.close
midnight plankBOT
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real pivot
midnight plankBOT
real pivot
so using chain rule for z_t I get
z_t = f_x(x_t) + f_y(y_t) = f_x(2ts) + f_y(2)
whats the next step
z_ts = f_x(x_t)(x_s) + f_xy(x_s)(y_s) + f_y(y_t)(y_s) ?
oh wait is it:
z_ts = f_xx(x_t)(x_s) + f_xy(x_t)(y_s) + f_yy(y_t)(y_s) + f_xy(y_t)(x_s)
-2(2ts)(t^2) + 5(2t)(3) + 2/3(2)(3) + (5)(2)(t^2)
0 + 0 + 4 + 0 = 4?
shit idk
midnight plankBOT
@real pivot Has your question been resolved?
real pivot
<@&286206848099549185>
robust forge
-2(2ts)(t^2) + 5(2t)(3) + 2/3(2)(3) + (5)(2)(t^2)
0 + 0 + 4 + 0 = 4?
0+0+4+0 = 4 that is correct 
craggy owl
brain died a bit
midnight plankBOT
brain died a bit
craggy owl
What am I doing wrong?
craggy owl
could it be asking for something else?
craggy owl
yea?
viral dagger
whats it asking
craggy owl
the amount of cell phones will minimaze the cost
viral dagger
mhm
viral dagger
so, is that asking for the cost?
viral dagger
yea
viral dagger
its asking in thousands
viral dagger
my first answer was 13.8 *1000
if you do this your basically saying there is 1380 thousand phones
craggy owl
like 13.8 *100
viral dagger
no
craggy owl
so itd be in thousands
viral dagger
yeah sorry
fuck how do i say it
if i say the answer is just 13.8 will you understand me
craggy owl
alr
just this part
was making me rethink everything
ah
omg
isee
im dumb
thank you
the thousand is already in the answer-----
viral dagger
yeah thats what i wanted to say i had no idea how
craggy owl
viral dagger
good job
midnight plankBOT
viral dagger
bye
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chilly cobalt
Find the amount of (A,B) such that A and B are subsets of {1, 2, 3, 4, 5, 6}
and. |A| |B| = |AUB| |AUB|
midnight plankBOT
Find the amount of (A,B) such that A and B are subsets of {1, 2, 3, 4, 5, 6}
and...
chilly cobalt
I got that A = B and |A| = 1,2
small jasper
Are you sure? A=B={1,2,3,4,5,6} is possible.
nova yoke
any A=B works
and with a bit of effort you can show that A=B is necessary as well
small jasper
Are you sure? A=B={1,2,3,4,5,6} is possible.
Also, is this question written correctly?
Is $|A \cup B|$ actually written twice on the right hand side?
grand pondBOT
Civil Service Pigeon
midnight plankBOT
@chilly cobalt Has your question been resolved?
floral apex
for what class?
hard shard
heres a hint: the function of air density is based on what?
floral apex
hello?
bawangs hint is good
you could think about this as maybe like, what'd be the easiest way to do this?
and to me, itd be easiest to add up all these slices
if in each slice, the density was the same all over the slice
because if we have something like idk $\sum _{\text{slice}} \text{density}(s,w)$
grand pondBOT
jan Niku
floral apex
where s and w are the other two variables describing some point on our one dimensional slice
this is pretty not so bad if density is constant over that slice, i think
does that help at all
hard shard
yeah its f
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twilit coyote
how to express U(n) in function of n? I want a brief demonstration if possible.
queen ermine
Try
Like
Computing the first 2
for n = 0 and n = 1
and n = 2
and look at what you have
Oh nvm I dun goofd
floral apex
are you sure its possible 
twilit coyote
are you sure its possible <:thonk:406575732563902485>
i mean
what makes u doubt that
floral apex
well i mean it wouldnt be hard to write down a recurrence relation you cant solve just like its not hard to write down a differential equation with no solution
just asking though
nothing poking at it seems straightforward but im pretty bad at math
have you tried oeis?
twilit coyote
hm?
