can I use weak induction?
#help-39
summer imp
You could make it work with weak, but it's awkward. Instead of proving the statement P(n) for all n, you would essentially need to change the statement to the equivalent statement P(n) and P(n-1) for all n and handle two cases at once.
Again they're equivalent, so you're free to use strong induction all the time if you want
stoic imp
can we prove this using strong induction
summer imp
.
summer imp
So now what would be your induction hypothesis?
stoic imp
2 < k < m holds
summer imp
<=
summer imp
both
stoic imp
2 <= k <= m
summer imp
So you should write that your statement holds for 2 <= k <= m.
summer imp
And now you want to prove that P(m+1).
stoic imp
how do I do it
summer imp
What is P(m+1)?
summer imp
I see no m+1 in there.
stoic imp
@summer imp
jolly parrotBOT
Renato
stoic imp
now yes ?
summer imp
Yes
This is what you want to prove.
Now you're given some recursive definition of a_n. Apply it to a_(m+1)
stoic imp
in particular we know that P(k) holds for 2 <= k <= m
summer imp
How is a_n defined?
stoic imp
,, a_{m + 1} = (m + 1)(1 + a_m)
jolly parrotBOT
Renato
stoic imp
this shit still depends on am
summer imp
Hence why you use induction.
stoic imp
,, a_{m + 1} = (m + 1)! \sum_{k = 1}^{m} \frac{1}{k!} \ (m + 1)(1 + a_m) = (m + 1)! \sum_{k = 1}^{m} \frac{1}{k!}
jolly parrotBOT
Renato
stoic imp
@summer imp
stoic imp
,, a_m = m! \sum_{k = 1}^{m - 1} \frac{1}{k!}
jolly parrotBOT
Renato
summer imp
Yes good continue.
stoic imp
,, a_{m + 1} = (m + 1)(1 + a_m) \ a_{m + 1} = (m+1) \left(1 + m! \sum_{k = 1}^{m - 1} \frac{1}{k!}\right)
jolly parrotBOT
Renato
summer imp
Yes/
stoic imp
,, a_{m + 1} = (m + 1)(1 + a_m) \ a_{m + 1} = (m+1) \left(1 + m! \sum_{k = 1}^{m - 1} \frac{1}{k!}\right) \ a_{m + 1} = (m + 1) + (m+1)! \sum_{k=1}^{m - 1} \frac{1}{k!}
jolly parrotBOT
Renato
summer imp
Yes
stoic imp
(m+1)! / (m-1) = (m+1).m.(m-1).(m-2)! / (m-1) = (m+1).m.(m-2)!
,, \sum_{k = 1}^{m} \frac{1}{k!} = \frac{1}{m!} + \sum_{k = 1}^{m - 1} \frac{1}{k!} \ \left(\sum_{k = 1}^{m} \frac{1}{k!} \right) - \frac{1}{m!} = \sum_{k = 1}^{m - 1} \frac{1}{k!}
jolly parrotBOT
Renato
stoic imp
(m+1)!/m! = (m+1).m!/m!
bingo
,, a_{m + 1} = (m + 1)(1 + a_m) \ a_{m + 1} = (m+1) \left(1 + m! \sum_{k = 1}^{m - 1} \frac{1}{k!}\right) \ a_{m + 1} = (m + 1) + (m+1)! \sum_{k=1}^{m - 1} \frac{1}{k!} \ a_{m + 1} = (m + 1) + (m+1)! \cdot \left(- \frac{1}{m!} + \sum_{k = 1}^m \frac{1}{k!}\right) \ a_{m + 1} = (m+1)! \sum_{k = 1}^m \frac{1}{k!}
jolly parrotBOT
Renato
stoic imp
@summer imp
summer imp
So then P(k) for 2 <= k <= m implies P(m+1) and by strong induction P(n) holds for all n in N.
Notice how you didn't need to use anything other than the case k=m to prove k=m+1.
stoic imp
whats your point?
@summer imp
strong induction is more useful than knowing weak induction
summer imp
My point is just that assuming P(k) holds for 2<= k<= m was unnecessary in the end. You could've just assumed that P(m) holds.
And the argument would've been the same.
stoic imp
I still prefer it
summer imp
It's a matter of style. I was just pointing it out.
summer imp
It's always the same thing :
base case
induction hypothesis : Suppose (your induction hypothesis about P(m))
induction step : Then P(m+1).
By the principle of mathematical induction, P(n) holds for any natural >= (your base case).
stoic imp
It's always the same thing :
base case
induction hypothesis : Suppose (your ind...
can you help me with the proof structure for this specific exercise
summer imp
Well you have all the pieces. You've done the base case. You've written down your induction hypothesis. You've proved the induction step.
summer imp
It's always the same thing :
base case
induction hypothesis : Suppose (your ind...
Try writing something that puts those together like this
stoic imp
It's always the same thing :
base case
induction hypothesis : Suppose (your ind...
but I want to use strong
summer imp
It's the same thing. You induction hypothesis will be that P(k) holds for 2 <= k <= m
The format is always the same
stoic imp
.close
rigid terrace
I'm forgetting how to do something simple.
Going through a power series to find the convergence interval, I've manipulated it into geometric series form and found that r = (x - 4) ^ (-7).
This means the power series converges on | (x - 4) ^ (-7) | < 1.
rigid terrace
I should be able to solve that the convergence interval is (−∞,3) ∪ (5,∞). I've forgotten how.
cobalt hinge
do you remember the ratio test perchance (i don't expect you to)
rigid terrace
finding the infinite limit of the absolute value of series a sub n+1 / series a sub n < 1 ?
cobalt hinge
yea
so just do that with this is all
find what $x$ satisfies $\lim_{n\to\infty}\qty|\frac{a_{n+1}}{a_n}|<1$
jolly parrotBOT
;(
cobalt hinge
or like
a geometric series with ratio r converges with |r|<1 is also another way you can do this (so you're halfway there)
you can use that |x^n|=|x|^n to simplify the inequality
rigid terrace
that's right, I should be able to do that..
just curious, should it be simple to see | (x - 4) ^ (-7) | < 1 and solve for the interval being one away from 4? I'm wondering how the speed would compare to the limit ratio test, if I remember how
my instruction just says this:
rough forge
The step is simply skipped
jolly parrotBOT
cobalt hinge
that's right, I *should* be able to do that..
just curious, should it be simple...
i mean its common enough (the geometric series, that is) for you to be able to recognize it
the interval solving part not as much imo
its a little bit of algebra that you may or may not know cause inequalities are a bit tricky
long nova
how do i know the direction of DA?
pearl pondBOT
how do i know the direction of DA?
