Alright give me a moment to write it down
#help-27
violet raptor
violet raptor
Yep
The answer is 11
I assumed the numbers to be x , x+2 , x+4
And then did as the question asked
charred pollen
why did u use x+2 i thought to get odd u use 2x+1
violet raptor
(x)² + (x+2)² - (x+4)² = 65
violet raptor
why did u use x+2 i thought to get odd u use 2x+1
Not really you can try that with any odd number and notice that it won't add up
charred pollen
okay
violet raptor
An example is to assume x to be 3
And then do as you say
The next number would be 7
And the question tells you that the numbers are odd and consecutive
violet raptor
I assumed the numbers to be x , x+2 , x+4
But if you try this it would add up no matter what
charred pollen
and one exapnded it w = x^2 + x^2+4x+4-x^2+8x+16=65
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violet raptor
np have fun dude
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plain grail
hey can anyone help me with this
devout snowBOT
hey can anyone help me with this
upper schooner
@ me plz
Well, do you know how to solve quadratics, at least?
It may help to make a substitution to make the quadratic you want more apparent
plain grail
Well, do you know how to solve quadratics, at least?
yes
so sub 3^x as like 'b' or smth
aight thx
that works
.close
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cold bone
Which of the following is(are) NOT the squares of 3х3 matrix with real entries?
cold bough
you can start by noticed that det(A^2)=det(A)^2>=0
cold bone
you can start by noticed that det(A^2)=det(A)^2>=0
but B has determinant value greater than 0
cold bough
but B has determinant value greater than 0
yes but A and B are not like that
cold bone
as far as I know, having determinant greater than 0 doesn't imply that it can be expressed as square of some matrix with real entries
cold bone
yes but A and B are not like that
A and C, but I get those
problem is with B
how should one can conclude about it?
the one method I can think of is to find some example for which B is square of that
But in examination it is not that convenient to take that much time to just find that
so is there any other method?
sand dove
You can also view B as a diagonal block matrix
B is made of 2 diagonal blocks
"1"
and -I_2
cold bone
You can also view B as a diagonal block matrix
I am not familiar with that term, can you explain a bit please
cold bough
sand dove
oh wait
cold bough
I defined q as ...
cold bough
deg q is 3 or les
sand dove
sorry
cold bough
np
sand dove
yes ok the problem is that
sand dove
but q(l) dividing EITHER ... OR is not true
yes
this is indeed the problem
because l^2-Id is factorable
q(l) = (l^2+id)(l-id) for example
cold bough
oh yes right ... t^2-1 is not irreducible in R
sand dove
so
cold bough
it would have been right if it had been
sand dove
$\begin{pmatrix}1&0&0\0&0&1\0&-1&0\end{pmatrix}$
woven radishBOT
rafilou2003
cold bough
sand dove
oh and to be exact P(t) = (t^2-1)(t^2+1) and not +/-Id, that's when you evaluate in a matrix
cold bone
And I forgot to mention it was supposed to be answered by only high school or a little above level of mathematics😭
pre-uni stuff
cold bough
it is always interesting see other ways even though the guy has no knowledge about minimal polynomial
sand dove
If you wanna find S such that S² = B
Just find a similar diagonal block matrix S1, S2
Such that S1² = B1
And S2² = B2
sand dove
oh so for this I can just focus on a 2 by 2 matrix
yes since you can just pick 1 for the upper left coefficient
and then it's all about finding a square root of -I_2
cold bone
and then it's all about finding a square root of -I_2
I think I get the idea
sand dove
so I'm guessing you have an idea of what thing done twice would amount to rotation of 180 degrees
frozen pelican
How do you solve questions that are like, Person A does a thing in an hour, Person B does the thing in two hours, how fast do they do it if they work together?
devout snowBOT
How do you solve questions that are like, Person A does a thing in an hour, Pers...
olive jasper
How do you solve questions that are like, Person A does a thing in an hour, Pers...
If A does it in 5 hours then how much A does in 1 hour ? x/5
If B does it in 3 hours then how much B does in 1 hour ? x/3
In 1 hour they combine can do x/3+x/5 =8x/15
Now suppose they finish the complete task in t hour , so
8x/15 * t = x
t = 15/8```in 1 hour they will do 1 and 1/2 things
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green crypt
Why is the determinant of collinear points zero?
devout snowBOT
Why is the determinant of collinear points zero?
solid hull
Why is the determinant of collinear points zero?
collinear points will be on the same line and therefore also parallel
so the determinant is 0
green crypt
Why is the determinant of parallel points zero then?
solid hull
same reason if I'm interpreting correctly
green crypt
I mean why is it zero? How does one visualise it
solid hull
I mean why is it zero? How does one visualise it
personally this video helped me a lot
and the series
green crypt
I see
solid hull
idk if it will directly answer your question though.
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lavish nimbus
Is the result of $$\lim_{x\to 1} \frac{\sin(x-1)}{x^2+3x-4}$$ just $\frac00$, which is just Ø?
woven radishBOT
Good
Compile Error! Click the 
reaction for more information.
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cold bone
the what?
cold bone
**Good**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
you're supposed to do mathematical manipulation here to make the x=1 sub viable
try to convert it into some standard limit you know
lavish nimbus
So changing u with x-1 gives sin(1)/6 as result?
cold bone
So changing u with x-1 gives sin(1)/6 as result?
no
agile elbow
Do you know about l'hopital rule ?
lavish nimbus
Do you know about l'hopital rule ?
