Thank you guys
#help-36
maiden raven
final saddleBOT
Available help channel!
queen fossil
Hello, I'm trying to perform LU decomposition and i've tried the same matrix twice and yet I can't multiply them to get the original matrix back, you can see the solutions
final saddleBOT
Hello, I'm trying to perform LU decomposition and i've tried the same matrix twi...
rare girder
Hello, I'm trying to perform LU decomposition and i've tried the same matrix twi...
without even reading it myself yet, it's very likely you just have a random arithmetic error
after reading it, however, I think this is an error
by what you've done to the id matrix, it seems like you're saying the opposite of adding 3 copies of R3 to R2 is subtracting 3 copies of R1 from R2
but R1 has nothing to do with R3; shouldn't the left matrix read (1 0 0; 0 1 -3; 0 0 1) after this operation?
in particular, [\begin{bmatrix}1&0&0\-3&1&0\0&0&1\end{bmatrix}\begin{bmatrix}8&-6&2\0&-5&5\2&-4&3\end{bmatrix}=\begin{bmatrix}8&-6&2\-24&13&-1\2&-4&3\end{bmatrix}\neq\begin{bmatrix}8&-6&2\-6&7&-4\2&-4&3\end{bmatrix}=\begin{bmatrix}1&0&0\0&1&-3\0&0&1\end{bmatrix}\begin{bmatrix}8&-6&2\0&-5&5\2&-4&3\end{bmatrix}]
soft zealotBOT
Flip
rare girder
Hello, I'm trying to perform LU decomposition and i've tried the same matrix twi...
hope this helps
final saddleBOT
@queen fossil Has your question been resolved?
late rose
in particular, \[\begin{bmatrix}1&0&0\\-3&1&0\\0&0&1\end{bmatrix}\begin{bmatrix}...
holy latexer
rare girder
holy latexer
what's texma, you may ask
faint fern
What's texma?
rare girder
texma balls
queen fossil
by what you've done to the id matrix, it seems like you're saying the opposite o...
i was told that that was the point of lu decomposition, we're supposed to get the negative of the factors used and plug into id matrix. do you have a solution for this though, it would really help
final saddleBOT
i was told that that was the point of lu decomposition, we're supposed to get th...
desert mantle
yes you are. but you have to subtract the correct rows
you have to subtract a multiple of row 1
you did row 3
that messes stuff up
ornate tree
. @ebon plume
ebon plume
yes sirr
ornate tree
Alright, now you can post your question here
ebon plume
and what happens
ornate tree
the channel where you posted was occupied by someone
ebon plume
ohk
SO HOW CAN I MASTER STRAIGHT LINE IN 7 HOURS
SHOULD I GO 1 HOUR THEORY AND THEN ALL QUESTIONS OR JUST THEORY
ornate tree
I'm not sure about your question, are you referring to questions regarding linear function?
ebon plume
No the chapter straight lines
ornate tree
I see
ebon plume
wait your chinees
craggy plank
SO HOW CAN I MASTER STRAIGHT LINE IN 7 HOURS
ebon plume
ohh you must not know then
ornate tree
wdym
ornate tree
where are you from
uhh, let's focus on your problem
ebon plume
alr my bad bro
ivory bear
Im a JEE asprint
hi there
ornate tree
Do you have any specific questions about "lines"?
ivory bear
SHOULD I GO 1 HOUR THEORY AND THEN ALL QUESTIONS OR JUST THEORY
questions will benefit more tbh
ebon plume
Do you have any specific questions about "lines"?
not particularly sorry
ivory bear
theory wont give much insight
warm python
theory wont give much insight
ebon plume
questions will benefit more tbh
hmm and where should i do the theory from
warm python
Tbf, true for JEE
ebon plume
Tbf, true for JEE
oh alr
ivory bear
hmm and where should i do the theory from
maybe 1shot using pw or smth else
warm python
Very few theorms are insightful
ivory bear
Tbf, true for JEE
???
ebon plume
do they cover all topics
ivory bear
Very few theorms are insightful
kind of but not. problem solving skills are more imprtant- likr the approach to a problem
ebon plume
alr got it
ornate tree
spring haven
this conversation is so cooked
ornate tree
Can I close this?
ebon plume
this conversation is so cooked
why
ebon plume
Can I close this?
wdym close ?
ivory bear
end it
ornate tree
wdym close ?
Shut down the channel
ebon plume
just pick up a book and start reading
that works too
ebon plume
Shut down the channel
so where can we discuss then
ornate tree
@ebon plume We'd appreciate if you're willing to provide specificed questions either from your textbook or homework.