long nova
i know the magnitude is 3q
but how can i determine if DA is from D to A or if its AD from A to D
or do i assume its -3q since its parallel to CB
cobalt hinge
you determine that based on calculations
DA itself is just a line segment, not a vector
until you assign it direction it stays that way
long nova
so if i want to express DB as DA + AB would DA be 3q or -3q?
cobalt hinge
i would say -3q since vector BC = 3q
long nova
so parallel vectors are opposite of each other?
cobalt hinge
until you assign it direction it stays that way
^^
BC has the upwards direction, so AD will have the same sign, whereas DA will have opposite
looking at where the vector is travelling to and from
long nova
oh so since AD and CB are parallel, they should share the same direction? thus DA is opposing it so its negative?
cobalt hinge
parallel in a direction sense, yeah
DA and BC would be antiparallel, that's all i'm trying to say here
pearl pondBOT
cobalt hinge
:D
pearl pondBOT
Available help channel!
stoic imp
pearl pondBOT
jolly parrotBOT
Renato
stoic imp
,w simplify 2a^2 - b^2 -2(a^2 - 3b^2)
jolly parrotBOT
stoic imp
,w simplify -3(2a^2-b^2) + a^2 -3b^2
jolly parrotBOT
stoic imp
d = gcd(2a^2-b^2, a^2 - 3b^2)
d | 5b^2
d | 5a^2
=> d | gcd(5b^2, 5a^2) => d | 5.gcd(b^2, a^2) => d | 5.gcd(a,b)^2 => d | 5.7^2
,w divisors 245
jolly parrotBOT
stoic imp
also from gcd(a,b) = 7 we get that 7 | a, 7 | b and that 5 does not divide b
pearl pondBOT
@stoic imp Has your question been resolved?
pearl pondBOT
@stoic imp Has your question been resolved?
toxic zinc
is it 49?
$5|a, \gcd(a,b)=7$ calculate $\gcd(2a^2 - b^2, a^2 - 3b^2)$, okay so \ $\gcd(2a^2 - b^2, a^2 - 3b^2) = \gcd(5b^2, a^2 - 3b^2) = \gcd(b^2,a^2-3b^2)$, since $5\nmid b \Rightarrow 3b^2 \not\equiv 0 \pmod{5}$, so $ \gcd(b^2,a^2-3b^2) = \gcd(a^2,b^2) = 49$
woven matrix
well, 7 divides a and b so divides 2a²-b² and a²-3b², at least you know the gcd won't be 5
it can only be 7, 35, 49, or 245 in the first place
toxic zinc
is it correct?
jolly parrotBOT
amywinehouse11
woven matrix
seems correct to me
errant solstice
sorry for interrupting, but just to clarify, are we allowed to basically give helpees the solution directly like this?
woven matrix
not really but renato solved 95% of it and found d | 245, I hinted he couldn't do random stuff with the 5
so he kinda was supposed to find the last step
it is recommended to not give a full sol but sometimes it's hard to not add a detail
errant solstice
fair enough. sorry for interrupting again.
stoic imp
can someone explain
woven matrix
you said d | 5a² and 5b², that's true
but what you could conclude was that since it divides b² and a²-3b², it doesn't contain a 5
since 5 divides a but not b, it doesn't divide a²-3b²
so your gcd is gcd(b², a²-3b²)
you removed the 5 of 5b² from knowing 5 doesn't divide d
and gcd(b², a²-3b²) is gcd(a², b²)
and you already figured out this one was 49
hence, the answer is 49
woven matrix
how what ?
toxic zinc
think of the prime decomposition of numbers if you have gcd(a,b), and 5|a but 5 doesnt divide b, then 5 cannot appear as a result of this gcd so you can eliminate all prime factors of 5 of a and its gonna be the same gcd
stoic imp
how is gcd(5b^2, a^2 - 3b^2) = gcd(b^2, a^2 - 3b^2)
toxic zinc
think of the prime decomposition of numbers if you have gcd(a,b), and 5|a but 5 ...
.
5b^2 is a multiple of 5, and a^2 - 3b^2 isnt
bcs a^2 is a multiple of 5, but 3b^2 isnt
until you dont think about prime decomposition you arent gonna be good at number theory
woven matrix
if you want another way to write it to convince you, it's about Euclid's lemma
amy justified that d was coprime with 5
but if d divides 5b² and is coprime with 5, by Euclid's lemma, d divides b²
stoic imp
but if d divides 5b² and is coprime with 5, by Euclid's lemma, d divides b²
this is assuming d is prime
woven matrix
nope
(the proof of this generalization is also quite easy, it's just multiplying Bezout's identity)
stoic imp
woven matrix
I mean I can give you the proof of this generalization if it's what convinces you
stoic imp
n | ab
gcd(n,a) = 1
nx + ay = 1
bnx + bay = b
bay = 0 (mod n)
bnx = 0 (mod n)
b = 0 (mod n)
woven matrix
if (a : n) = 1, by Bezout, there are x, y st ax+ny = 1, so bax+bny = b
then if n divides ab, ab = nq, so nqx+bny = b, so n(qx+by) = b and n divides b
quite trivial and doesn't depend on n being prime, as you can see
stoic imp
quite trivial and doesn't depend on n being prime, as you can see
it's not exactly euclids lemma is more like a corollary
woven matrix
on wiki it's called Euclid's lemma, in the language I learnt about it, it's called Gauss' lemma
what do you want me to call whatever thing that has 70 different names
stoic imp
what i mean is that euclid lemma gauss lemma etc never talk about coprimality
woven matrix
and it's not a corollary of euclid's lemma
it's a generalization
it's stronger, not the opposite
woven matrix
what i mean is that euclid lemma gauss lemma etc never talk about coprimality
well the gauss lemma I learned is this one so it definitely did, but you can call it generalized Euclid or generalized Maribel I don't think I care that much about its name
from now on it will be Maribel's lemma
stoic imp
what i mean is that here p is prime so its one or the other
but if p is not prime then it can also divide both, that's why we need coprimality
woven matrix
d is coprime with 5
it's very easy to be coprime with a prime
it just needs to not divide you
since d divides a²-3b², 5 doesn't divide d
so d and 5 are coprime
however, by Maribel's lemma, since d divides 5b² and is coprime with 5, it divides b²
then, since being a common divisor of 5b² and a²-3b² implies to divide b², it's in the set of common divisor of b² and a²-3b², so gcd(5b², a²-3b²) = gcd(b², a²-3b²)
I mean I thought about this argument because you didn't sound very convinced by thinking of the prime factorization, but if you don't like it, amy explained the prime factorization very well
woven matrix
maribel's intervene latter
when I write it
the fact that 5 doesn't divide d has been detailled in all explanations until now
if 5 divided d, since d divides a²-3b²
5 would divide a²-3b²
oh you mean here too
yeah you could use maribel's again
stoic imp
a^2 -3b^2 = 3b^2 (mod 5)
woven matrix
a^2 -3b^2 = 3b^2 (mod 5)
you can't write -3 = 3 mod 5 like you did here