Do I just use it till I get some constant in denominator?
agile elbow
Yes
lavish nimbus
if you change x-1 to u
then the limit will u goes to 0
Why's that?
agile elbow
You are getting it in one time though
cold bone
Why's that?
because as x goes to 1
x-1 quantity goes to 1-1 which is 0
agile elbow
cos(x-1)/2x + 3 after applying l'hopital rule
Putting the limit 1 will get you your answer 👍
lavish nimbus
because as x goes to 1
x-1 quantity goes to 1-1 which is 0
Alright, think I got it.
Thanks for the help:)
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digital tiger
Hello, I need to understand how to create fractions to solve x given a text, statement
The bus, traveling at a constant speed, traveled 120 km. If he had driven at a speed of 12 km/h higher, it would have taken him 20 minutes less on the road. How fast was the bus going?
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Hello, I need to understand how to create fractions to solve x given a text, sta...
gusty nexus
Hello, I need to understand how to create fractions to solve x given a text, sta...
x = vt
120 = vt
120 = (v+12)(t - 1/3)
-1/3 because t is time in hours
digital tiger
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sturdy mango
are questions which have with replacement in it always gonna be indepdent events since sample space goes back to same state
devout snowBOT
are questions which have with replacement in it always gonna be indepdent events...
crude wasp
are questions which have with replacement in it always gonna be indepdent events...
as in like n balls are taken out of a bag with replacement?
if so then yeah the events should be independent
sturdy mango
yeah
crude wasp
but i think it's generally not a good idea to try to memorise "if a question says x" then the events are independent
use ur intuition mostly
sturdy mango
yeah i thought maybe i obsereved something
that could be useful as a rule of thumb lol
crude wasp
if so then yeah the events should be independent
and like there could be questions where taking n balls out of a bag with replacement might not be independent
sturdy mango
ill just check
sturdy mango
and like there could be questions where taking n balls out of a bag with replace...
how comee
crude wasp
and like there could be questions where taking n balls out of a bag with replace...
like i.e. maybe it's not mixed very well so ur like more likely to take out the ball you just put in etc.
like you can create a question using that as a premise
anyway i don't like learning rules of "if X is true then Y"
you'll just have to do questions and eventually u'll pick it up
compact fulcrum
In need of a statistician's help! I am doing research on evaluating campus journalism restrictions on senior high school student journlaists utilizing a quantitative method and surveys. I also plan on using the stratified sampling technique. How would I know if the participants I gathered are enough to represent the whole population? And how would I use stratified sampling technique in this situation?
devout snowBOT
In need of a statistician's help! I am doing research on evaluating campus journ...
@compact fulcrum Has your question been resolved?
compact fulcrum
<@&286206848099549185> im confused, please enlighten me
crude wasp
In need of a statistician's help! I am doing research on evaluating campus journ...
you can try your luck with #probability-statistics
compact fulcrum
Alrighty, Thanks Ly!
crude wasp
you might find some statisticians who are willing to help with ur question
compact fulcrum
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shut gorge
good day
uncut crow
bruh
shut gorge
junior chasm
bruh
shut gorge
bruh indeed
limpid dove
bruh
vast drift
the user name deserves a praise
shut gorge
i dont even have a direction
shut gorge
the user name deserves a praise
thanks so much it took me some time
limpid dove
what kind of ancient magic language is it even
crude wasp
basically part D
hint: ||induction||
warm fulcrum
No 
rose rock
It's just so distracting
uncut crow
there are rules but you can just break them
shut gorge
hint: ||induction||
how to use induction anyways
uncut crow
Can u change ur username?
btw you can message modmail
warm fulcrum
there are rules but you can just break them
And where has that gotten you before, Harper?
uncut crow
And where has that gotten you before, Harper?
punished
polar chasm
btw you can message modmail
I don't really mind his username that much
dense lynx
the end of an age
shut gorge
i ended up with A^100=A-I
wait no A^100(A-I)=(A-I) and i dont know matrix division
i dont even know where to start
polar chasm
how to use induction anyways
I think that you should show that
A^(k+1) = (k+1)A - kI
by induction
i havent actually tried it though
which i probably should
yeah, it works fine
polar chasm
I think that you should show that
A^(k+1) = (k+1)A - kI
try proving this by induction
crude wasp
I think that you should show that
A^(k+1) = (k+1)A - kI
that might not necessarily be true (as in A^n might be equal to different things depending on the parity of n)
shut gorge
whar
crude wasp
(i suspect it'll be stuffA - stuffI for n odd, the other way round for n even)
but yes the idea is that you try finding out what A^n equals for small values of n
shut gorge
also what lead you to think the question can be solved by induction when u first looked at it
crude wasp
then you can make a prediction on what A^n equals
then you can prove ur prediction using induction
crude wasp
also what lead you to think the question can be solved by induction when u first...
to answer ur q
2 things:
- often when a question has some big number somewhere, the main interesting part is not that big number in particular, but can u show it for a general number n
- also with this question, as u discovered, if we know the value of A^99 we'll know the value of A^100
whenever u have this sort of "if I know it for a smaller value of n, i know it for a bigger value of n" that screams induction
shut gorge
noted with many thanks
crude wasp
nw!