This way we can help you better
ornate tree
Roger that
craggy plank
.solved
final saddleBOT
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radiant carbon
Can I ask a question about databases here
final saddleBOT
Can I ask a question about databases here
ornate tree
yes ask plz
radiant carbon
It's not really maths tho
In this example, there is a repeating group of attributes relating to certificates. For example, Abdel Patel has gained two certificates. The group of attributes that repeat are: CourseCode, Description, AssessmentDate, Fee, Instructor (now split into InstructorFirstName and InstructorLastName), and Email (now renamed to InstructorEmail).
how are those attributes repeating?
for each record, there is only one of each of those attributes
gentle barn
Say 4 and 5, they both have the same attributes for SO0112.
final saddleBOT
final saddleBOT
✅
radiant carbon
Say 4 and 5, they both have the same attributes for SO0112.
how is this in NF1 form then
it also has repeating attributes
but apparently its good
gentle barn
What do you mean by "NF1 form"?
gentle barn
Does each record have a primary key?
radiant carbon
yes
gentle barn
Which?
radiant carbon
MemberId?
gentle barn
Is the data atomic?
radiant carbon
yes
radiant carbon
yes
but i just realised it doesnt matter
when you have your first table, you check if there are repeating attributes and split them off into a new table
you don't also check if the new table contains repeats (like i just tried to do)
.close
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deft scarab
need help with moment of a force problem
final saddleBOT
need help with moment of a force problem
@deft scarab Has your question been resolved?
tardy hamlet
Hello just want to make sure I didn’t get anything wrong before I go too far
soft zealotBOT
Sending query to Wolfram Alpha, please wait. 
Sending query to Wolfram Alpha, please wait.
tardy hamlet
Huh?
loud sundial
bot broke
the x coordinate of your mean data point is a little off
are you expected to eyeball the line of best fit?
as in eyeball two points that are on it?
or do it properly with least squares
tardy hamlet
Yes
loud sundial
eyeball or least squares
tardy hamlet
I think he said eyeball it
loud sundial
scatterplot seems fine
tardy hamlet
Is the e mean point wrong??
Gang I can’t become a professional engineer of robots 🥀
loud sundial
Is the e mean point wrong??
the x coordinate of your mean data point is a little off
should be this
which rounds to 2.15
loud sundial
with your points, the slope you calculated is fine
then you changed the denominator from 54 to 53?
loud sundial
idk how strict the eyeballing is though because your slope is off by around 1
loud sundial
yes
loud sundial
are you using new points
tardy hamlet
Yes
loud sundial
what points are you using
tardy hamlet
(2.15,81.02) and (0,100)
loud sundial
did you round your slope to the nearest tenth or something
tardy hamlet
Yes
loud sundial
then yes it rounds to -8.8
tardy hamlet
Was I not supposed to
loud sundial
Was I not supposed to
I mean
I wouldn't
but I also have no context for what's going on in your class
tardy hamlet
Will it still get similar answers
tardy hamlet
Okay what the heck
tardy hamlet
😀 let me try again
loud sundial
you could just not round it
like earlier you left it as a fraction
you can do that
tardy hamlet
I keep that like that???
loud sundial
why not?
loud sundial
you rounded this to -8.8
so you lose that -0.02790698... of accuracy
if you want to be really picky, you also lose accuracy when rounding 103/48 to 2.15
up to you when you want to draw the line of the lost accuracy being insignificant
tardy hamlet
So what I have so far is alright 👍
loud sundial
sure
tardy hamlet
Dang algebra is tricky
thin cloud
Given a 4-digit square number, knowing that if we add the thousands digit by 3 and subtract the units digit by 3, we get a new square number.
final saddleBOT
Given a 4-digit square number, knowing that if we add the thousands digit by 3 a...
thin cloud
Given a 4-digit square number, knowing that if we add the thousands digit by 3 a...
Find that number
vast zephyr
-# I'm just validating my solution.
fathom meteor
Given a 4-digit square number, knowing that if we add the thousands digit by 3 a...
a^2+3000-3=b^2 -> a^2+2997=b^2 for integer solutions a and b where 1000 <||= a^2 <||= 9999 for algebraic representation
vast zephyr
Given a 4-digit square number, knowing that if we add the thousands digit by 3 a...
