Sorry about that
#help-49
brisk crag
tribal tartan
all good
tribal tartan
you too
midnight plankBOT
midnight plankBOT
Available help channel!
limber heron
midnight plankBOT
limber heron
How does my teacher get to the answer? (In red)
Where the arrows point
I know he uses the trigonometric table/triangle as I’ve drawn below
But how
How does sin pie/4 make root2/2?????
shrewd bronze
are you familiar with radians?
limber heron
Yeah
shrewd bronze
thats in radians
ur chart is in degrees
pi/4 is 45 degrees
so sine of that would be root 2 / 2
hazy pewter
limber heron
How do I know if it’s positive or negative? My teacher uses SATC but idk how to use that
limber heron
How do I know if it’s positive or negative? My teacher uses SATC but idk how to ...
He uses it in working out
limber heron
Isn’t it the same thing?
shrewd bronze
yeah basically
i think CAST is easier
u start in quadrant 4 and go counterclockwise
limber heron
Do you go back each quadrant however many times is in the denominator?
shrewd bronze
no
so say u had 11pi/6
that would be in the fourth quadrant
hence the sine value is negative
do you know about reference angles?
limber heron
do you know about reference angles?
I’ve heard of them
limber heron
that would be in the fourth quadrant
How do u know tho
shrewd bronze
well 2pi is a full circle (360 degrees)
and 11pi/6 is close to 12pi/6 which is 2pi
it would be in the 4th quadrant
limber heron
7/3 is close to 6/3 which means it’s 1/2?
shrewd bronze
no
11pi/6 is just below 2pi
which is where the positive x axis is
so it is below it so its in the 4 th quadrant
its between 3p/2 and 2pi
limber heron
So how would 7pi/3 be in the first quadrant?
Sorry if I’m slow
I just wanna see ur way of working
shrewd bronze
so 7pi/3 is just above 6pi/3
its 2pi + pi/3
so its one full rotation and then rotate by pi/3 radians
pi/3 is 60 degrees
so its in the first quadrant
an easy way to do it would to just convert the radians to degrees
limber heron
Okay thanks man I get it now
midnight plankBOT
@limber heron Has your question been resolved?
bright shoal
Here for the help
cobalt dragon
slope of x + 2y=5
midnight plankBOT
slope of x + 2y=5
cobalt dragon
all I know is measure angle and tan inverse. but how to get slope from equation only
midnight plankBOT
@cobalt dragon Has your question been resolved?
neat sandal
Say i was checking this series for absolute convergence, would it be ok to compare it with 1/n'2 or does it have to be 1/n'3
midnight plankBOT
Say i was checking this series for absolute convergence, would it be ok to compa...
neat sandal
comparision test
Because i did it with 1/n'2 and it worked, absolutely convergent
so?
dense harness
Doesn’t matter what you use as long as it is larger than your series
neat sandal
so literally any number would suffice
midnight plankBOT
Available help channel!
pastel tree
Show that If $n \in Z_+$ and is an odd number $8 | (n^2 - 1)$
midnight plankBOT
Show that If $n \in Z_+$ and is an odd number $8 | (n^2 - 1)$
grand pondBOT
Merineth
pastel tree
My suspicion is that we solve this with induction?
full plume
**Merineth**
what coincidence am doing this exact question as an assignment
fossil knot
that'd work
pastel tree
what coincidence am doing this exact question as an assignment
I assume you don't live in Sweden?
full plume
what coincidence am doing this exact question as an assignment
With a little bit of weird twist
full plume
I assume you don't live in Sweden?
ye am asian lol
pastel tree
The fuck, Jönköping?
full plume
lemme solve it rq
pastel tree
that'd work
$(n^2-1) = 8k$
grand pondBOT
Merineth
pastel tree
Would it be appropriate to write it as such?
The reason being $a | b \implies b = ak$
grand pondBOT
Merineth
pastel tree
Oki good
Quick question tho
For the base case
Would it be appropriate to use 1 as my positive Z_+ and bneing odd?
Because if that is the case i get a division with 0, which is undefined
$(1^1-1) = 8k$
grand pondBOT
Merineth
pastel tree
Yeah i meant that, sorry
Okay so our base case holds
Our assumption would be :
$(p^2-1) = 8k$
grand pondBOT
Merineth
full plume
we just gotta solve this right?
fossil knot
$((p+2)^2-1) =8m$
You don't want to use 8k
since it's not going to be 8 times the same number
pastel tree
Right sorry forgot about that
pastel tree
we just gotta solve this right?