polar chasm
that might not necessarily be true (as in A^n might be equal to different things...
wait, really?
ill dm u my proof if you dont mind
crude wasp
wait, really?
well that was my guess since
A^0 = I
A^1 = A - 0I
but i haven't actually done the q
don't have pen&paper with me rn
crude wasp
ill dm u my proof if you dont mind
it might be the case that it is just true for all n >= 1
polar chasm
Ah
my proof starts at n = 2
as a base case
it could start at n = 1, but i use the n = 2 case later anyway
crude wasp
fairs
anyway my point was more that if the question didn't work with A^n = nA - (n-1)I
then it doesn't mean induction doesn't work, just means that you should see what small cases evaluate to
polar chasm
yeah, thats fair
tawdry venture
devout snowBOT
fossil locust
what have you tried?
gusty nexus
Cos theorem
pure flower
!status yes
devout snowBOT
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
restive river
what is cos theorem 
pure flower
,wolf cosine theorem
woven radishBOT
gusty nexus
You didn't mean it ig?
gusty nexus
cos identities?
No
restive river
bro i meant cos theorem whether u mean cos identities or not
fossil locust
bro i meant cos theorem whether u mean cos identities or not
this okay
junior chasm
this
restive river
cosine rule, ok
junior chasm
lmao we got the same image
gusty nexus
,w solve 33 + 44 - 234*cos(x) = 2
woven radishBOT
riemann
supple knot
no triangle though
tawdry venture
i learnt the bottom one
restive river
back to the main point
tawdry venture
i havent done this in ages
fossil locust
can someone step out the process of isolating C for me
$2bc \cos C = a^2 + b^2 - c^2$
add $2bc \cos C$ to both sides, then subtract $c^2$ from both sides
woven radishBOT
higher's secret brother
restive river
and then just apply cosine law
fossil locust
you want to isolate cos C not c btw
tawdry venture
you want to isolate cos C not c btw
wtf why
tawdry venture
does C not?
fossil locust
no, c is a side
fossil locust
does C not?
I mean you first have to rearrange for cos C
then you can arccos both sides to get the angle C
fossil locust
,w arccos((2^2 + 4^2 - 3^2)/(2 * 2 * 4)) in degrees
woven radishBOT
fossil locust
oh wait C is correct
yeah that's not the smallest
basically if you get a negative value inside the arccos, that means the angle will be obtuse
tawdry venture
what the fuck does trhat mean
fossil locust
tawdry venture
wtf is an arccos
fossil locust
what the fuck does trhat mean
,calc (2^2 + 3^2 - 4^2)/(2 * 2 * 3)
woven radishBOT
Result:
-0.25
i think thats specialist
fossil locust
wtf is an arccos
cos^(-1)
tawdry venture
ohh
fossil locust
arcsin = sin^(-1) and arctan = tan^(-1) btw
tawdry venture
why did i get 0.51 tho
fossil locust
to get (a^2 + b^2 - c^2)/(2ab)
fossil locust
that's in radians not degrees
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lunar vault
How tf do this limit is proven $\lim_{x \to 2}x^3+3=11$??? 😭😭😭
I've been trying and can't got it
woven radishBOT
Gui
woven radishBOT
Gui
polar chasm
Are you supposed to find delta just for epsilon = 1?
lunar vault
yup
polar chasm
okay I see
so you are supposed to find $\delta$, such that
$\abs{x-2} \le \delta \implies \abs{x^3 + 3 - 11} \le 1$
lunar vault
yep
woven radishBOT
MæthIsAlwaysRight
woven radishBOT
Gui
lunar vault
and I think that's fine right now but idk
lunar vault
really?
polar chasm
**Gui**
actually, no. Sorry.
x^3 - 2^3 isn't equal to that
one number is wrong
here is the formula
lunar vault
so it's 2x instead
eager nova
so it's 2x instead
Yes
lunar vault
ohhh
fuck
even though, I'm not sure how to continue cause all videos I've watch is trivial from there...
should I convert that into (x+1)(x+2) and from there narrow it down or what?
lunar vault
well, as long as I've seen, when you get the factor you want, after that you narrow down the other factor to find the delta
idk if the term is that, I used Google translator since the Spanish word is acotar
lunar vault
nvm I'm like stupid, and didn't factorize it correct
polar chasm
it actually cant be factorized. Anyway, you could probably try bounding x^2 + 4x + 4 near x = 2 here.
try calculating its value at x = 2
polar chasm
so it's 12
x^2 + 2x + 4 is 12 at x = 2, yes
polar chasm
and how does that helps
if you now calculate it at say x = 1 and x = 3, you could get a reasonable bounds on it.
polar chasm
if the upper bound was e.g. 20, then you'll have that
|x-2| * |x^2 + 2x + 4| <= |x-2| * 20, which you hope is < 1 (epsilon)
and the important point is that you can actually limit the value of |x-2| by delta
so you could maybe choose such a delta, such that |x-2| * 20 < 1 (epsilon)
polar chasm
that is what epsilon =1 means?