woven matrix
so 5 divides b² by maribel's or by the fact that 2 is invertible mod 5
pick your favorite
which is a contradiction
because gcd(a, b) = 7 has no 5
and 5 divides a
stoic imp
the inverse of 2 in mod 5 is
woven matrix
3
stoic imp
ty
woven matrix
d is coprime with 5
there are a lot of ways to justify that 5 doesn't divide d, and then it follows from here
stoic imp
so 5 divides b² by maribel's or by the fact that 2 is invertible mod 5
if the inverse exist then what
2b^2 = k (mod 5)
b^2 = 3k (mod 5)
woven matrix
b² = 0 mod 5
stoic imp
but 5 does not divide b
woven matrix
in this hypothesis
woven matrix
but 5 does not divide b
yeah that's the point of a proof by contradiction
you asked why 5 doesn't divide d
I say if it divides d it divides a²-3b²
so it divides 2b² so it divides b² because 2 is invertible
but it can't divides b² because it can't divide b
stoic imp
gcd(5,2)=1
woven matrix
and here is the contradiction
woven matrix
gcd(5,2)=1
that happens to be a synonym of being invertible mod 5, indeed
stoic imp
that happens to be a synonym of being invertible mod 5, indeed
yes
this is what I was asking earlier
woven matrix
but you don't really need it you can just use the inverse
stoic imp
that happens to be a synonym of being invertible mod 5, indeed
then by maribel 5 | b^2 => 5 | b
woven matrix
2b² = 0 so 6b² = 0 so b² = 0
maribel can be used here but is not needed if you're inverting 2 mod 5
woven matrix
then by maribel 5 | b^2 => 5 | b
yeah you could say that too
maribel's can always be used for this kind of argument
stoic imp
so we get that 5 | 5b^2 but not that 5 | a^2 - 3b^2
stoic imp
why
woven matrix
so we get that 5 | 5b^2 but not that 5 | a^2 - 3b^2
which is not the case
stoic imp
so 5 | a²-3b²
I see using that divisibility is transitive
how is gcd(5a^2, b^2) = gcd(a^2, b^2)
woven matrix
the exact chain starts from your original problem gcd(2a²-b², a²-3b²)
it's equal to gcd(5b², a²-3b²)
= gcd(b², a²-3b²) (what we just proved with Maribel's and contradiction)
= gcd(b², a²) (trivial, we add left side 3 times to right side)
= (gcd(a, b))² = 49
stoic imp
also I am asking something different
woven matrix
how is gcd(5a^2, b^2) = gcd(a^2, b^2)
you could prove it again with Maribel's
if d | 5a² and d | b², 5 doesn't divide b, so doesn't divide d
so d divides a² by Maribel's, since d coprime with 5
since d | 5a² and d | b² => d | a², gcd(5a^2, b^2) = gcd(a^2, b^2)
I mean there are at least 30 possible chains
most of them didn't convince you and ended in a "how?"
at some point I had to prove things 3 times a different way
I probably didn't do only optimal things, for sure
gcd(2a²-b², a²-3b²)
= gcd(5b², a²-3b²)
= gcd(b², a²-3b²) (what we just proved with Maribel's and contradiction)
= gcd(b², a²)
= (gcd(a, b))² = 49
is already a very clean answer in my opinion
stoic imp
if d | 5a² and d | b², 5 doesn't divide b, so doesn't divide d
5 does not divide b, so 5 does not divide d?
woven matrix
yes that's the contradiction we wrote 10 times
if 5 divided d
it would divide a²-3b² and 5b²
so would divide b² so b
contradiction
so 5 doesn't divide d
(5 | d => 5 | b) <=> (5 doesn't divide b => 5 doesn't divide d)
I've proved every step 3 different times atp Idk what you don't like in the proof
stoic imp
is that the contrapositive
woven matrix
yes
stoic imp
(5 | d => 5 | b) <=> (5 doesn't divide b => 5 doesn't divide d)
I think this is a good way to put it
woven matrix
this is the most redundant but at this point I write it in every possible way
stoic imp
this is the most redundant but at this point I write it in every possible way
is good to have options, I have to think on the spot for the exam
woven matrix
if you write that much in 3 different ways in an exam I assure you you won't have time to score point
gcd(2a²-b², a²-3b²)
= gcd(5b², a²-3b²)
= gcd(b², a²-3b²) because 5 doesn't divide a²-3b²
= gcd(b², a²)
= (gcd(a, b))² = 49
is already a very, very reasonable proof
stoic imp
if you write that much in 3 different ways in an exam I assure you you won't hav...
I just need to write it in one way, whatever I can come up with on the spot
stoic imp
.close
pearl pondBOT
pearl pondBOT
Available help channel!
steady aspen
steady aspen
nope
pearl pondBOT
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
tropic saddle
how to start any geometry problem: make a sketch
tropic saddle
how does your sketch look like
steady aspen
its a triangle...
split void
upload it
steady aspen
alright
calm wing
hint: draw a line segment horizontally on the bottom AB (=1)
and draw a ray from A at a 20.21 degree angle
split void
infinite line sounds weird but thats the point
calm wing
wanted to be explicit xd
tropic saddle
(a ray)
calm wing
hint: draw a line segment horizontally on the bottom AB (=1)
and draw a ray from...
then every point C on that ray (call it R) creates a triangle ABC with some sidelength AC, i.e. x
calm wing
yeah i did too originally lol but the key is that you know the angle
so you need a ray
steady aspen
then every point C on that ray (call it R) creates a triangle ABC with some side...
i see so like the number of points c is like the number of non congruent triangles i can form?
calm wing
we haven't gotten to congruence yet
as i wrote it right now there are infinitely many points C
steady aspen
as i wrote it right now there are infinitely many points C
yeah
how do we move forward from there?
steady aspen
alrighty hold on
representation on ms paint, i dont have a phone to take photos rn
i am drawing it correctly right?
calm wing
yup
calm wing
note that there exists an x s.t. this is a right angle
steady aspen
noted
calm wing
this means that there are a bunch of these blue lines which are the same length
calm wing
ok good
steady aspen
multiple choice
calm wing
i think i confused myself a bit, give me a sec..
steady aspen
lright
bitter herald
The majority of the options seem to be correct 
bitter herald
C must line on a circle centred at B with a radius of x, shouldn't it. So just count the amount of ways a line can intersect with a circle
calm wing
The majority of the options seem to be correct <:kekwait:1128611424562839622>
D can't be right
bitter herald
Yes
calm wing
but the rest seems to be correct
bitter herald
The others sure can
bitter herald
C must line on a circle centred at B with a radius of x, shouldn't it. So just c...