Let's call the 4-digit square number N and the new square number M, can you formulate the equation that is described by:
Given N, knowing that if we add the thousands digit by 3 and subtract the units digit by 3, we get M
?
fast smelt
you have a square number 1000a + 100b + 10c + d, and you're told 1000(a+3) + 100b + 10c + (d-3) is also square?
Or, equivalently t^2 = N and s^2 = N + 2997 are both square numbers. Find N.
final saddleBOT
@thin cloud Has your question been resolved?
regal hamlet
Do somebody know where can I find a demonstration that Hamilton's quaternions form a non-commutative ring?
final saddleBOT
Do somebody know where can I find a demonstration that Hamilton's quaternions fo...
deep condor
algebraically, all you need to do is to find two quaternions that do not commute.
by definition, i, j, and k are imaginary units, so their squares are -1, and i think it's definiton that says ijk = -1.
you could use those facts to deduce that ij is not equal to ji, and there's your example
or were you looking for something possibly visual?
final saddleBOT
@regal hamlet Has your question been resolved?
regal hamlet
or were you looking for something possibly visual?
I just want to see a formal proof
junior token
I just want to see a formal proof
that depends on what your definition of the quaternions is
to prove it formally, all you have to do is exhibit a counterexample to commutativity. As mentioned above, i and j will work
regal hamlet
Yup, ij = k but ji = -k; iirc
deep condor
to prove it's a ring, you can take the a + bi + cj + dk representation, and run through the ring axioms. i tried to look for a write-up of this, but it seems every single professor on earth has left this as an exercise to the student 💀
you can also show that every quaternion has an inverse and conclude that H is a division ring
i am currently trying to think of more interesting proofs, though
regal hamlet
to prove it's a ring, you can take the a + bi + cj + dk representation, and run ...
Hahaha yeah, it doesn't seem too difficult, but I wanted to take a look at it because I'm just starting
deep condor
just starting with rings or with studying quaternions? if you don't mind my asking
regal hamlet
both
deep condor
i see! then it would honestly be a good exercise to just prove every single ring axiom for the quaternions, if you wanted to show it's a ring. here are the explicit definitions for + and * in that case
to prove noncommutativity formally, you just need to show the existence of at least one pair of numbers where ab =/= ba
i unfortunately cannot think of a more concise proof - all the "big" isomorphisms of H, like R^4, really only show that R is a ring, and not much about H
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
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sand patrol
can anyone translate this....
final saddleBOT
can anyone translate this....
sand patrol
i can read the numbers but not the words
abstract bramble
we replace e^c_1 with c where c > 0 then (x^2 + 1)^2 * |y| = c
fuck is that doctor script after
valid carbon
'since(?) we(?) allow y'
sand patrol
everything i check my homework this happens so i can only read the numbers and not the text so idk how he got them
valid carbon
'to be positive or negative'
sand patrol
ohh okay now this makes more sense lol
valid carbon
humans are the best image recognition
actually im curious if gemini can do this xD
prolly can
serene tartan
can anyone translate this....
who the hell wrote this 😭
sand patrol
every homework question is like this like how do i prepare for my test </3
valid carbon
woah that is a pretty good translation xD
its perfect
proper dagger
oh oops
valid carbon
hanako ai beats you
time to be concerned about your job prospects
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Available help channel!
shy grove
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shy grove
i dont know how to continue from the yellow part
pliant shore
in the markscheme they say to divide the yellow part by t - 1
shy grove
i dont understand why we have to do that
pliant shore
by factoring out a linear polynomial from a 4th degree polynomial
you get a degree 4 - 1 = 3 polynomial
shy grove
OHHH
pliant shore
yeah and it turns out tan x = 1 is impossible in the given domain
shy grove
But how do we know that t-1 is a factor of the 4th degree polynomial
pliant shore
But how do we know that t-1 is a factor of the 4th degree polynomial
guess and check
so you sub in t = 1 and you get 0
shy grove
ohhhh i seee trial and error
pliant shore
by the factor theorem, t - 1 is a factor
pliant shore
no worries!
shy grove
.close
jagged flare
whats the point of generalizing and turning this into a graph theory
jagged flare
it seems much easier to just bound it to <=4 (doesent involve graph theory nor generalizatons) then find a path that works
fast smelt
it seems much easier to just bound it to <=4 (doesent involve graph theory nor g...
why <=4?
why not <=9?
jagged flare
what
why <=9?