they chose it for purpose of demonstration ig
lunar vault
I think I'm starting to understand but not sure
lunar vault
they chose it for purpose of demonstration ig
oh
polar chasm
I think I'm starting to understand but not sure
Our point will be choosing some delta, such that we can guarantee that if |x-2| < delta, then |x^3 - 8| < 1
lunar vault
oooohhhhh okey, now I got it
polar chasm
and we already simplified that to guaranteeing that if
|x-2| < delta, then |x - 2| |x^2 + 2x + 4| < 1
because then the conclusion follows from that
lunar vault
ooohhh okey okey, now I got it ig
polar chasm
So if we could place an upper bound on |x^2 + 2x + 4| (with reasonable distance from 2), which I will call U now, then we would only need to find delta, such that
|x - 2| * U < 1
but we can get |x - 2| as small as we want, by choosing small enough delta
so that will lead us to victory
lunar vault
So if we could place an upper bound on |x^2 + 2x + 4| (with reasonable distance ...
parting from this, would delta be 1/U?
polar chasm
unfortunately, |x^2 + 2x + 4| is unbounded
so we will need to place an upper bound, that works for x, which satisfy |x-2| < delta
which might look somewhat circular
so we can just claim that our delta will be definitely smaller than 1, because if it wont, then we can pick a smaller delta anyway
and you can upper bound |x^2 + 2x + 4| for x with |x-2| < 1 now
which is for 1 < x < 3
if that doesn't make much sense rn, don't worry too much about it
it will make sense once all the magic happens
polar chasm
and you can upper bound |x^2 + 2x + 4| for x with |x-2| < 1 now
for now, try doing this
find some constant upper bound
lunar vault
for now, try doing this
oh okey okey
polar chasm
try not to overthink it btw, just plug in x = 3 and x = 1
lunar vault
so, it would be 19 when x=3
polar chasm
yeah, and that works as an upper bound
lunar vault
oh okey, and then the same with x=1
and take delta as d=min(19,the other)
isn't it?
lunar vault
oh
polar chasm
so, it would be 19 when x=3
we will take this as an upper bound
lunar vault
let's recap what we have now
ty
lunar vault
we will take this as an upper bound
okey
polar chasm
so we have that if delta < 1, (which guarantees that 1 < x < 3) then
|x^3 - 8| = |x-2| |x^2 + 2x + 4| <= 19|x-2|
and our goal is making that < 1
smaller than epsilon
and keep in mind that |x-2| < delta
polar chasm
and our goal is making that < 1
can you pick some delta, that guarantees this?
delta that guarantees 19|x-2| < 1
lunar vault
so it would be 1/19
polar chasm
so delta < 1/19 works, because:
|x^3 - 8| = |x-2| |x^2 + 2x + 4| <= 19|x-2| <= 19delta <= 1 = epsilon
polar chasm
so it's the same process with the lower bound isn't it?
we actually dont need the lower bound
polar chasm
so delta < 1/19 works, because:
|x^3 - 8| = |x-2| |x^2 + 2x + 4| <= 19|x-2| <= ...
this is all we need, every single inequality there is justified
lunar vault
cause the number would be obviously bigger?
polar chasm
cause the number would be obviously bigger?
we only need upperbound, because the goal of it was being able to claim
|x-2| |x^2 + 2x + 4| <= 19|x-2|
lunar vault
oooohhhhh
polar chasm
so delta < 1/19 works, because:
|x^3 - 8| = |x-2| |x^2 + 2x + 4| <= 19|x-2| <= ...
we needed to justify every single one of this inequalities
|x^3 - 8| = |x-2| |x^2 + 2x + 4| is justified by algebra
|x-2| |x^2 + 2x + 4| <= 19|x-2| is justified by upper bounding x^2 + 2x + 4
lunar vault
yep, and that would work for every number lesser than 1/19,
polar chasm
19|x-2| <= 19delta by |x-2| < delta
and 19delta <= 1 = epsilon is justified by choice of delta
polar chasm
yep, and that would work for every number lesser than 1/19,
yes, we could choose any delta < 1/19
lunar vault
omg ty very much
polar chasm
in fact, you could've answered the question without doing any work
you couldve just said let delta = 1/100000000000000
lunar vault
it really helped me to understand it better
polar chasm
and you'd be most likely correct
polar chasm
omg ty very much
np
lunar vault
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vestal gate
devout snowBOT
supple knot
chain rule yes
vestal gate
is the highlighted part a general equation or is it differentiated?
supple knot
differentiated from the previous line
$\frac{dz}{dx} = \frac{d}{dx} y^{-n + 1} = (-n+1) y^{-n + 1 - 1} \cdot \frac{dy}{dx}$
woven radishBOT
riemann
devout snowBOT
@vestal gate Has your question been resolved?
fickle panther
devout snowBOT
fickle panther
How do i get the parenthesis
supple knot
,rotate
woven radishBOT
supple knot
if you're looking for an answer of the form x+a, ask yourself 5 * a = 15
if you've learned FOIL, then the 8 comes in when you add 5 with a
devout snowBOT
@fickle panther Has your question been resolved?
rich flint
I am trying to prove that the sum of k*binom(n,k) from k=1 to n equals n2^(n-1) using induction, and I'm on the inductive step. I split the sum into two, using pascal's identity and keep going from there, but I keep ending up with that +2 at the end. According to my inductive hypothesis, it should turn out to be (n+1)2^n.