Yeah more or less. We want to prove that our assumption = goal
grand pondBOT
Merineth
pastel tree
I'm not entirely sure how to make sense of it
pastel tree
$(p^2-1) = 8k \
((p+2)^2-1) =8m$
grand pondBOT
Merineth
full plume
actually
we can do this
since we got 2 equations now
so p^2 = 8k+1
and in 2nd equation we get
P^2 +4P - 3 = 8m
pastel tree
I think you did something wrong on the + sign?
full plume
which one?
pastel tree
$p^2+4p+3 = 8m \implies 8k+1+4p+3 = 8m$
grand pondBOT
Merineth
fossil knot
Well you can't say that p^2+4p+3=8m because we haven't proved it yet
full plume
i mean those were the equations i saw so
full plume
**Merineth**
p = -3,-1
fossil knot
$p^2 + 4p + 3 = p^2 - 1 + 4p + 4 = 8k + 4p + 4$ is a good start that makes use of the inductive hypothesis
full plume
you can just see what value you get from that
grand pondBOT
Ari
full plume
k=1
full plume
**Ari**
weird thing is that if you put -1 in P the equation = 0 but if you put -3 in P then its equal to 1
pastel tree
I'm not sure i follow but isn't the point to prove that the assumption implies that the p+2 is also true?
Meaning we manipulate our assumption to get our goal or manipulate our goal to end up at our assumption?
<@&286206848099549185> 
pearl idol
Induction isn't necessary here
I would factor (n^2 - 1) into (n+1)(n-1)
And then think about what n+1 and n-1 are divisble by
@pastel tree
pearl idol
n+1 is divisible when n is even Z_+ ?
n is odd
if it helps, try to think of a concrete example
like n = 11
pastel tree
that would be 12/8?
pearl idol
what do you mean?
pastel tree
I have no idea
pearl idol
what would be 12/8
pearl idol
yeah, but why is (12)(10) divisible by 8? what are each of the factors 12 and 10 divisible by?
pastel tree
12 = 2*6 = 2*2*3
10 = 2 * 5
GCD(12,10) = 2?
pearl idol
why calculate the gcd?
pastel tree
Not sure
pearl idol
yeah 12 = 2 * 2 * 3 and 10 = 2 * 5 that's correct
what parts of that are relevant for figuring out if (12)(10) is divisible by 8
pastel tree
hmm¨¨
pearl idol
what's the factorization of 8
pastel tree
Because 12 and 10 both have a factor of 2? And so does 8?
pearl idol
you're on the right track, but 8 has three factors of 2
so 12 and 10 both having one factor of 2 isn't enough
pearl idol
I believe in you, think about it for a little longer
do 12 and 10 only have one factor of 2 each?
pastel tree
no
pearl idol
then what?
pastel tree
12 has 2^2
10 has 2^1
pearl idol
yeah exactly
so since 12 is divisible by 4, and 10 is divisible by 2, when you multiply them they have to be divisible by 8
that seems to work for n=11, but the question is about any odd number, so let's see if the same procedure works for any odd number
what about n=77 for example
could you do the same sort of trick to show that (n+1)(n-1) is divisible by 8?
pearl idol
right
note that when we were doing n=11, n+1 was divisible by 4 and n-1 was divisible by 2
but when we were doing n=77, n+1 was divisible by 2 and n-1 was divisible by 4
so they sorta switched places
but what's important is that one of them is divisible by 2 and one of them is divisible by 4, right?
if that's the case then they'll multiply together to get something divisible by 8
pearl idol
yeah, if a is divisible by 2 and b is divisible by 4, then a = 2k and b = 4l, and ab = (2k)(4l) = 8(kl)
that's how you could prove that more formally
okay so now you just need to prove that one of n-1 and n+1 is always divisible by 4, and one is always divisible by 2, and you'll be done
pearl idol
does that make sense?
pastel tree
No 
I have no idea what we have done so far xD
The book proves a similar case but by induction
I've never tried to solve something like this before by not using induction
pearl idol
let's take it slower then
"if a is divisible by 2 and b is divisible by 4, then ab is divisible by 8"
do you understand why this is true
pastel tree
No i do not.
The book never mentioned something like this
c | a and c | b then c | (ax + by) for all x and y
that is the only thing that mentions is that is remotely close to what you mean
pearl idol
okay let's take it straight from the definitions then
if a is divisible by 2, what does that mean?
pastel tree
We are only given two definitions about divisibility from the book \ \
$a | b \implies b = ak$ \
$c | a$ and $c | b$ then $c | (ax+by)$
grand pondBOT
Merineth
pearl idol
yes, the first one
is the definition
the second one is not a definition, it's a theorem
pearl idol
alright cool
so in this case
2 | a
means that a = 2k for some number k
does that make sense?
pastel tree
That 2 evently divides a which results in k?
pearl idol
yes
pastel tree
oki
pastel tree
b = 3k
3 evenly divides b which results in k
pearl idol
right
but since we've already used the letter k for a = 2k, let's use a different letter here to not get confused
so let's say b = 3l
is that okay?
pearl idol
alright
so now if we multiply a and b together
we get (2k)(3l) = 6(kl)
is that okay?