<=4 FGC cause each trip takes 9 paths, whereas the total number of paths is 9c2=36, so 36/9=4 maximum FGC
fast smelt
sounds like you're using graph theory
jagged flare
not disjoint hamiltonian bs
final saddleBOT
@jagged flare Has your question been resolved?
final saddleBOT
@jagged flare Has your question been resolved?
mellow mortar
can someone just help this person 😭
Who has summoned me...
plucky rover
not disjoint hamiltonian bs
I mean you are still using the same intuition lol
mellow mortar
Make it quick, don't waste my time.
latent dragon
Make it quick, don't waste my time.
plucky rover
But yea they overcomplicated it
plucky rover
it seems much easier to just bound it to <=4 (doesent involve graph theory nor g...
I think they just wanted to give a generalization and went with it. Your method works for the specific case
cyan kayak
can someone just help this person 😭
Please stop doing this
mellow mortar
doing what/
*?
cyan kayak
Posting irrelevant things in help threads. If you don't know, keep the channel clear for people who do
plucky rover
Let the user decide if they want to tag helpers or not
latent dragon
alrighty then
jagged flare
why are they going to graph theory using disjoint hamilton paths, and why are they generalizing it? as it seems much simpler to just bound the <=4 and find a path that fulfills it
mellow mortar
why are they going to graph theory using disjoint hamilton paths, and why are th...
that's the question?
jagged flare
yeah
plucky rover
why are they going to graph theory using disjoint hamilton paths, and why are th...
Like I said, they probably just wanted to give and prove a generalization
What you said works perfectly fine
mellow mortar
why are they going to graph theory using disjoint hamilton paths, and why are th...
They use graph theory because it gives a stronger framework. Proving only for ≤4 is a one-time fix. Generalising with Hamilton paths handles all cases at once. Harder up front, but more powerful - solve the big problem, and the small ones fall automatically.
jagged flare
Like I said, they probably just wanted to give and prove a generalization
oh oops i didnt see that one
jagged flare
They use graph theory because it gives a stronger framework. Proving only for ≤4...
hmm i see
thank you!
jagged flare
ngl it looks ai generated
mellow mortar
ngl it looks ai generated
What?
mellow mortar
Dang, everyone tells me that I sound AI.
jagged flare
.solved anyways, thank you!
final saddleBOT
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Available help channel!
main sparrow
The growth of a virus is determined by the function p(t) , where is time in days. On what day is the growth rate of the virus at its maximum?
Zero idea
final saddleBOT
The growth of a virus is determined by the function p(t) , where is time in days...
thin cloud
P(t)' is growth rate
ornate tree
If you're trying to find the local maxima of a function, first of all you should come up with differentiation
main sparrow
If you're trying to find the local maxima of a function, first of all you should...
How do I even differentiate it
ornate tree
How do I even differentiate it
Have you learnt about diff?
main sparrow
Have you learnt about diff?
Yes I did
ornate tree
Alright, what formulas have you learnt?
main sparrow
This is 1/e^(x) wth
thin cloud
The growth of a virus is determined by the function p(t) , where is time in days...
could you send the original
main sparrow
could you send the original
thin cloud
I think they mean p(t) is the number of viruss in day t
If p(t) is the growth rate
then the maximum is just when the dom minimum
and the dom is a monotonic function
final saddleBOT
@main sparrow Has your question been resolved?
main sparrow
I think they mean p(t) is the number of viruss in day t
yes
they meant that
growth rate and speed of growth ratge
thin cloud
growth rate and speed of growth ratge
take differential of function first
vernal niche
how to start to think about this problem
final saddleBOT
how to start to think about this problem
plucky rover
Trial and error on some level I imagine
ornate tree
Is this a coding problem?
plucky rover
Doesn't look like it
ornate tree
hmm
loud sundial
Scaling also works
plucky rover
Right yeah it does
mental basin
Well we have a^2 + b^2 = c^2 and a + b + c = 1000
So we can solve this to get a line
loud sundial
Note that this takes advantage of the fact the triple is unique
vernal niche
It is like mix of both from https://projecteuler.net/problem=9
mental basin
We can turn this into a line
And then we just need to find an integer solution on the line
Apparently there is only 1
plucky rover
,w a² + b² = c² and a + b + c = 1000, all integers
soft zealotBOT
Requested by xavier_dragon
plucky rover
Fair enough
loud sundial
,w a² + b² = c² and a + b + c = 1000, all integers
Should be ||25 * (8,15,17)||
Whatever that is
plucky rover
Ah
vernal niche
Like I said scaling kills lol
what is scaling
loud sundial
There’s a standard set of triples you should know
Multiply everything it that triple by some integer to get a new triple
worthy wren
scaling pythagorean triplets preserves that property of them being triplets
loud sundial
Ex. (3,4,5) is a triple. Multiplying by 2 gives (6,8,10) also being a triple.
vernal niche
are the rest of triplets always multiples of (3, 4, 5) ?
loud sundial
No
||(5,12,13)||is also triple for example
Actually maybe the coding is useful for the multiplication
Random side thought
Not particularly relevant
vernal niche
oh okay hmm
loud sundial
Unless they want you to use the parameterisation to brute force more efficiently
plucky rover
are the rest of triplets always multiples of (3, 4, 5) ?