Can anyone find what I'm doing wrong?
devout snowBOT
I am trying to prove that the sum of k*binom(n,k) from k=1 to n equals n2^(n-1) ...
iron sun
In the third equality, how you are you getting that extra 1
rich flint
I computed the term for when k equals n+1 so I could rewrite the sum to go to n
iron sun
Yeah so what’s (n+1) times n choose n + 1?
iron sun
Let’s focus on the right factor, how many ways can you select n+1 objects out of n?
rich flint
ooh what its just 0
I thought I could expand the binomial and multiply it inside but it's just for when the binomial isn't 0?
iron sun
I don’t really see how you got 1, but by convention anything with k being strictly bigger than n in the formula for n choose k is zero, we otherwise have to deal with a (-1)!
rich flint
Do you reckon it's the same mistake for the extra 1 I got in the red?
I see it now
I thought the sum of a row of pascal's triangle started at k=1 but it's clearly 0, thank you for being patient
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frank siren
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fierce heath
Whats the original question
devout snowBOT
@frank siren Has your question been resolved?
lunar sentinel
I know, it's easy, but what should I do to simplify it?
devout snowBOT
I know, it's easy, but what should I do to simplify it?
misty crest
log base 2
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slim thistle
Can someone explain to me why the real values of x of the continuity of the function isnt [1.5,+oo[
devout snowBOT
Can someone explain to me why the real values of x of the continuity of the func...
woven radishBOT
soft nest
I suspect you said [1.5,infty] ?
soft nest
Can someone explain to me why the real values of x of the continuity of the func...
You’re almost right, but we can never reach infinity
slim thistle
I suspect you said [1.5,infty] ?
Yes
slim thistle
You’re almost right, but we can never reach infinity
Why not
soft nest
By definition if you reach “infinity” there exists your number +1
slim thistle
Ahhhh ok
Nono the bracket are the wrong way
But my question is how do you define all the real values of x
I know the answer and got it wrong
soft nest
$x \in \left(-\infty,-7.5\right) \cup \left(-7.5,-1.5\right] \cup \left[1.5,\infty\right)$
maiden pecan
Did you include (-infty, -1.5] as well
soft nest
Ah right
woven radishBOT
Pixelius
acoustic vault
its just the domain you found but you didnt consiuder that a * b is also positive when both are negative
slim thistle
What represents a and b in my problem
maiden pecan
(2x+3)(2x-3)
acoustic vault
(2x-3)(2x+3)
maiden pecan
But still they said that is not the answer
slim thistle
**Pixelius**
This is correct i just dont understand why and how to find this answer
maiden pecan
Oh ok
So yeah your problem was with splitting the (2x+3)(2x-3) >= 0
Find the zeros for the parabola (which you already did), and then figure out which intervals are greater than or equal to 0
acoustic vault
and remember the stricter bound 'wins' when doing the two cases
slim thistle
What does stricter bound mean
acoustic vault
like when you considered both (2x+3) and (2x-3) to be positive the x>3/2 is the one you keep
because thats when both are positive
x>-3/2 only works for (2x+3)
x>3/2 works for both because then x is also greater thgan -3/2 if that makes sense
slim thistle
Ok yes i understand this but if the stricter bound wins why is my continuity including values that could mess up my equation and make it an imaginary number
acoustic vault
it doesnt. remember you now only cosidered both to be positive
but if both are negative then their product is also positive
(2x+3)<0 and (2x-3)<0 means their product (2x+3)(2x-3) is positive the minus cancels
thats the case you forgot to do
slim thistle
How do i do that like on paper
What would my calculations look like
Do i have to do a graph of the parabole?
acoustic vault
no thats not necessary you just do the same as you just did
but where $(2x-3)\leq0$ and $(2x+3)\leq 0$
woven radishBOT
Hugaxi
acoustic vault
find what x should be then
slim thistle
So when i want to find the continuity and have a form of a*b i do this?
acoustic vault
its not that specific. you have just reduced your original problem to finding when a * b is positive right
and a * b is positive only in 2 cases which you need to do both
acoustic vault
sure i feel like thats a weird way to look at it though
slim thistle
Why
acoustic vault
you need to do it everytime you want the product of 2 numbers to be positive
doesnt matter how you get there
or what problem its in
acoustic vault
.close
devout snowBOT
slim thistle
.close
acoustic vault
i already did it for you
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cyan axle
devout snowBOT
acoustic leaf
you should really replace $\pm$ with either $+$ or $-$
woven radishBOT
cloud
acoustic leaf
because desmos is treating it as a variable
cyan axle
I just did it
But the questions just asking for a set that makes a limacon
Like almost any set looks like it’ll make one
Am I missing something?
Well….it looks like the shape so
.close
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tender wind
for this vector
devout snowBOT
for this vector
tender wind
or not vector but i have to calculate the result, it gives me 0 +( 1 2 3)
in this case is my answer undefined
or ( 1 2 3)
acoustic leaf
it doesn't make sense to add a scalar and a vector
misty crest
is this supposed to be the first vector dotted with the sum of the second and third?
tender wind
it doesn't make sense to add a scalar and a vector
but its 0
0 is still a sclar
scalar?
So in this case its undef?
tender wind
is this supposed to be the first vector dotted with the sum of the second and th...