pastel tree
yea
pearl idol
alright
and now
this says that ab = 6(kl)
so in other words, ab is 6 times some integer
6 | ab
pastel tree
yup
pearl idol
does that conclusion make sense?
okay
so that proves that if 2 | a and 3 | b, then 6 | ab
you can similarly prove that if 2 | a and 4 | b, then 8 | ab, which is what we'll use for this problem
pastel tree
okay
pearl idol
okay
so now we want to prove an important lemma
if n is odd, then either n+1 or n-1 is divisible by 4
if we can prove this, then that will help us a lot to prove that 8 | (n+1)(n-1)
pearl idol
okay
well there are a couple different cases for what the remainder of n is when we divide by 4, right?
it can be either 0, 1, 2, or 3
pastel tree
how do you know that?
pearl idol
what other possibilities can there be?
pastel tree
I don't know, i've never thought about when i divide something with n i get a remainder which is less than n
pearl idol
well let's do an example, what's the remainder when you divide 11 by 4?
pastel tree
Is this what we are trying to prove?
pearl idol
3
yeah, exactly, it can't be something greater than 4 like 7 bc it's the stuff left over after you divide by 4
pearl idol
Is this what we are trying to prove?
yeah that's another way to do it
pastel tree
This is so odd to me, I've read the book thoroughly and made sure that i understood everything. I even took the time to look over lessons about what i learned as lectures on Youtube and it made perfect sense. But this isn't something that's mentioned at all
There is a lot of hidden knowledge that i'm expected to know beforehand
pearl idol
I think there is a learning curve with number theory, this is all stuff that you could prove using the definitions you're already given in the book, but the problems won't be straightforward applications of methods you've already learned
it'll probably require you to put in more novel thinking than math classes you've taken before
pastel tree
Isn't that a problem in itself? That the problems given are already way beyond straightforward applications
pearl idol
but once you get the hang of it, it'll feel good
pearl idol
Isn't that a problem in itself? That the problems given are already way beyond s...
I don't think this problem is particularly beyond what you've learned
if you've learned the definition of divisibility and the fact that odd numbers can be written as 1 plus a multiple of 2
pastel tree
It's very difficult for me to answer these problems as they aren't mentioned or shown in the book
pearl idol
it'll take some time to get used to, but I have full confidence that you can solve these types of problems, maybe with some hints along the way
pastel tree
if you've learned the definition of divisibility and the fact that odd numbers c...
If you are referring that a | b is b = ak then yes but the fact that an odd number can be written as 1 plus a multiple of 2 is not something i've learned ever
pearl idol
every math student hits this sort of bump along the way at some point
pearl idol
If you are referring that a | b is b = ak then yes but the fact that an odd numb...
what is the definition of odd that you've learned so far?
pastel tree
No definition has been shown for odd or even numbers
pearl idol
I see, that's a problem then; what do you think an even number is?
pastel tree
A number that is divisible by 2 with a remainder of 0
pearl idol
Right, that's correct
n is even if 2 | n
or in other words, n is 2m for some number m
and then any other number is odd, or in other words, it's one off of a even number
n = 2m + 1 for some number m
pastel tree
makes sense
pearl idol
awesome
pastel tree
I just fail to see how this applies to my problem
pearl idol
your problem is about odd numbers, so you need some sort of definition of what an odd number is
let's go back to considering the cases for what the remainder is when you divide n by 4
it can either be 0, 1, 2, or 3
pastel tree
Yea
pearl idol
now, you can rule out two of these cases by the fact that n is odd
for example, can the remainder be 0 when you divide n by 4?
pearl idol
I'm not talking about n^2 - 1 right now, I'm just talking about n
pastel tree
oh
pearl idol
If n is odd, can the remainder be 0 when you divide n by 4?
pastel tree
No
pearl idol
yeah that's correct, why?
pastel tree
Any odd number divided by an even number results in a remainder?
pastel tree
I'm not sure, my intuition says no but i honestly dont know
pearl idol
yeah so let's think about it this way
if the remainder is 2 when you divide n by 4
then that means that n = 4m + 2 for some number m, right?
n is 2 plus a multiple of 4
pastel tree
ok, yes
pearl idol
yeah, so then n = 2(m+1)
in other words n is two times something, so it's even
but we said n is odd, so this isn't possible
therefore, the remainder when you divide n by 4 can only be 1 or 3
does that make sense?
pearl idol
n = 2(m+1) is the same as n = 4m +2 ?