west iron
Looks like a Mobius function
twilit coyote
Looks like a Mobius function
never heard of that
west iron
Could be overkill
floral apex
numerator appears to be OEIS A060819
west iron
I'd start by trying polynomial division
feral sedge
how to express U(n) in function of n? I want a brief demonstration if possible.
if u just plug in numbers u will figure it out fairly easily
twilit coyote
i found a way to do this but
how
twilit coyote
if u just plug in numbers u will figure it out fairly easily
pretty sure i wont waste my time
floral apex
and the denominator is a shifted version of the top
twilit coyote
this isnt a special sequence
twilit coyote
how will i do that
floral apex
$U_n = \frac{ (n+7) }{ \text{gcd}(n+7, 4) }\frac{ \text{gcd}(n+4,4) }{ (n+4) }$
grand pondBOT
jan Niku
twilit coyote
**jan Niku**
my gad
floral apex
hmm might be off by 1
feral sedge
$U_n = \frac{ (n+7) }{ \text{gcd}(n+7, 4) }\frac{ \text{gcd}(n+4,4) }{ (n+4) }$
u don't need to express it like this
floral apex
i think i am, actually
nah, I'm just stealing from OEIS
this is where i'd start
PERSONALLY
only because im bad at math
plain osprey
my gad
prove that An is arithmetic by calculating its three first values
then express Vn in function of n since its arithmetic
then substitute it
in
using equations
solve for Un
west iron
,w x = (5x-1)/(x+3)
grand pondBOT
twilit coyote
wtf
twilit coyote
it has some fixed points
whats right
floral apex
i dont remember
west iron
It's not an ap
floral apex
i didnt think so
west iron
Maybe the numerator is at least in an unreduced version
west iron
anyways
floral apex
it appears that the numerator is a translated version of the denominator
why not try starting there
if u really dont want to just rip the sol from oeis
altho i should scribble to make sure its actually helpful
twilit coyote
if u really dont want to just rip the sol from oeis
idek whats oeis
the hell is that
west iron
consider the sequence An = 1/(Un + 1)
This is like proof by asspull
It probably works but there's 0 motivation
wait
don't you want Un-1 on the bottom anyways
grand pondBOT
jan Niku
plain osprey
.
floral apex
idek whats oeis
oeis is the hammer for figuring out sequences next to other techniques
plain osprey
It probably works but there's 0 motivation
most likely expressing a function in terms of n would require an arithmetic sequence
cause u can express those in terms of n
floral apex
use a computer to calculate whatever, 25 terms, put them into oeis
it tells you some esoteric function that generates that sequence
floral apex
check the next 75 terms or so and see if theyre right
floral apex
but whatever this is
it appears to be the relationship between the numerator and denominator
theyre translated off each other
feral sedge
it tells you some esoteric function that generates that sequence
this isn't even necessary
twilit coyote
why am i so dumb and i cant understand anything
plain osprey
cause yes
feral sedge
since the discussion here is a mess. it's not ur fault
west iron
oeis is the hammer for figuring out sequences next to other techniques
Well he asked jan what oeis was and he replied with this
So it's probably not his fault he can't follow
oeis is an online encyclopedia of integer sequences
floral apex
i guess i figured theyd have googled it i'm not super together tonight the obvious thing to do would be just explain, thats my bad
twilit coyote
no
twilit coyote
oeis is an online encyclopedia of integer sequences
is this a site
west iron
yes
floral apex
it is
west iron
yeah oeis probably not the way to do this
plain osprey
do that
floral apex
you do what the other people are suggesting
this is something youd do when you need the answer for some other reason
plain osprey
yeah oeis probably not the way to do this
isnt my way efficient still tho
plain osprey
did i say +1
west iron
yes
west iron
consider the sequence An = 1/(Un + 1)
here
plain osprey
its what my school does
and wants us to do
its also a method
lets see
+1 doesnt work
yeah -1 probably
twilit coyote
do i js follow ur method
plain osprey
did u understand tho
twilit coyote
eh
west iron
my intuition is that the sequence harmonically converges
checking fixed points shows it would have to converge to 1
near eagle
i think it does
west iron
so subtract one and now it converges harmonically to 0
take the reciprocal and now it's an AP
west iron
but shittier
Weird way of spelling "correct"
west iron
np lol
plain osprey
ur cooked
west iron
midnight plankBOT
west iron
rip
plain osprey
we did all we could man
near eagle
i think it converges to 2
plain osprey
we provided algebra
near eagle
:/
plain osprey
we even pulled calculus
west iron
It would be weird to converge to something that isn't a fixed point
plain osprey
@twilit coyote if u want the answer tho based on what i did
uh
am i allowed to tell him
west iron
Idk I won't tell
plain osprey
i got struck by a certain 77^2 guy after i answered for smn
plain osprey
ill dm ya
near eagle
thnks
plain osprey
nvm i cant
near eagle
why?