(1x2+2-4)
misty crest
do you think 0 isn’t a scalar?
tender wind
I mean
misty crest
i mentioned that because if you take the dot product of the first two then you get a scalar which can’t be added to a vector
tender wind
i got mixed up with the null vector then
misty crest
0 is not 0
devout snowBOT
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warped moth
why does an object thrown straight up (assume no air resistance) always have the same magnitude of velocity when it comes back to the starting point
devout snowBOT
why does an object thrown straight up (assume no air resistance) always have the...
vast drift
why does an object thrown straight up (assume no air resistance) always have the...
if there is no air resistance then the only force acting upon is gravity
so the acceleration upwards will be -g
warped moth
i know
vast drift
downwarsd will be positive g
warped moth
-9.8 m/s^2
vast drift
if you are experiencing the same amount of acceleration over the same period of time
warped moth
but u have a starting velocity when thrown
and dont have a starting velocity at the peak of the motion
vast drift
the magnitude of the acceleration experienced is the same
you are experiencing it over the same period of time
hence the change in velocity will be the same
the only difference is direction
eager nova
Do you think if you throw harder the object won’t be higher?
warped moth
it will be
warped moth
hence the change in velocity will be the same
true but lets say u throw the ball at 10 m/s
oh
vast drift
for the sake of convenience lets just make your initial velocity 9.8
warped moth
i get it
vast drift
ok
warped moth
thanks
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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.
atomic dome
Solving for x?
How much about it do you know
Okay hold on
\begin{align}
\frac{1}{8}[5(x-10)]-10=10\\
\frac{1}{8}[5(x-10)]=20\\
[5(x-10)]=160\\
x-10=32\\
x=42
\end{align}
What is step 1?
Then what
Try to think of it as multiplying both sides by 8
So that the left side becomes 8/8
You have two options
You can divide by 5, or distribute the 5 into the x-10
I would choose the first option
But whichever makes most sense to you
Yes
What’s left?
woven radishBOT
mari
atomic dome
See that wasn’t so hard, you did it all yourself
Stair?
Sure
What about that
Okay
How is that related
I’m not following
I know what you mean by dark and white points
But not where this is coming from
For what
For what problem
Do you need anymore help
You have to be more specific and show the problems if you need help
I won’t be able to help
I’m sure someone here knows French and can help
still zephyr
There are not classes $A$ and $B$ such that $A \in B \in A$
devout snowBOT
There are not classes $A$ and $B$ such that $A \in B \in A$
woven radishBOT
Halex
devout snowBOT
@still zephyr Has your question been resolved?
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@still zephyr Has your question been resolved?
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@still zephyr Has your question been resolved?
exotic vortex
I need help on 2 problems. The first one is this: a jet leaves the Charlotte North Carolina airport traveling at an average rate of 564 km an hour. Another jet leaves this airport 1/2 hour later traveling at 744 km in the same direction using an equation to find how long the second jet will take to overtake the first.
devout snowBOT
I need help on 2 problems. The first one is this: a jet leaves the Charlotte Nor...
exotic vortex
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faint gorge
yo
faint gorge
Someone wamted to discuss things
long pasture
oh.
faint gorge
My proof
long pasture
math related?
faint gorge
First inequality doesnt hold
But here
I have another proof of this guess i will redo this because some people act they never seen math
(I just woke up)
faint gorge
Then I will do it properly just for your sake
I will also prove that sine is a trigonometric function
And that addition is closed between trigonometric functions and polynomials
supple knot
bacc is mad yo
faint gorge
Before that I will prove that a real number is real
long pasture
i think the point here is that we can't proof sin(x)≤x²+x using only graph?
faint gorge
vocal tartan
Actually your proof works
faint gorge
i think the point here is that we can't proof sin(x)≤x²+x using only graph?
I did this too but still not satisfying
long pasture
ah
faint gorge
Maybe I should do it with absolutr values
vocal tartan
just need to deal with the issue of the sign of sin(x) - x
since you've shown sin(x) - x <= x^2 but a priori maybe |sin(x) - x| > x^2
though I will still point out: any proof that uses the fact that sin' = cos is pointless
since what you're trying to prove is sin'(0) = cos(0), if you expand definitions.
so you may as well just use it directly
long pasture
though I will still point out: any proof that uses the fact that sin' = cos is p...
i understand the confusion... I remember having these type of error when i was doing elemtery analysis
faint gorge
though I will still point out: any proof that uses the fact that sin' = cos is p...
So you are saying it's pointless in a sense of doing an epsilon delta proof
vocal tartan
It's pointless in the sense that you're using a general result to prove a specific case without just applying the general result.
And if your goal is to practice epsilon-delta proofs this isn't a particularly good example, considering how simple your delta is.
vocal tartan
No, I'm just saying that the epsilon-delta part of the proof is not interesting, so it doesn't make for good epsilon-delta practice
supple knot
This conversation sounds familiar
faint gorge
This conversation sounds familiar
because you still didn't prove your hypothesis
supple knot
vocal tartan
yes it's a continuation of that convo
faint gorge
it's an analytical continuation, cause i was left with jump discontinuities
From what I have understood so far is that epsilon delta proofs should be elementary and thus should not make really use of functional properties in the first palce
but then an approximation with the taylor expansion would be also uninteresting in that sense
cause this implies also use of the derivative
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strong musk
Its physics not math tho
devout snowBOT
Its physics not math tho
strong musk
Someone explain this
If the image sends
Holy
FYI this is a practise aptitude test
This is not homework. I am not in school
restive river
have you ever used a water hose?
atleast played with it ?