sorry
2(2m+1)
another way to think of it is that 4m is an even number and 2 is an even number, so when you add them, you get an even number
but that's not possible since n is odd
pearl idol
I'm so lost haha <:monkey:651816857153699840>
don't worry, we're almost at the end
pastel tree
The problem here is that
- I have to know beforehand that i can write n as n = 2k + 1 which is the definition for an odd number
- The def of an odd number is only figure out by the definiton of an even number
- The def of an even number isn't something that i have ever thought about
- to rewrite the entire equation in terms of 2k+1 giving (2k+1)^2 -1 and then further getting to 4k^2+4k and in turn also know that i have to factor out 4k(k+1)
- Understand that and even number x odd results in an even
- And then finally try to get my head around the fact that 4k(k+1) has that 4 is div by 4 and k(k+1) is div by 2 giving 4 x 2 = 8 meaning that 4 x 2 = 8 also implies that n^2-1 is also div by 8
It's just too much hidden knowledge for me to even start the problem solving
Is this a me problem or are there people who alredy know all of this and when they get their first problem (like mine) are able to solve it without any problem or help?
pearl idol
it def differs from person to person, and I don't know exactly what you've already learned in your textbook, I'm just trying to help you bridge the gap
there are plenty of others who struggle like this too though, you're not alone
pastel tree
I'm just not sure how i go about learning this
pearl idol
I think doing practice problems and asking them about here is prob one of the best ways
pastel tree
Yeah you are most likely right
The problem is that i have no idea what we are doing, and this is very common when i ask for help
pearl idol
I def relate to that feeling of having no idea what any of the words in a problem mean or how to get started though
pastel tree
I wish i wasn't so stupid
pearl idol
I think every math student has experienced that at some point
you're not stupid!
you just haven't learned these definitions/approaches yet
ppl also come into classes with different backgrounds, and that's totally normal
it doesn't mean you can't succeed
pastel tree
I mean, this will be my third try on Discrete mathematics ,_. I'm not sure i can lol
pearl idol
Third time's the charm, as the saying goes :)
pastel tree
Yeah i'm betting my life on it lol xD
pearl idol
Let's finish this problem real quick and then we can talk more about the big picture
pastel tree
Oki
pearl idol
So, since n is odd, it has to be either a remainder of 1 or 3 when we divide by 4 (it can't be an even remainder)
That means it's either one more than a multiple of 4 or one less than a multiple of 4
(remainder of 1 means that n is equal to a multiple of 4 plus 1, and remainder of 3 means that n is equal to a multiple of 4 minus 1)
I know that's a little bit of a jump, but does that sorta make sense?
pastel tree
Yeah i think so
pearl idol
Alright
So we can split up into two cases
If n is one more than a multiple of 4
That means 4 | n-1
and n+1 is even bc n is odd, so 2 | n+1
Putting it together, that means 8 | (n-1)(n+1), which is what we wanted to prove
On the other hand, if n is one less than a multiple of 4, then 4 | n+1, and 2 | n-1, so again we have that 8 | (n-1)(n+1)
And that's the end of the proof
pearl idol
Is this what we are trying to prove?
This proof is a different way from the picture you sent but if you want we can go over that proof too ^
pastel tree
Watched another proof in the meantime
pearl idol
Yeah that's another way to do it, which is the same way as the picture you sent
Both of the proofs require this sort of case-by-case reasoning though
In the proof I showed you, it was whether n had a remainder of 1 or 3
In that proof, it's whether k is even or odd
pastel tree
If someone asked me now if i could prove it then i'd be able to replicate what they did in the video / the solution they found on the forum.
But the problem mainly is that I would've never figured this out on my own because i'm missing crucial information about the definitions for odd and even numbers
pearl idol
Yeah that information about odd/even numbers is good to keep in your mind going forwards
Definitely the textbook/class should've defined what odd/even mean before giving you this problem, so that's an oversight on their part if they didn't
pastel tree
I didn't even understand that it wasn't an induction problem considering the problem they used in the book used induction on a similar problem
In the books similar exaxmple to what we did was
$4 | (6^n-2^n$
grand pondBOT
Merineth
pearl idol
Right
I mean I think with math, for each problem, you'll always have to try multiple techniques to find the one that works
It's not usually gonna be obvious which technique works
pastel tree
But how did you see that my case didn't use induction?
pearl idol
Like, here the proof is by case-by-case reasoning, but in that problem, the proof is by induction
pastel tree
(sat for nearly 4 hours trying to solve that one by induction yesterday to no avail also) xD
pearl idol
But how did you see that my case didn't use induction?
Usually I'd have to try a couple different methods to see which one works. In this instance, I got a little lucky because after factoring n^2 - 1 into (n-1)(n+1) and noticing that n is odd, I could tell that both factors were divisible by 2, so that route seemed promising. And then after a little more thinking, I realized that one of them actually has to be divisible by 4 which proves the thing we wanted.
One way to tell that induction is useful is that the situation with n+1 can be directly related to the situation with n
pastel tree
Usually I'd have to try a couple different methods to see which one works. In th...