plain osprey
friend first
near eagle
done
midnight plankBOT
Available help channel!
midnight plankBOT
floral apex
what have you tried?
for part c
do you know what a left hand riemann sum with dx=1 means
@grave haven
i was typing at the same time as you 😭 where could you possibly have gone
grand pondBOT
x
floral apex
sure
but you can write x_i better
theyre evenly spaced right
whats x_0?
whats n?
oky
that doesnt answer the question though 
whats x_0?
these should go what, x0, x1, x2, ...
and theyre evenly space
I guess, maybe you could explain how early into this you get stuck, don't let me drag you along
unless you are stuck now
you have a sequence in your sum
I'm asking you to define it
I'm telling you its arithmetic lets say
$x_i = x_0 + i \cdot d$
grand pondBOT
jan Niku
floral apex
whats d? whats x_0?
do you believe that this is the form for x_i?
evenly spaced along some interval?
okay
Are you able to answer my questions? or what's giving you trouble
this what?
they're numbers
Yea
delta x is given right
floral apex
**x**
in your sum
but you have stuff written there you havent defined
you need to define n
and you need to define x_i
then, everything in your answer is just a number
instead of some general form
I'll be honest you're racing the clock against my sleeping pill @grave haven
Is there any way you can decrease the latency a little here
I worry I'm going to lose you
if not no biggie I just have to hand you off
midnight plankBOT
@grave haven Has your question been resolved?
midnight plankBOT
@grave haven Has your question been resolved?
craggy owl
what's wrong with my domain?
midnight plankBOT
what's wrong with my domain?
sharp coral
the domain of the inverse function is the same as the range of the original function
midnight plankBOT
midnight plankBOT
Available help channel!
subtle minnow
Please solve Q8.
midnight plankBOT
Please solve Q8.
midnight plankBOT
@subtle minnow Has your question been resolved?
subtle minnow
<@&286206848099549185>
mystic patio
what have u tried
subtle minnow
Firstly I don’t understand how it has 3 solutions
Then put t= mod of x-2
And made the equation quadratic in terms of t
Then I checked the solution.
Well here’s the solution for you
Please explain the solution
mystic patio
that's quite neat of a solution
have u tried writing the roots out in terms of K ?
i think the root 0 would give u some possibilities and the root positive is your condition of k
subtle minnow
No idea
mystic patio
delta
subtle minnow
have u tried writing the roots out in terms of K ?
I did everything but nothing made sense
mystic patio
really? lemme try 1 min
subtle minnow
Got it!!!