Which goes back to this
steady aspen
C must line on a circle centred at B with a radius of x, shouldn't it. So just c...
i see can you draw the circle?
like
calm wing
C must line on a circle centred at B with a radius of x, shouldn't it. So just c...
i think this is it
steady aspen
im having a bit trouble witht hat-
bitter herald
Im on phone 
steady aspen
oh okay so like
bitter herald
Maybe artemetra can
steady aspen
can't c be any circle?
it just needs to have its centre at b right?
OHHHHHHHHHHH
i get it
bitter herald
calm wing
steady aspen
we are looking for the case where it intersects the maximum amount of
calm wing
like that
steady aspen
points
bitter herald
She sees da wae
calm wing
i see da vision 😮
the inner circle corresponds to 0 points when x is too small (i.e. 0 such triangles exist)
the one in the middle is 1 point
the outer circle is 2 points, i.e. two triangles
bitter herald
this meme is almost 10 years old now
When you realise you are getting old 
calm wing
you can also have this situation where x is big enough that there's only 1 point but that's still 1 triangle
so the answer is a,b,c
steady aspen
hm yeah
anything btw i can invoke or like
or is this it
like
the graphical solution
calm wing
you can draw the triangles in each case
pearl pondBOT
calm wing
pearl pondBOT
Available help channel!
ocean hazel
(x+b)^2/2=y/6
In this scenario cross multiplying works because its the same as multplying both sides by 2 and then both sides by 6, but with cross multiplying we do the same thing but faster right?
ocean hazel
$$\frac{(x+b)^2}{2} = \frac{y}{6}$$
jolly parrotBOT
Fahad07
ocean hazel
that worked
fleet ridge
I guess cross multiplication is faster, but its upto personal preference
ocean hazel
I guess cross multiplication is faster, but its upto personal preference
Yeah I know it works, I just wanted to confirm that my logic and reasoning behind why it works is correct.
This is basic stuff, I should have a thorough understanding of it and not just memorise it
Anyways thanks for the confirmation guys
.close
pearl pondBOT
ocean hazel
<@&268886789983436800>
pearl pondBOT
Available help channel!
pearl mauve
Can sum1 please check this it looks super long so i think it could be wrong it just looks very wrong to me 😕
pearl pondBOT
Can sum1 please check this it looks super long so i think it could be wrong it j...
@pearl mauve Has your question been resolved?
pearl mauve
Can sum1 please check this it looks super long so i think it could be wrong it j...
<@&286206848099549185>
spiral pivot
Question about your problem: why do you have this being the integral of a series on the other side?
Oh, a very weird separable equation
So your integration of u seems fine
Did you have a specific question or concern though?
@pearl mauve
pearl mauve
Did you have a specific question or concern though?
I just wanted to know if i did anything wrong since it looks super wrong to me
Also i was using an approximation to a function thats why the number looks super weird
The series was the taylor polynomial at t = 0 of ln(1/4 t + 4)
Also i already solved the ode using numerical methods but since my function is a polynomial near t = 0 if i use my code to solve for u(5/4) ≈ 30.78...
Does that mean if i sub into my analytical one it should be close to 0 or would that not work since i did a taylor near 0 and 5/4 is not close to 0 and have to pick another number near 0 and test on my analytical solution?
pearl pondBOT
@pearl mauve Has your question been resolved?
pearl pondBOT
@pearl mauve Has your question been resolved?
spiral pivot
I just wanted to know if i did anything wrong since it looks super wrong to me
!original
pearl pondBOT
I just wanted to know if i did anything wrong since it looks super wrong to me
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.
spiral pivot
It might simply be that the work you're asking about is correct, but you've made a mistake on a previous part, so the results you're getting are wrong in a previous step, but you've only been able to thoroughly check them at this step.
pearl mauve
!original
to solve an ode
du/dt +f(u)g(t)=0
f is a cubic and g is ln(1/4t+4) i used numerical methods to write f approximately as u can see and for g i used taylor polynomial at t=0
The cubic is kinda messy since it depends on my student id so i cant really send it
spiral pivot
@pearl mauve why are you expanding the log btw? You can just integrate it normally.
$\int \ln(t/4 + 4) , \d{t} = -t + (t + 16) \ln(t/4 + 4)$
jolly parrotBOT
OmnipotentEntity
pearl mauve
<@1151900682526400682> why are you expanding the log btw? You can just integrat...
Bc the question said to use taylor polynomials
Its basically approximating and solving analytically
Idk why he told us to do that tho
spiral pivot
!original
pearl pondBOT
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.
pearl mauve
!original
Ignore the bottom this is f(u) and then i used bisection and newton raphson to approximate the roots so i could write f(u)≈(u-a)(b-u)^2
And as i said before g(t)= ln(1/4*t + 4) which i approximated by an n degree taylor polynomial
So the ode we solve is du/dt +f(u)g(t)=0 with u(0)=u_0
That's basically all the original text has 5 parts with tons of writing its not gonna help if i send it i just simplified it if u really need it i can send but its super long i promise u. 😭
And they want the solution in h_n(u(t),t)=0
pastel umbra
I won't lie, I'm not convinced you understood what original means here
Omni's asking for the original question, as it was stated to you, verbatim
pearl mauve
I won't lie, I'm not convinced you understood what _original_ means here
I literally said it bro
pastel umbra
Be that a screenshot, a photo of a book, etc-
pearl mauve
Be that a screenshot, a photo of a book, etc-
Its not a book
Its from a question the teacher sent
And the question is 5 parts with 10+ paragraphs
Im not gonna send 5 parts of something i already know which is 10+ paragraphs of text filled with my alpha and beta which my student id takes
pastel umbra
Unless the ODE is given entirely divorced from the other parts, it is possible you have the wrong ODE to begin with
pearl mauve
du/dt + f(u)g(t)=0
pearl mauve
Unless the ODE is given entirely divorced from the other parts, it is possible y...