Makes sense
pearl idol
$4 | (6^n-2^n$
Also: you don't necessarily have to use induction on this problem if you notice that you can factor 6^n - 2^n
6^n - 2^n = (6-2)(6^(n-1) + 6^(n-2) 2 + 6^(n-3) 2^2 + ... + 2^(n-1))
And then 6-2 = 4, so the whole thing is divisible by 4
So another good strategy is to try to write things in different forms and see what pops up, like if you can factor it then factor it, if it's already factored then try expanding it to see if that makes the problem easier, and so on
pastel tree
I'll keep that in mind
pearl idol
Yeah definitely math feels like a bag of tricks sometimes, and that can be disheartening
It takes a while of doing exercises to sort of learn the ropes and get a feel of what methods might be useful and what methods probably aren't
But it's also nice in the sense that there's no one that can't learn math, once you're given the right tools and a few hints here and there you can do any problem that the course throws at you, and it doesn't require you to be a genius or anything; it just takes time and practice
pastel tree
I really wish and hope that is the case
pearl idol
I wish you all the best of luck
Do you have any more questions that you're working on
pastel tree
Yeah a quick one.
What is the easiest way to find gcd(3071,851) ?
Euclides?
3071 = 851 * 3 + 518
851 = 518 * 1 + 158
....
....
Like such?
pearl idol
Yeah, use the Euclidean algorithm
midnight plankBOT
pearl idol
you're welcome! good luck
midnight plankBOT
Available help channel!
strong finch
hi is this correct?
midnight plankBOT
hi is this correct?
strong finch
srry for the poor quality
junior solar
Yeah that's correct.
midnight plankBOT
midnight plankBOT
Available help channel!
glacial hull
midnight plankBOT
glacial hull
Is this true?
prime hornet
,, \frac{dz}{du} = sec^{2}u
grand pondBOT
higher!
prime hornet
so $dz = (sec^{2}u) du$
grand pondBOT
higher!
prime hornet
there is no variable x in sight
pearl idol
<@&286206848099549185>
Please don't ping Helpers before 15 minutes have passed
glacial hull
there is no variable x in sight
Yes
glacial hull
Please don't ping Helpers before 15 minutes have passed
Srry
This was js a one liner question
.close
midnight plankBOT
midnight plankBOT
Available help channel!
bleak pier
midnight plankBOT
@bleak pier Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
twilit field
Prove that if $f$ is continuous on an open interval containing 0, $\lim_{h\ \rightarrow0}\left(\frac{1}{h}\right)\int_0^hf=f\left(0\right)$
midnight plankBOT
Prove that if $f$ is continuous on an open interval containing 0, $\lim_{h\ \ri...
grand pondBOT
ƒ(Why am. I here)=I don't Know
zealous schooner
L’Hopital’s rule 
zealous schooner
As you should
zealous schooner
but I wanted to use this theorm
What theorem
hollow oyster
Derivative definition
twilit field
typing it tn
twilit field
Derivative definition
Yeah, or this
zealous schooner
Derivative definition
This only works if you assume the fundamental theorem of calculus
pearl idol
Prove that if $f$ is continuous on an open interval containing 0, $\lim_{h\ \ri...
wait, how did you already get this far? I swear last time I checked, you were learning the definition of real numbers
zealous schooner
And then it’s basically the same as LH
twilit field
wait, how did you already get this far? I swear last time I checked, you were le...
I just realised I'm not doing proof based calc
I thought lang was proof based
but no
sinful trout
how does eric keep tabs on all the helpers lol
sage olive
bro has a list
hollow oyster
I thought lang was proof based
Spivak?
sinful trout
fr
twilit field
hollow oyster
bro has a list
Bro is stalking everyone
pearl idol
I just realised I'm not doing proof based calc
huh? this question asks you to prove something though
twilit field
using theorm 5.1
pearl idol
how does eric keep tabs on all the helpers lol
I just remember last time they asked about calculus, it was way beyond what they'd learned already with proof-based calculus
twilit field
huh? this question asks you to prove something though
yeah, I know, but most proofs are omitted
sinful trout
I just remember last time they asked about calculus, it was way beyond what they...
ah
honestly its nice to see someone actually ask abt this kinda stuff
zealous schooner
using theorm 5.1
Yeah then it just becomes F’(0)=f(0)
Just follows by definition
zealous schooner
I thought you didn’t have this
hollow oyster
Lmao
twilit field
I thought you didn’t have this
didn't have what
oh, I thought I had to prove theorm 5.1 again 
cobalt roost
I thought you didn’t have this
Hi, fancy seeing you here
cobalt roost
Nice
zealous schooner
oh, I thought I had to prove theorm 5.1 again <:KEK:586240877358350341>
Well that still isn’t too hard
It’s just squeezing it out
twilit field
at h,right?