Take an odd number
Square it
Split it in half and round up and down
You get a triplet
loud sundial
(Note this is not exhaustive. Ex. ||(20,21,29)||.)
plucky rover
(yes I should have mentioned that.)
loud sundial
I mean it wasn’t directly relevant so 
I have a nasty habit sometimes where I give a bare minimum answer that technically answers but omit a lot of other stuff that has educational value
Actually does this sound rude
plucky rover
I have a nasty habit sometimes where I give a bare minimum answer that technical...
I have the opposite problem most of the time lol
Also no it doesn't dw
Not to me at leas
time to disappear
vernal niche
is it possible from solving?
vernal niche
.close
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radiant carbon
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radiant carbon
where did i go wrong
i differentiated the general quadratic function
to get 2ax + b
it's at a max at x = 90
so 2a(90) + b = 0
so 180a + b = 0
in ax^2 + bx + c, c = 3 in this case as we can see and read
27 = a(120)^2 + 120b + 3
27 = 14400a + 120b + 3
7200a = 24, because we can sub in b = -180a
a = 24/7200
b = -180a, so b = -3/5
so the equation should be H = 24x^2/7200 - 3x/5 + 3
but it's not
when I plug in 120, it doesn't output 27
if you could explain why its wrong it would be appreciated
final tangle
how did you get
7200a = 24
you skipped some steps above
can you show the full work
after
27 = 14400a + 120b + 3
radiant carbon
27 = 14400a + 120(-180a) + 3
27 = 14400a - 21600a + 3
-7200a = -24
7200a = 24
i see it now, it should be 7200a = -24 right?
final tangle
yes
final tangle
don't
final saddleBOT
radiant carbon
.reopen
final saddleBOT
✅
radiant carbon
i have one more question
craggy plank
Alright
radiant carbon
im not sure abt this
i put doesn't account for side to side ball movement
but that's prolly not right
craggy plank
gentle barn
Are you familiar with potential energy?
radiant carbon
Are you familiar with potential energy?
nah
gentle barn
Then can you imagine yourself throwing a ball that follows the trajectory?
radiant carbon
Then can you imagine yourself throwing a ball that follows the trajectory?
yeah
sure
gentle barn
Can you precisely throw a trajectory, that has no angle factor?
radiant carbon
Can you precisely throw a trajectory, that has no angle factor?
wdym? like if i could throw the same trajectory without calculating what angle to throw at first?
gentle barn
Like it wouldn't go a bit to the left or right.
gentle barn
That's a factor. The trajectory is ideal.
radiant carbon
because the angle would have an impact on distance that the ball lands at?
gentle barn
Yes. Diagonal is longer than the side.
radiant carbon
.close
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radiant carbon
final saddleBOT
final saddleBOT
@radiant carbon Has your question been resolved?
loud sundial
b. It's given that $$P(X=4)=P(X=2)=0.35$$
Suppose that we want to roll $r$ $4$'s. Then, there are $(60-r)$ of everything else. Using the binomial probability formula yields that this has a probability of $$\binom{60}{r} 0.35^r 0.65^{60-r}.$$ Now, consider what the possible values of $r$ are.
soft zealotBOT
Civil Service Pigeon
loud sundial
You should end up with some kind of ||summation||.
As a check, the sum of the digits to the answer to part b is 22.
loud sundial
c. Honestly, I'd just do casework on each value of $X$. For example, if $X=1$, then $Y=12$ and $Y-X=11$, which is not at most $4$. So, we know $X=1$ is not possible.
soft zealotBOT
Civil Service Pigeon
loud sundial
As a check, when you express your answer to part c as a decimal, the sum of the digits of the answer is 13.
final saddleBOT
@radiant carbon Has your question been resolved?
radiant carbon
**Civil Service Pigeon**
yes it was this
but
there was another way of writing it
B(...) = ...
loud sundial
B(...) = ...