@strong musk
you could think of it that way
or use the equation
A1v1=A2v2
here A represent the area of the hose and v the velovity of water
but since its an aptitude test,they are probably expecting you to do it by the first method
devout snowBOT
@strong musk Has your question been resolved?
strong musk
atleast played with it ?
Yeah so i thought it’d be increased pressure and velocity
restive river
correct!
strong musk
That was wrong on the test tho
restive river
Yeah so i thought it’d be increased pressure and velocity
you mean this answer is wrong ?
strong musk
It doesent give me an answer to why
Yeah
I put that as the answer
It said it was wrong
restive river
hmm thats a problem
lets read the question again
iam sure the answer is right
lets wait till someone else also verifies it
how did you come to the conclusion that the pressure also increases ?
@
@strong musk
strong musk
how did you come to the conclusion that the pressure also increases ?
Just used common sense or at least what I thought was common sense
Thought about using a pressure washer
visual hazel
how did you come to the conclusion that the pressure also increases ?
P = F/A
restive river
Yeah so i thought it’d be increased pressure and velocity
can you verify
restive river
well the answer is correct
strong musk
1: Low velocity, high pressure, 2: high velocity low pressure
restive river
idk why test is showing its wrong
strong musk
The answer is thus
I’m confused
This is a pilot aptitude test if that helps anymore idk
restive river
answer key is wrong
:))
if you dont want common sense answers
here are some formulae
A1v1=A2v2
P=1/2 rho v^2(rho is density)
visual hazel
not sure if we can use this,we dont know the force
well we're not calculating anything
its just to show that area and pressure are inversely proportional
strong musk
if you dont want common sense answers
I just want to know how to understand it
I thought the answer was high pressure and high velocity
Why is it saying that’s wrong tho
restive river
cause the key is wrong
devout snowBOT
strong musk
cause the key is wrong
.reopen
devout snowBOT
✅
strong musk
cause the key is wrong
Wdym
I searched answer on Google it says answer is So the velocity increases and the pressure decreases
Something to do with Bernoulli principle
Idk
restive river
gtg
visual hazel
<@281970066764070912>
oh damn i havent studied bernoulli's principle in so long i forgot about it
bernoulli's principle basically states that the higher velocity of a fluid is, the lower the pressure of it
thus it should be high velocity low pressure
rigid pewter
a ball is thrown up in the air. 4m in the air, it's lost half its velocity. what's its maximum height?
not rlly sure how to write equations for this
tbh i forgor what i tried exactly, it was a test
this is solvable with just kinematics (we haven't covered conservation of energy yet but i tried that too)
devout snowBOT
> a ball is thrown up in the air. 4m in the air, it's lost half its velocity. wh...
cold bone
> a ball is thrown up in the air. 4m in the air, it's lost half its velocity. wh...
HINT: use v^2 - u^2 = 2ax
thin basin
yeah
rigid pewter
u?
cold bone
v is final velocity
u is initial velocity
a is acceleration due to gravity
x is displacement
and 2 is 2
rigid pewter
HINT: use v^2 - u^2 = 2ax
oh zamn i actually got it right💀
i think i worked my way to this formula from 1/2at^2+vt but i felt like i was schizomathing
thx
.close
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Available help channel!
soft umbra
int main() {
int num;
scanf("%d", &num);
int number=num;
int i=0;
int a=0;
int b=0;
int count=0;
int matrix [num][num];
while(i<=num-1) {
matrix[a][b]=count;
count++;
a++;
}
i++;
while(i<=2*num-1) {
{
while(b<num-1&&i<=2*num-1) {
matrix[a][b]=count;
count++;
b++;
}
i++;
while(a>number-num&&i<=2*num-1) {
matrix[a][b]=count;
count++;
a--;
}
i++;
num--;
while(b>number-num&&i<=2*num-1) {
matrix[a][b]=count;
count++;
b--;
}
i++;
while(a<=num-1&&i<=2*num-1) {
matrix[a][b]=count;
count++;
a++;
}
i++;
num--;
}
}
printf("%d", matrix[2][1]);
}
soft umbra
I feel like creating a matrix like what I shown in the ss
The above is the input and the below is the output
I have done most of it, but it turns out there are some mistakes in it.
After looking up in ChatGPT, I couldn’t get where I have mistake
The matrix looks like a cyclone instead of a snake
thin basin
int main() {
int num;
scanf("%d", &num);
int number=num;
int i=0...
what lang is this?
soft umbra
I need some help to figure out the mistake, appreciate it
thin basin
c?
soft umbra
yes
thin basin
i dont know c 
pure flower
The matrix looks like a cyclone instead of a snake
hm?
rigid pewter
\`\`\`
format code blocks w/ 3 ticks
\`\`\`
I don't know c either but I can read it and see I guess
soft umbra
ty
rigid pewter
those didnt escape but u get the idea
soft umbra
those didnt escape but u get the idea
I get the idea, but there is a mistake
thin basin
is the first while loop
sullen island
we're just talking about the formatting of your code on discord mate, it's barely readable
rigid pewter
anyways spiral matrix? is it always square?