Its not
pastel umbra
That's why we ask, as a general rule
pearl mauve
du/dt + f(u)g(t)=0
^^
Its literally this
With u(0)=u_0
Thats all
Every other part is to approximate f(u) using a root finding technique and analyses it its not useful in the context of my question
And then to approximate g as an n degree taylor polynomial
Which i already gave lmao
pearl pondBOT
@pearl mauve Has your question been resolved?
pearl pondBOT
@pearl mauve Has your question been resolved?
split void
Well we still require the question with the entire context.
mint anchor
How to understand functions like TREE(3) SSCG(3) graham's number. And doing manipulations on very large numbers. And what topics should I learn to get good at these concepts?
errant solstice
I'd suppose all of these fall under number theory.
honest vigil
TREE(3) I think has roots in graph theory though.
so is Graham's number.
so the computation might be NT but the problems that these numbers arose from are usually other fields.
errant solstice
hm, technically also SSCG(3). so all of these are graph-theoretical functions/numbers.
pearl pondBOT
@mint anchor Has your question been resolved?
sharp smelt
pearl pondBOT
sharp smelt
I feel I'm tripping here (6.1.2)
So the $\lambda$ in the poisson distribution is $30,345p$?
jolly parrotBOT
Wai
sharp smelt
so $\Pi_{i=0}^{21} \frac{ (30345p)^{i} e^{- 30345p}}{i!}$?
jolly parrotBOT
Wai
slender viper
So the $\lambda$ in the poisson distribution is $30,345p$?
yeah it's Poisson(Np)
slender viper
so $\Pi_{i=0}^{21} \frac{ (30345p)^{i} e^{- 30345p}}{i!}$?
but this is wrong
slender viper
conceptually, the likelihood is P(data|model)
sharp smelt
conceptually, the likelihood is P(data|model)
so x_i instead of i
slender viper
why do you have x_i
sharp smelt
why do you have x_i
the formula calls for it, does it not
sharp smelt
not sure what formula you were using
this
slender viper
I don't see $x_i$ in this formula
jolly parrotBOT
Element118
slender viper
just $\lambda$ and $k$
jolly parrotBOT
Element118
sharp smelt
then what am I doing wrog
slender viper
maybe you have a likelihood formula you aren't showing
and that is where you have the $x_i$ from?
jolly parrotBOT
Element118
sharp smelt
maybe you have a likelihood formula you aren't showing
Isn't the likelihood function, the product of pdfs at the points
slender viper
Kinda, but you only have one point of data, 22
sharp smelt
right so $\Pi_{k=1}^{21}\Pi_{i=0}^{k} \frac{ (30345p)^{i} e^{- 30345p}}{i!}$?
slender viper
The product occurs if you have multiple points
jolly parrotBOT
Wai
slender viper
A product of one term probably doesn't need the $\prod$ operator
jolly parrotBOT
Element118
sharp smelt
A product of one term probably doesn't need the $\prod$ operator
I don't get it
slender viper
The question says there's only one observation, 22
sharp smelt
The question says there's only one observation, 22
so just the pmf at k=21
sharp smelt
so just $\frac{ (30345p)^{22} e^{- 30345p}}{22!}$
jolly parrotBOT
Wai
slender viper
yeah that's just it
woven river
im back, cuz this time is hard
pearl pondBOT
im back, cuz this time is hard
woven river
I understood the hint, but have no idea how to create such sequence
"...which the values of the function f tends to 0", what if f outputs big numbers? f is not really represented in some expressions so thats why im confused
broken moth
I understood the hint, but have no idea how to create such sequence
first fix x then there exsits some y_1 such that the property holds
then use y_1 ito deduce the existence of some y_2 with the property
use this repetitively then you can see that you will obtain some sequence f(y_n)
tending to 0
try it yourself it is not very hard to get the idea
woven river
omg
thats so good
brb
I wonder how u thought of this instantly, I need that mindset @broken moth
broken moth
I wonder how u thought of this instantly, I need that mindset <@1050723956895789...
give it time
thorny radish
there is a problem where y_n might be all over the place, like you could have y_(2n+1) be 0 and y_(2n) be 1
broken moth
there is a problem where y\_n might be all over the place, like you could have y...
we dont care about y_n
we need (f(y_n))
thorny radish
we dont care about y_n
we need (f(y_n))
to show that there exists a value z such that f(z) = 0 it is not sufficient to show that f gets arbitrarily close to 0
broken moth
to show that there exists a value z such that f(z) = 0 it is not sufficient to s...
yes thats it
and you can obtain this using squeezing
and since f is continuous on that interval it follows directly the existence of z
woven river
ok this is my draft so far
broken moth
ok this is my draft so far
less or equal to not equal
woven river
less or equal to not equal
what
thorny radish
consider the function f(x) = 1/x on [1, ∞). then f gets arbitrarily close to 0 yet does not attain it
woven river
which part
jolly parrotBOT
Roufaid
broken moth
ok this is my draft so far
and you must show the existence of (y_n) by induction
you cannot say we do this repetitively in the proof
broken moth
is because I can't find the lim later
you can by squeezing
woven river
and you must show the existence of (y_n) by induction
you cannot say we do this...
y_n exists in [a,b] so why should we need to prove its existence
thorny radish
and you must show the existence of (y_n) by induction
you cannot say we do this...
you totally just can
and the existence of (y_n) does not follow by induction, it follows from the axiom of choice
broken moth
consider the function f(x) = 1/x on [1, ∞). then f gets arbitrarily close to 0 y...
but we are working on a closed interval
so D' is included in D we dont have any problem having limit inside the closed intervals and mind that it will settel at a value that is not inside
because every sequence converges inside the interval
thorny radish
but we are working on a closed interval
so D' is included in D we dont have any...
this is simply not clear and the proof is not obvious
again not every sequence converges, consider x_(2n+1) = 1/2^(2n+1) and x_(2n) = 1/2^(2n)
broken moth
again not every sequence converges, consider x\_(2n+1) = 1/2^(2n+1) and x\_(2n) ...
yes i can agree with that but in our construction
we dont care where (y_n) settels
woven river
is it like this @broken moth
broken moth
again not every sequence converges, consider x\_(2n+1) = 1/2^(2n+1) and x\_(2n) ...
both converge to 0
thorny radish
yes but this requires you to separate x_n into two subsequences
you need to actually do this
broken moth
you need to actually do this
why?
thorny radish
because otherwise you cannot say that there exists some z with f(z) = 0
the idea is you need to find a subsequence of y_n that converges in [a, b]
this is the only way you get to use continuity
woven river
ohh I get u
broken moth
the idea is you need to find a subsequence of y\_n that converges in [a, b]
wait wait
let me ask you a question
woven river
create two sequences where all elements are negative and positive respectively
broken moth
our construction
of y_n
is in [a,b] right?