zealous schooner
No, a derivative is at some particular point right
zealous schooner
(F(h) - F(0))/h
twilit field
yeah, got it
hollow oyster
(F(h) - F(0))/h
Assuming FTC holds true
twilit field
$\frac{\left(\int_0^hf\left(h\right)-\int_0^0f\left(0\right)\right)}{h}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
rigght?
zealous schooner
Assuming FTC holds true
Yeah but they already have that
zealous schooner
**ƒ(Why am. I here)=I don't Know**
Yeah
hollow oyster
Yeah but they already have that
Oh then it's easy
zealous schooner
Only the version which assumes continuity though
zealous schooner
**ƒ(Why am. I here)=I don't Know**
Wait no what
Don’t omit the dx parts
$\lim_{h\to 0}\frac{\int_0^h f(x)\dd{x}-\int_0^0 f(x)\dd{x}}{h}$
grand pondBOT
kheerii
twilit field
I don't follow, isn't it $\frac{F\left(h\right)}{h}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
yeah
hollow oyster
No why F(0) can be anything
zealous schooner
So you can still write it as (F(h)-F(0))/h
grand pondBOT
ƒ(Why am. I here)=I don't Know
zealous schooner
No why F(0) can be anything
They assumed $F(x)=\int_0^xf(t)\dd{t}$
grand pondBOT
kheerii
zealous schooner
**ƒ(Why am. I here)=I don't Know**
Yes, and the limit of this is just F’(0)
hollow oyster
Oh okay
zealous schooner
By definition
zealous schooner
Yes according to your theorem
hollow oyster
Yes
midnight plankBOT
hollow oyster
i'm going to fail uni fr
Nah
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slender cipher
Hi everyone out there,
I was trying to learn the Complexity Involved in reducing a Non singular matrix into Row Echolon Form Using Gaussian Elemination To find the solution for system of linear equations, I was watching Gilbert Strang's 18.06 Linear Algebra Have attached the Lecture Summary Notes here The calculation for the Complexity is mentioned under title "How expensive is elimination?" I feel the calculation have been taken wrong and there and the result derived over there is (n^3/3). Where I got a result of (n^3-n^2)/2
Can someone help with this
midnight plankBOT
Hi everyone out there,
I was trying to learn the Complexity Involved in red...
@slender cipher Has your question been resolved?
bleak pier
midnight plankBOT
bleak pier
It says x is real then what will be the relation to get all real values
For given expression
midnight plankBOT
@bleak pier Has your question been resolved?
hollow oyster
oh i see
hollow oyster
i graphed it tbh
hollow oyster
desmos
hollow oyster
I can solve it by d>=0
idt this works
hollow oyster
Without desmos?
wait lemme see
bleak pier
Yeah sure
hollow oyster
i got this when i searched online
bleak pier
https://math.stackexchange.com/questions/2786727/if-x-in-r-and-fracx-ax-cx-b-can...
Can anyone explain this 2nd solution?
.close
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bright shoal
@mighty zodiac
midnight plankBOT
<@1191788649327644814>
bright shoal
Come
mighty zodiac
S
bright shoal
In terms of k times derivative of quadratic term in denominator + constant
Like 2x+5=k*d/dx(7-6x-x^2)+c
This will help you to write the above linear factor as k.times derivative + c
@mighty zodiac hlo?
mighty zodiac
I don't understand
bright shoal
Listen
mighty zodiac
S
bright shoal
Did u understand this statement?
bright shoal
See we have a quadratic in denominator
Ok find its derivative
And tell m
E
Bro
bright shoal
Na bro
mighty zodiac
?
bright shoal
Bro listen
mighty zodiac
S
bright shoal
Just tell me derivative of 7-6x-x^2
mighty zodiac
-2x-6
bright shoal
Keep responding
mighty zodiac
S
bright shoal
Listen
mighty zodiac
d=-2x-6
bright shoal
First write 2x+5 in terms of -2x-6
mighty zodiac
S
bright shoal
U can separate the linear term and constant into two diff integrals
mighty zodiac
S
mighty zodiac
U can separate the linear term and constant into two diff integrals
We separate it ?
bright shoal
Yes
Because in one we will get constant in numerator
And in one we get derivative of below term in numerator
Did u understand
mighty zodiac
No
bright shoal
2x+5
bright shoal
Bro listen
2x+5 can be written as k(-2x-6)+C
Once u write it as this u can separate the integrals
In one u will have k(-2x-6)/√quad
mighty zodiac
Wht opposite bro?
mighty zodiac
Ok
mighty zodiac
But what about 1//√quad
If I can't do log then what to do?
midnight plankBOT
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drifting root
hows this work?
midnight plankBOT
hows this work?