thin basin
the condition is i <= num - 1 but i is never changed
pure flower
lemme just
int main() {
int num;
scanf("%d", &num);
int number=num;
int i=0;
int a=0;
int b=0;
int count=0;
int matrix [num][num];
while(i<=num-1) {
matrix[a][b]=count;
count++;
a++;
}
i++;
while(i<=2num-1) {
{
while(b<num-1&&i<=2num-1) {
matrix[a][b]=count;
count++;
b++;
}
i++;
while(a>number-num&&i<=2num-1) {
matrix[a][b]=count;
count++;
a--;
}
i++;
num--;
while(b>number-num&&i<=2num-1) {
matrix[a][b]=count;
count++;
b--;
}
i++;
while(a<=num-1&&i<=2*num-1) {
matrix[a][b]=count;
count++;
a++;
}
i++;
num--;
}
}
printf("%d", matrix[2][1]);
}
Much better.
soft umbra
the condition is i <= num - 1 but i is never changed
it does
thin basin
```c
int main() {
int num;
scanf("%d", &num);
int number=num;
in...
thnx
soft umbra
tysm
thin basin
i ++ is outside the loop
soft umbra
I intends to put it outside
cinder nova
int main() {
int num;
scanf("%d", &num);
int number=num;
int i=0;
int a=0;
int b=0;
int count=0;
int matrix [num][num];
while(i<=num-1) {
matrix[a][b]=count;
count++;
a++;
}
i++;
while(i<=2*num-1) {
{
while(b<num-1&&i<=2*num-1) {
matrix[a][b]=count;
count++;
b++;
}
i++;
while(a>number-num&&i<=2*num-1) {
matrix[a][b]=count;
count++;
a--;
}
i++;
num--;
while(b>number-num&&i<=2*num-1) {
matrix[a][b]=count;
count++;
b--;
}
i++;
while(a<=num-1&&i<=2*num-1) {
matrix[a][b]=count;
count++;
a++;
}
i++;
num--;
}
}
printf("%d", matrix[2][1]);
}```the one before misses the multiplications
thin basin
omg do you really have to write *so* much code for something in c lmao
for any language lol
pure flower
for any language lol
I can prolly do that in python in like half the lines max lmao
then again most of yours is just formatting
soft umbra
the one before misses the multiplications
got eaten by discord, lemme send the file here
pure flower
i would love to see
lemme try then maybe lmao.
pure flower
got eaten by discord, lemme send the file here
you can always use a pastemyst ig
cinder nova
got eaten by discord, lemme send the file here
no need, if I copy from my phone it contains those
soft umbra
soft umbra
<@982507190566932510> how do you break the first while loop?
which one?
thin basin
npp
final dirge
how do i get help
devout snowBOT
how do i get help
final dirge
oh I thought i have to do the “/l
“/“
The profit for family business is X^3 + 8X^2 +4X - 14 and there are x-1 members to share these profit, how much will be the profit of each?
I have the answer but idk how to get it
rigid pewter
sounds like they're asking you to do polynomial division
final dirge
Yess
devout snowBOT
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devout snowBOT
@final dirge Has your question been resolved?
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@final dirge Has your question been resolved?
gloomy sparrow
Om gonna jump off
devout snowBOT
Om gonna jump off
gloomy sparrow
Where tf did + x came from
Please is 12am here and my will to live is slipping away
acoustic leaf
x(y+1) = xy + x
magic sun
!done
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If you are done with this channel, please mark your problem as solved by typing .close
@gloomy sparrow Has your question been resolved?
fast grail
How does the formula of equalibrum work
devout snowBOT
How does the formula of equalibrum work
supple knot
How does the formula of equalibrum work
do you have an actual problem with more context
cold bone
equilibrium of what?
cold bone
what does k supposed to be in 1 k/ft and 6k?
fast grail
idk does not matter what it is though
77^2 how would you solve this?
I would do 720 * 9 + 1 * 10 + 6 * 16 = b * 18
fast grail
do you have an actual problem with more context
give me five minutes of your time bro 🙏
<@&286206848099549185>
shell stream
yes sir
fast grail
Do you know how to solve this?
shell stream
what am i solving for
fast grail
the force on A and B
fast grail
Yeah, but tbh I don't know if that matters
fast grail
Yeah
shell stream
so 1kgf is the torque being applied at different points that are 1 feet away?
shell stream
what is 6k?
fast grail
some downard force on the beam
shell stream
alright
fast grail
I also don't understand the 1 * 10 * ( 8 +10/2)
shell stream
so thats the solution?
fast grail
Yeah
shell stream
if the length of the stick about the fulcrum is 10 inches, how come torque is being applied at different that are one feet away from one another?
weirf
weird
why do you play in these strange units
fast grail
imma be so fr, I don't think the units matter at all
how are you getting ten inches ?
shell stream
sorry 9 inches
fast grail
Bro I shoulda gone to class lol
shell stream
the information is really vague
fast grail
The weight of the beam is in the center so it's 9' from A I think
shell stream
fulcrum for a lever is the centre of gravity
fast grail
Dude I lowkey think you know to much to solve this problem
fast grail
Nah
shell stream
alright
devout snowBOT
@fast grail Has your question been resolved?
devout snowBOT
@fast grail Has your question been resolved?
restive river
Hey!
restive river
Looking to get into calculus on Khan Academy from algebra 2/trig ASAP albeit my basis in algebra is a bit weak now, would you recommend I start with the "Get Ready for Precalculus" course and then move onto AP Calculus AB/BC?
supple knot
Looking to get into calculus on Khan Academy from algebra 2/trig ASAP albeit my ...
help channels are for math problems. try #serious-discussion or #discussion for course advice.