if it ever converges will it get outside [a,b]?
thorny radish
no
broken moth
the idea is you need to find a subsequence of y\_n that converges in [a, b]
ok you edited it now
you are right
he must say this to
woven river
what's going on
thorny radish
it simply will not in general
broken moth
it simply will not in general
yes you are right
ok this is fixable
use bolzano
y_n is bounded
so it hase a convergent subsequence
ok yeah you are right he needs to write this detail
broken moth
what?
your steps are right
just before taking the limit justify why y_n must converge
ok it will not but since it is bounded it has a convergent subsequence call it y_k
thats all you need
thorny radish
you can't just tell them the solution like this
they don't even know where the issue lies
woven river
your steps are right
just before taking the limit justify why y_n must converge ...
why do we need to tell y_n must converge when the sequence has elements of f(y_n)?
woven river
how do you actually find c such that f(c) = 0
wait isn't it y_n
broken moth
wait isn't it y_n
no
thorny radish
yea but the question asks you for an actual value, not a sequence
broken moth
it is not y_n
woven river
how about instead of making one sequence, I make two, where I take all positive and negative values of f respectively
thorny radish
you can do that
so say you have a sequence y_n such that f(y_n) is all positive. what then?
broken moth
so say you have a sequence y\_n such that f(y\_n) is all positive. what then?
this may be empty
woven river
then the other one negative, but I can't seem to reach the final conclusion
thorny radish
yeah it's surprisingly difficult right
if y_n converges we would be done. do you see why?
broken moth
yeah it's surprisingly difficult right
it is not about being difficult
taking y_n a sequence of positive values of f is not exhustive
how can you guarentee that there is no f that is non-negative for all values of x satisfying the property?
woven river
if y\_n converges we would be done. do you see why?
well this would be done if the sequence is like jumping from positive to negative then reaching to 0
like y1 >0, y2 < 0, y3 > 0,...
broken moth
how can you guarentee that there is no f that is non-negative for all values of ...
or maybe a non-positive function f satisfying the property
thorny radish
well this would be done if the sequence is like jumping from positive to negativ...
be careful
think about whether the sequence being positive or negative really matters
woven river
think about whether the sequence being positive or negative really matters
I think it does, since we want to show that there exists a negative and positive value of f
then we can get f(c) = 0
thorny radish
like y1 >0, y2 < 0, y3 > 0,...
you are confusing values of y_n being positive or negative with f(y_n) being positive or negative
woven river
you are confusing values of y\_n being positive or negative with f(y\_n) being p...
my bad
thorny radish
I think it does, since we want to show that there exists a negative and positive...
the function f(x) = x² on [-1, 1] attains 0 at 0 but is never negative
woven river
how else am I gonna use IVT to prove f(c) = 0
thorny radish
you are not going to use IVT
to summarise the situation we are given some sequence (y_n) such that f(y_n) converges to 0. we need to use this somehow to find c with f(c) exactly 0
again you should answer why (y_n) converging in [a, b] means that we would be done
woven river
wait
what if
since I already found that lim n-> inf f(y_n) = 0
I can use Sequential Continuity Theorem that the limit I mentioned is equal to f(c) for some number c
thorny radish
what is c
woven river
the number in [a,b]
woven river
f : [a,b] -> R is continuous at c in [a,b] iff for every y_n converging to c in [a,b],
lim f(y_n) = f(c)
ye I just realized a flaw, need to show y_n converges to c
woven river
I wanna curse
thorny radish
you should have a mental visualisation of what's happening, it makes organising your thoughts easier
something like this
woven river
is the [---] part [a,b]?
thorny radish
yeah
mint anchor
Which branch is being discussed (js asking pls don't mind)
thorny radish
baby anal
-ysis
woven river
I am stuck now
worldly jewel
this is lowkey diabolical without having topological tools
thorny radish
here is an illustration that may or may not confuse you further. if we have the function f(x) = 1/x on [1, ∞), then f gets arbitrarily close to 0 yet does not attain it
so somehow your argument needs to rely on the domain being [a, b]
woven river
didnt we make a sequence out of [a,b]
thorny radish
the argument we used to define our sequence didn't really rely on the nature of [a, b], it came from the question just telling us we could find some domain value with less than half of what we have
but from here we need to use the nature of [a, b]
woven river
well, it is bounded
thorny radish
another example is f(x) = x² on (0, 1]
woven river
oh so that c might be a lol
wait since the sequence is bounded, can I just make a subsequence converging to c by bolzano
thorny radish
yeah if you know that then sure
woven river
then since it converges to c and we know that f(y_n) converges to 0, that subsequence must converge to 0
thorny radish
mhm
pearl pondBOT
pearl pondBOT
Available help channel!
flint spindle
Can anyone pls tell me the answer of q17
pearl pondBOT
Can anyone pls tell me the answer of q17
flint spindle
I got answer as B
hoary relic
Can anyone pls tell me the answer of q17
This server is not about handing out answers, we can only help you with figuring it out
flint spindle
This server is not about handing out answers, we can only help you with figuring...
ya I figured it out and got answer as B but book's answer is A
<@&286206848099549185>
valid nova
!15m
pearl pondBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
honest oyster
ya I figured it out and got answer as B but book's answer is A
Well let's see how you got the answer then
honest oyster
I'm not convinced that (2-a)(c-2) implies either both are 1 or both are 3, since that assume a and c are integers (I think they infact are in this case but that doesn't justify the fact we have to assume it)
flint spindle
I'm not convinced that (2-a)(c-2) implies either both are 1 or both are 3, since...
hmmm....
flint spindle
I'm not convinced that (2-a)(c-2) implies either both are 1 or both are 3, since...
ya but still is my answer wrong sir?