drifting root
i get the denominator but why the numerator lose the abs val
drifting root
highkey thought i start from the proj u v cause of the abs
like how are we abs the proj u v that way
young spruce
the magnitude of the projection of v onto u is simply the component of v along u
young spruce
u.v is scalar
drifting root
that makes sense
young spruce
the component is scalar
to put it simply, the projection is like multiplying the component by a unit vector
so instead of just the length that v casts along u, you'd get the vector with the same length
young spruce
try graphing everything down first
drifting root
parallel to line L means smth with the gradient?
ok
sorry it took so long
ah wait
the gradient is -3/4
so i can write it as (4i - 3j)?
not unit vector
and then from that do the unit vector?
i come into the problem of why cant i write it as (-4i + 3j) though
<@&286206848099549185>
drifting root
Ask me what do you need help
if the parallel vector is smth like (4i - 3j) because of -3/4, then why cant it be writtenas (-4i + 3j)
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civic moth
sorry it took so long
There is a direct formula for distance between a point and line u can search that on web
manic bison
midnight plankBOT
manic bison
apparently the answer is 6 , can someone explain how
Got this , dunno how to go further
<@&286206848099549185>
feral sigil
cobalt roost
, rotate
grand pondBOT
feral sigil
This is where I got so far , I didn't get 6 but got 5.7, There might be silly error.
Is it right @cobalt roost
manic bison
is there any way to solve it without knowing the values?
feral sigil
I don't think so , normally in high school here in India we learn values of : 18,22.5,36,and sometimes 7and1/2( all angles here is in degrees)
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echo prism
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@echo prism Has your question been resolved?
midnight plankBOT
@echo prism Has your question been resolved?
pastel tree
How many divisors does n have? \
$n = 2^{12} \cdot 3^8 \cdot 5^6 \cdot 7^2 \cdot 11^4 \cdot 13^3 \cdot 23 \cdot 151$
midnight plankBOT
How many divisors does n have? \\
$n = 2^{12} \cdot 3^8 \cdot 5^6 \cdot 7^2 \cdo...
grand pondBOT
Merineth
pastel tree
hmm
grand pondBOT
normalAtmosphericPa=101,325
sudden topaz
how many divisors does this have?
pastel tree
Well my guess would be 1? Since i can choose either p_1 or p_2 to divide m with
sudden topaz
Well my guess would be 1? Since i can choose either p_1 or p_2 to divide m with
let e1 = 1, e2 = 2
pastel tree
oh hold on
sudden topaz
that would essentially be saying that `m = 3 * 5 * 5`
$m=2^2\cdot 3^3$
grand pondBOT
normalAtmosphericPa=101,325
grand pondBOT
Merineth
pastel tree
so 5?
grand pondBOT
Merineth
sudden topaz
$8=2^3$
grand pondBOT
normalAtmosphericPa=101,325
pastel tree
yes
sudden topaz
what do you notice?
how many divosors does 24 have?
list them all
hint: $2^3\cdot 3 = 24$
grand pondBOT
normalAtmosphericPa=101,325
pastel tree
$24 = 212 = 226 = 2223$
grand pondBOT
Merineth
grim vector
$24 = 3^1 * 2^3$
grand pondBOT
YakuBros
grim vector
Maybe
sudden topaz
Consider $m=p_1^{e_1}p_2^{e_2}$ where $e_1,e_2\geq 1$
ok anyways
the number of divisors is precisely the number of ways of choosing the exponents of the prime factors
this is a combinatorial problem
so for the 24 example
for the first prime factor 2, I could choose 1,2,3
also 0
grim vector
the number of divisors is precisely the number of ways of choosing the exponents...
Hmm not sure
sudden topaz
and then 0 or 1 and exponents for 3, the second prime factor
pastel tree
So the number of divisors for 24 is 4? 2*2*2*3
sudden topaz
So the number of divisors for 24 is 4? `2*2*2*3`
no
grim vector
the number of divisors is precisely the number of ways of choosing the exponents...
This is not true
pastel tree
This is the correct method?
sudden topaz
ye4s
Let $n=p_1^{e_1}p_2^{e_2}\cdot...\cdot p_ke^{e_k}$ for primes $p_i$, integers $e_i\geq 0$
grand pondBOT
normalAtmosphericPa=101,325
grim vector
But you forgot 3^0 in the explain so to be more easy, the number of divisors is the sum the (exponent + 1)
So for 24 = 3^1 * 2^3 = (1+1) + (3+1)= 6
sudden topaz
But you forgot 3^0 in the explain so to be more easy, the number of divisors is ...
yes
1 for the allowing for 0 as an exponent
which is basically omitting the square-free term
pastel tree
$24 = 212=226 = 2223 = 2^33^1$\
$D(24) = (3+1)(1+1) = 8$ ?
grim vector
1 for the allowing for 0 as an exponent
I got the first thing you said but it leads to forgot it at the first time
grand pondBOT
Merineth
sudden topaz
i.e., $n=p_1\cdot ... \cdot p_k$
grand pondBOT
normalAtmosphericPa=101,325
pastel tree
Why is the answer 8?
grim vector
$24 = 2*12=2*2*6 = 2*2*2*3 = 2^3*3^1$\\
$D(24) = (3+1)*(1+1) = 8$ ?