We made the equation quadratic in terms of t
And t is mod x-2
Thus mod of x-2 has 2 solutions
Which means x has 4 solutions in total
Now, for 3 distinct solutions for x
2 values of x must be equal
mystic patio
0
subtle minnow
Yeah
But one case im still getting confused with
Let’s say the equation in t has two roots t1 and t2
Each t1 and t2 will give 2 values of x
Let’s say t1 gives x1 and x2 and t2 gives x3 and x4
So for 3 distinct solns 2 of the xs must be equal
Why can only x1 = x2 or x3=x4
Why can’t it be x1=x3 and we’d still get 3 solutions
mystic patio
So for 3 distinct solns 2 of the xs must be equal
not necessary
cause t1/2 don't always give 2 xs
t = 0 only gives 1 x
and since u proved that one of the t has to be zero
mystic patio
Why can only x1 = x2 or x3=x4
this happen
subtle minnow
Also is this true that mod gives equal roots only when it is equal to 0?
mystic patio
mod of a linear equation ye
subtle minnow
Ok thanks
That’s the entire question
It was only tricky
Almost all the questions here have some trick behind them and they don’t even require bulky solutions
.close
midnight plankBOT
subtle minnow
mod of a linear equation ye
One more question
Will it be k=2 always
Even for the other non zero root of t?
mystic patio
oh hold up
mystic patio
Even for the other non zero root of t?
you wonders if K would still be the same if u plug in the other root right
K would have to be 2 cause f(t=0)=0 is not a possibility but a true equation
k would change if it is either f(t=0)=0 or f(t=other t)=0
but in your case, both have to happen at the same time
midnight plankBOT
Available help channel!
twilit field
I feel like I've screwed up big time here (Y/N)
midnight plankBOT
I feel like I've screwed up big time here (Y/N)
modern sapphire
the stray is 3
modern sapphire
you just need to reduce -2 to 1
twilit field
I multiply R_1 by -3/4.5 and add it to R_3
modern sapphire
yeah
modern sapphire
Also, why not follow the algorithmic process? Like from leftmost column to rightmost?
That leaves less chances to be confused
twilit field
The guassian algorithm that is?
modern sapphire
Yeah
twilit field
That's the next section in my book
modern sapphire
Ohh
twilit field
I think the aim is to motivate a need for the guassian algorithm via such examples
modern sapphire
but yeah, if you convert it to upper triangular or any triangular, it makes the process more mechanical and you get easier time doing it
modern sapphire
I think the aim is to motivate a need for the guassian algorithm via such exampl...
I dont think gaussian algorithm is any different. It is just the one order of operations that is most natural for the computers to follow. All row ops do the same thing basically
twilit field
Does this look about right?
modern sapphire
seems alright
But I wouldnt rely on me. Just verify with any random online calcs
twilit field
,w solve 2x+y+z=-1;x+2y+z=0;3x-2z=5
grand pondBOT
hard shard
also btw you only need to make it upper triangular
twilit field
Well, I've messed up somewhere
modern sapphire
also btw you only need to make it upper triangular
tbf, back substitution is also elementary rw ops
hard shard
tbf, back substitution is also elementary rw ops
true, but you could avoid a few row ops that way
modern sapphire
true, but you could avoid a few row ops that way
but only in programs. Humans dont calculate 0*0 anyways
hard shard
im having a stroke reading fractions of decimals
hard shard
dont build bad habits now
hollow oyster
dont build bad habits now
*dont build bad habits ever
twilit field
Is this better?
twilit field
*dont build bad habits ever
Hi, convergence !
hollow oyster
Hi, convergence !
hello wai hows uni going?
hollow oyster
i see ,wait what tutorial?
hollow oyster
iirc dont you know that already
twilit field
I do
twilit field
Right so far?
twilit field
also are you getting along with your classmates
Math and physics students, yes
hollow oyster
Math and physics students, yes
thats good,have fun over there
twilit field
Does this look fine? The solutions seem to check out
modern sapphire
Now make the left hand side identity matrix (I wanna see 0.5/4.5 on right 
)
runic hamlet
dont use mixed fractions
twilit field
Now make the left hand side identity matrix (I wanna see 0.5/4.5 on right <:hype...
here you go
midnight plankBOT
midnight plankBOT
Available help channel!
twilit field
Chat could any of y'all give me some questions similar to question 50?
midnight plankBOT
Chat could any of y'all give me some questions similar to question 50?
twilit field
Or even similar to 49
surreal moon
Chat could any of y'all give me some questions similar to question 50?
${(p, q) : p,q\in\bN, \gcd(p, q)=1}$