@honest oyster
honest oyster
Gtg right now, hope someone else can help
flint spindle
<@&286206848099549185>
valid nova
<@&286206848099549185>
!15m
pearl pondBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
valid nova
dont ping helpers again and again
flint spindle
bro 15 mins gone
flint spindle
wait 15minutes before pinging them
Ya as he left that's why I pinged again
proper nova
bro
proper nova
Ya as he left that's why I pinged again
ping when it's been a long time since no one answered you
not just pinging randomly and hope to get some help
valid nova
try converting log10x - 1 to log10x - log10(10) then log10 (x/10)
see if you can do something from there
flint spindle
See this <@1108269834497703976>
my solution...
shadow elm
should i maybe solve it 😃
flint spindle
From the 3rd. equation
flint spindle
log10 a+c = something something
how does a+c becomes something something
I took log10 x =a, log10 y = b, log10 z =c
flint spindle
From the 3rd. equation
...
valid nova
I took log10 x =a, log10 y = b, log10 z =c
yeah. well
log(a)(b)=c
then a^c = b
here log10(a+c) = 2+(c-1)(a-1)
so 10^[2+(c-1)(a-1)] = a+c
shadow elm
@flint spindle when you made the equations i,ii,iii . try to subtract i and ii
valid nova
<@895883670395695104>
can you sub in the value of a,b, and c in your equation and tell me if that satisfies it
valid nova
this one
valid nova
ya it's satisfying sir
can ya send me the solution
flint spindle
can ya send me the solution
mine?
flint spindle
@valid nova
shadow elm
<@1414569100159619145> when you made the equations i,ii,iii . try to subtract i ...
did you try this?
flint spindle
did you try this?
gtg sir, I will try tomorrow
shadow elm
!done
pearl pondBOT
If you are done with this channel, please mark your problem as solved by typing .close
chilly pond
Can anyone pls tell me the answer of q17
ioqm de rha hai
flint spindle
(a−2)(c−2)=1
(2-a)(c-2)=-1 is the same sir
valid nova
(2-a)(c-2)=-1 is the same sir
you wrote +1
chilly pond
normal jee adv mock
agreed
chilly pond
true
valid nova
wait. i will solve from scratch i am getting confused
valid nova
$\log_{10}(2yz) = 4 + (\log_{10} y - 2)(\log_{10} z - 1)$
jolly parrotBOT
TheAstorPastor
valid nova
$\log_{10}(2xy) = 4 + (\log_{10} x - 1)(\log_{10} y - 2)$
jolly parrotBOT
TheAstorPastor
valid nova
$\log_{10}(zx) = 2 + (\log_{10} z - 1)(\log_{10} x - 1)$
jolly parrotBOT
TheAstorPastor
valid nova
$\log{10}(2yz) = \log{10} 2 + b + c$
jolly parrotBOT
TheAstorPastor
valid nova
$\log{10}(2xy) = \log{10} 2 + a + b$
jolly parrotBOT
TheAstorPastor
valid nova
$\log_{10}(zx) = a + c$
jolly parrotBOT
TheAstorPastor
valid nova
can we say log10(2)=k ?
@flint spindle ?
k+b+c=4+(b−2)(c−1) - equation(1)
k+a+b=4+(a−1)(b−2) -equation(2)
a+c=2+(c−1)(a−1) -equation(3)
you got (a-2)(c-1) as 1
subtract 1 from 2
$$(a - c)(3 - b) = 0$$
jolly parrotBOT
TheAstorPastor
valid nova
similarly with others, yoy get
(a−b)(3−c)=0,(b−c)(3−a)=0
combining them all gets me
a=b=c = 1
a=b=c=3
for being 1 you get x=y=z as 10
for 3 you get x=y=z as 1000
shadow elm
subtract 1 from 2
(a-c) = (b-2)(a-c) is what im getting
valid nova
and x1>x2
shadow elm
same thing ig yeah
valid nova
same thing ig yeah
mhm
shadow elm
mb
valid nova
and x1>x2
so x1 is 1k and x2 is 10
now you just check out the table
@flint spindle do you get it?
pearl pondBOT
@flint spindle Has your question been resolved?
neon dock
Please help me to solve the following question :- For what value of p is the coefficient of x2
in the
product (2x – 1)(x – k)(px + 1) equal to 0 and the
constant term equal to 2 ?
split void
expand the product?
neon dock
i exactly dont know what to do.. It would be better if anyone would help me
plush bramble
i exactly dont know what to do.. It would be better if anyone would help me
expanding means (a+b)(c+d) = ab + ad + bc + bd
split void
i exactly dont know what to do.. It would be better if anyone would help me
I just told you what to do.
pearl pondBOT
flint basalt
i cant solve
this channel is to ask for help. if you still need help then ask, dont give up and say you cant solve it
neon dock
OK THANKS FOR AN INSPIRATION
ACTUALLY I M IN CLASS 10 , and wanna solve olympiad level question
shadow elm
I *just* told you what to do.
bit rude imo... its better to stop responding instead of saying thats
shadow elm
ACTUALLY I M IN CLASS 10 , and wanna solve olympiad level question
itll be better if you get familiar with basics first
neon dock
ok...
shadow elm
start with , "what does expanding a product mean"
neon dock
So what are the basics that I must know ??
split void
bit rude imo... its better to stop responding instead of saying thats
It'd to draw attention to the helper's statement 
split void
So what are the basics that I must know ??
Multiplication.
Of Algebraic expressions
ignore my speelings
do you know what is $(a+b)(c+d)$
jolly parrotBOT
Annie Maqionde
flint basalt
.reopen
pearl pondBOT
✅ Original question: #help-39 message
flint basalt
(so it doesnt lock)
neon dock
**Annie Maqionde**
yes. ac+ad+bc+bd
pearl pondBOT
Show your work, and if possible, explain where you are stuck.
pearl pondBOT
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
show what you've done so far
neon dock
onexpanding the eqn (2x-1)(x-k)(px+1)=0 I got, 2x2-2kx-px=0. I f alpha and beta are the roots of this eqn then > alpha+beta=-(2k-p) and alpha*beta=-1/2
neon dock
actually I dont have any webcam
flint basalt
are you able to take a photo on your phone?
pearl pondBOT
split void
.reopen
pearl pondBOT
✅ Original question: #help-39 message
split void
please do not close unless the doubt has been cleared
neon dock
can you tell me if my approach for question is correct or not?
split void
here it is
No that's wrong and I'll explain why.\
$(a+b)(c+d)(e+f)$.\
Whenever faced with such a situation, ignore $(e+f)$\
Expand $(a+b)(c+d)$\
= $(ac+ad+bc+bd)(e+f)$\
Now do the needful\
$ = e(ac+ad+bc+bd) + f(ac+ad+bc+bd)$
jolly parrotBOT
Annie Maqionde
neon dock
ok...
split void
did you understand?
neon dock
yes
final eqn :- 2px3-2kpx2-px2+kpx+2x2-2kx-x+k=0
actually I am too late to sleep so I want to close this discussion
.close I will come here tommorow
pearl pondBOT
round garnet
guyz what you are yapping about
round garnet
**Annie Maqionde**
wut is this
split void
!redir
pearl pondBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
pearl pondBOT
Available help channel!
sharp smelt
I'm sort of confused
pearl pondBOT
I'm sort of confused
sharp smelt
Does this mean Q(2+√3)?