No add
You have to add not times
At the end
sudden topaz
Why is the answer 8?
apply the formula carefully
pastel tree
What?
D(24) = (3+1)x(1+1) = 4 x 2 = 8
How is that wrong?
i only have e^1 and e^2
where e^1 is 3 and e^2 is 1
I count 8. Are you both wrong?
@grim vector@sudden topaz?
sudden topaz
D(24) = (3+1)x(1+1) = 4 x 2 = 8
D(n) = number of divisors of n
read the definitions carefully
pastel tree
$D(n) = (12+1)(8+1)(6+1)(2+1)(4+1)(3+1)(1+1)(1+1) = 13973542*2$
grand pondBOT
Merineth
sudden topaz
How many divisors does n have? \\
$n = 2^{12} \cdot 3^8 \cdot 5^6 \cdot 7^2 \cdo...
.
pastel tree
No add
You said this is wrong
why?
I applied the formula correctly afaik
and i got the right answer
.close
midnight plankBOT
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summer ravine
I choose a perfect channel.
I genuinely need help with this question:
$Q. 5$ Prove that the 3/4 the (sum of the (sides of a triangle) (perimeter)) < sum of (the three medians)
midnight plankBOT
I choose a perfect channel.
I genuinely need help with this question:
$Q. 5$ P...
grand pondBOT
Meolve
summer ravine
I don't know why Apollo bro's channel is constantly being seperated.
zealous schooner
I think you’re staying the question incorrectly
Hmm, hold on
We have $3(a^2+b^2+c^2)=4(l_a^2+l_b^2+l_c^2)$
grand pondBOT
kheerii
midnight plankBOT
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.
summer ravine
ok
but first, bro know's many alternatives. to commands.
The original question was not that.
It was:
I did that after two inequalities by knowing:
AB+BC > 2AD (where AD is the corresponding median)
and summing up the three inequalities and proving subsequently.
I need help with the first one.
I mean the first two-containing inequality.
Because we know that 3/4 of x < x (if x is positive)
or 3/4 (mod x) < mod (x)
zealous schooner
Draw the three medians
The point they intersect at is the centroid
Then use the property that the centroid divides the median in the ratio 2:1
summer ravine
going from the vertex through which it's drawn to the opposite side? the ratio
summer ravine
Then use the property that the centroid divides the median in the ratio 2:1
ohk got it.
zealous schooner
going from the vertex through which it's drawn to the opposite side? the ratio
Yeah
zealous schooner
Then just spam triangle inequality probably
summer ravine
Then use the property that the centroid divides the median in the ratio 2:1
I shall try to prove this:
thanks 🙂
.close
midnight plankBOT
summer ravine
But you forgot 3^0 in the explain so to be more easy, the number of divisors is ...
How can 24 = 6?
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muted jewel
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muted jewel
I did it on y=mx+b first so y=3x/2 -4 then in general form is -3x/2 +y+4=6x-2y-8=0
Can someone tell me if I'm correct
With 6x-2y-8=0
grim vector
Also what does that mean?
The coefficient are in an interval I, maybe defined before
muted jewel
Oh yeah I see
muted jewel
The coefficient are in an interval I, maybe defined before
And could you please elaborate on this I'm confused still
grim vector
And could you please elaborate on this I'm confused still
Is there an interval called I ?
muted jewel
No at least I don't think because it doesn't show on the graph
grim vector
Anyway, the définition is that A,B and C are reals numbers, with A and B arent zero at the same time
If A is zero, B wont
And if B is zero
A wont
muted jewel
Alright thanks
midnight plankBOT
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plain compass
can someone can help me multiplying 6345 324 please
midnight plankBOT
can someone can help me multiplying 6345 324 please
plain compass
is 6345x324
midnight plankBOT
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uncut topaz
hello, whas the formula on how to find the price of a pizza slice
midnight plankBOT
hello, whas the formula on how to find the price of a pizza slice
rose trout
It's usually written on the pamphlet
uncut topaz
its not
rose trout
But if we have the price for the pizza and we assume equal slices, then the price will be (price of the pizza)/(number of slices).
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drowsy thunder
what happend in this is how did they get rid of the square root
midnight plankBOT
what happend in this is how did they get rid of the square root
grand pondBOT
faiyrose
drowsy thunder
ohhh i see
grand pondBOT
faiyrose
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eager fjord
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subtle blaze
What have you tried
eager fjord
well i tried to look at it because there are the congruency markings
turns out i forgot more basic geometry then i thought
subtle blaze
Well look at the picture, and imagine rotating that left triangle
eager fjord
ok