Well, for $\mathbb{Q}(2+\sqrt{3})$, I believe $(1,\sqrt{3})$ serves as a spanning set, which is linearly indepndent as $a+b\sqrt{3}=0$ would require $\frac{-a}{b}=\sqrt{3}$ which isn't possible for rational (a,b) so the degree of the extensions is $2$?
oh come on
jolly parrotBOT
Wai
woven matrix
I don't know your background in extension theory, so I'll start with some light remarks
do you know what the degree of a number over Q mean?
and also, Q(2+sqrt(3)) is just Q(sqrt(3)) since 2 is in Q, but how does it relate to what you're trying to say?
sharp smelt
I don't know your background in extension theory, so I'll start with some light ...
I assumed the degree of a number here referred to Q(2+√3)
that is the smallest field extension of Q containing 2+√3
woven matrix
yes it's called an extension not a degree
the degree of a number over Q is the degree of its minimal polynomial in Q[X]
woven matrix
but you were still right about one of your points
as I said, Q(2+sqrt(3)) is just Q(sqrt(3))
and clearly, sqrt(3) is of degree 2
since x²-3 cancels it
so 2+sqrt(3) is of degree 2
sharp smelt
right as the minimal poly is x^2-3
so in very rudimentary terms the degree of an element,t, over a field is the degree of the monic of the smallest degree such that t is a root of said poly
I'll read the theory from D&F rn, but just wanted to be clear
woven matrix
the degree of n over Q is the degree of its minimal polynomial, and it also happens it's its dimension as a vector space over Q
one example is that you said 1, sqrt(3) spans Q(sqrt(3)) = Q(2+sqrt(3))
it was also a way to conclude 2+sqrt(3) is of degree 2
smoky gull
I'll close this now, it's past 12 am 🙏
-# oh r u indian
pearl pondBOT
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Available help channel!
daring bay
can somene help here
pearl pondBOT
can somene help here
summer imp
I would assume that by touching the line g they mean that this line is tangent to the graph of f(x) at the point (1,0).
Although it's worded somewhat poorly.
That would mean that the slope of f(x) at x=1 is the same as the slope of g(x).
daring bay
I would assume that by touching the line g they mean that this line is tangent t...
huh
but why like
it just says that it touches the line
it doesnt say anything about tangent tho
wait
yea this is rly rly weird
they have the points f(1) = 0, which i understnad
and f'(1) = 2
for some reason
summer imp
but why like
Because otherwise this piece of information is redundant. Both f and g intersect the x-axis at x=1.
So obviously they would touch in the strict sense
daring bay
Because otherwise this piece of information is redundant. Both f and g intersect...
oh also
''touching''
is also different than intersecting right
in this caes
summer imp
This is why interpreting it as "being tangent" makes more sense.
daring bay
This is why interpreting it as "being tangent" makes more sense.
yep ty makes sense now
pearl pondBOT
@daring bay Has your question been resolved?
acoustic tangle
Hiii
acoustic tangle
I don’t understand this integration question
Like I integrated from y=5->7
But I’m not sure if I’m finding the whole area
ebon skiff
!show
pearl pondBOT
Show your work, and if possible, explain where you are stuck.
acoustic tangle
Ok
acoustic tangle
!show
I’ll try to show what I’m confused abt
Am I just finding this area when I integrate ?
reef magnet
Why do you integrate from 5 to 7
acoustic tangle
Why do you integrate from 5 to 7
Bc y=5 here
And I don’t want the area under the curve to the left of the dot
reef magnet
Why do you integrate with y as a variable
acoustic tangle
Because the area is between the curve, x=14 and the y axis
reef magnet
What i would do is extend that line at x=2 to separate a square and another shaded area that we can calculate with the integral from 2 to 14 of 7-y dx
reef magnet
Because the area is between the curve, x=14 and the y axis
Oh
reef magnet
I get 51.875 as an answer when i do calculations according to the method i proposed
acoustic tangle
The answer is just 44/3
reef magnet
Ok
acoustic tangle
Ok
Oki nvm
I have another unrelated question
Im not sure about ib
It’s the second one but I thought it would be the fourth
pearl pondBOT
@acoustic tangle Has your question been resolved?
acoustic tangle
<@&286206848099549185>
pearl pondBOT
@acoustic tangle Has your question been resolved?
graceful breach
lemme take a look
ok
so
when the mean is equal to the median
the distribution will be perfectly symmetrical
the mean is greater than the median when there’s a right skew
for 2
remember that a geometric distribution represents the number of trials until the first success
and remember that binomdist is typically unimodal
pearl pondBOT
@acoustic tangle Has your question been resolved?
simple shale
i haven't done functions in a sec can someone tell me if this is correct?
if f(x)=8/(x-2) +2 and the domain is (2, 4), then the range is (2, 6), no?
idk why the mark scheme says it's (6, infinity)...
dense jasper
i haven't done functions in a sec can someone tell me if this is correct?
if f(x...
,w 8/(x-2)+2=7, 2<x<4
jolly parrotBOT
pearl pondBOT
Show your work, and if possible, explain where you are stuck.
simple shale
sorry i don't have any working :<
i just have to find the range given the domain is (2, 4)
i thought y=2 is a horizontal asymptote cuz of the +2 translation so all f(x) within that domain should be greater than y=2
and at x=4, f(x)=6 so the range should be less than 6
cuz it's an increasing function
that was my reasoning
dense jasper
$$2<x<4 \implies 0<x-2<2 \implies \frac{1}{2}<\frac{1}{x-2}<\infty$$
For some intuition, notice that as you divide $1$ by increasingly small positive numbers, the result gets larger and larger (tending to $\infty$).
jolly parrotBOT
Civil Service Pigeon
dense jasper
,w graph 1/x
jolly parrotBOT
jolly parrotBOT
dense jasper
also all of that counts as working/prior reasoning, which you should include in your post when you first ask for help.
simple shale
okay i just got it 💔
dense jasper
okay i just got it 💔
pearl pondBOT
If you are done with this channel, please mark your problem as solved by typing .close
simple shale
.close
pearl pondBOT
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Available help channel!
minor eagle
how do i solve this, idk how to go step by step
pearl pondBOT
how do i solve this, idk how to go step by step
humble root
how do i solve this, idk how to go step by step
Hi! Before anything, do you know what a "base three numeral" is?
minor eagle
i have a slight idea but can you remind me
blazing garden
i have a slight idea but can you remind me
Basically, you’re every number is based on powers of 3. And you’re only allowed to use the digits
0, 1, 2
minor eagle
i see
humble root
The classic number system that we use is called base-10 (decimal), because every number can be written in terms of powers of 10.
For example, 123 is the same as 1 * 100 + 2 * 10 + 3 * 1. Here, every number we multiply by has a base of 10.