$B(n,p)$ where $n$ is the number of trials and $p$ is the probability of success in each trial?
soft zealotBOT
Civil Service Pigeon
radiant carbon
$B(n,p)$ where $n$ is the number of trials and $p$ is the probability of success...
yes
anyways
loud sundial
so r would be 30?
There are multiple values of $r$ that you have to consider here.
soft zealotBOT
Civil Service Pigeon
radiant carbon
X ~ B(60, 0.35)
P(X > 30) = 1 - P(X <= 30)
loud sundial
X ~ B(60, 0.35)
P(X > 30) = 1 - P(X <= 30)
So what are the values of $r$ you have to consider?
soft zealotBOT
Civil Service Pigeon
loud sundial
aka how do you compute $P(X \leq 30)$?
soft zealotBOT
Civil Service Pigeon
radiant carbon
aka how do you compute $P(X \leq 30)$?
P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 30)
loud sundial
P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 30)
good
btw imma go in about 3 minutes so you've been warned
radiant carbon
btw imma go in about 3 minutes so you've been warned
thats okay im good now
.close
old quarry
final saddleBOT
worldly mesa
!statusd
final saddleBOT
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
worldly mesa
First identify the pattern
old quarry
(-1)^r/(3r-2)
worldly mesa
yes
now give me a sec
ok. first write is in sigma notatation
$F(x) = - \sum_{n=0}^{\infty} \frac{x^{3n+1}}{3n+1}$
soft zealotBOT
ExpertEsquieESQUIE
worldly mesa
so when we plug in -1 we get our series
Now my idea is to differentiate the power series which will remove the 1/(3n+1)
and we get a geomtric series and a close form for F'(x)
and then integrating and getting a closed form for F(x)
old quarry
oh ok
thanks but im a bit too sleepy rn to properly understand what u said..sorry
ill open this tmmr
.close
final saddleBOT
worldly mesa
one thing
old quarry
yeah
worldly mesa
you need to do the steps I did here carefully
especially the differentation
just to prove it allowed
old quarry
oh
worldly mesa
or at least understand why its allowed
worldly mesa
in the morning
final saddleBOT
Available help channel!
sonic hazel
may someone please help me with this
final saddleBOT
may someone please help me with this
forest ember
may someone please help me with this
Do you recognise f(x)?
final saddleBOT
@sonic hazel Has your question been resolved?
flat nova
im kinda a beginner
pls try to confirm if this is correct
13 y/o
just ignore the |x| part and focus on the linear function inside
mx+b, m for slope increase, b for y-intercept
-1 is to move the 2 x-intercepts
i think
wait
bold zenith
There’s a rule against giving answers so please don’t do that again
final saddleBOT
There’s a rule against giving answers so please don’t do that again
bold zenith
.close
final saddleBOT
bold zenith
The channel was already closed, open a new one.
I don’t think there’s a difference between equation and expression here anyway
final saddleBOT
Available help channel!
brisk haven
they’re all vectors
(i+j) x k
my book says it’s -j + i but i got i x k + j x k
brisk haven
should i give components to each vector in order to simplify further?
edgy mauve
should i give components to each vector in order to simplify further?
Do u know the property of cross product of unit vectors
edgy mauve
but j x i = -k
Yes but u dont have any use of it here
brisk haven
okay so what do i do
edgy mauve
Do u know how it works
brisk haven
yeah
dawn merlin
Guys
edgy mauve
Expand first or derivate first?
In what context?
dawn merlin
This
edgy mauve
In this case expanding might be better option
dawn merlin
In this case expanding might be better option
Thank you
final saddleBOT
@dawn merlin Has your question been resolved?
dawn merlin
Do you have anything else to ask?
Yeah, can I ask later?
final saddleBOT
dawn merlin
Wait how does this work
ornate tree
Yeah, can I ask later?
Sure, how long would it take?
dawn merlin
How does the channel work
craggy plank
.unsolved
final saddleBOT
✅
ornate tree
How does the channel work
The channel will disappear if you leave it for too long
dawn merlin
Sure, how long would it take?
Idk sorry, I have 2 unsolved question because my answer is differ from the answer I decided to finish the ones I know and then ask
proper dagger
after how long will you be back
if it's like 10 minutes, the channel can stay open until then, but if it's like an hour, consider letting this close and grabbing another channel when you come back.
craggy plank
Idk sorry, I have 2 unsolved question because my answer is differ from the answe...
yeah, consider claiming another one when you’re back
.solved
regal hamlet
Let $f \in \mathcal{R}(\alpha)$ on $[a, b]$ and $p > 0$. Prove that if $\int_a^b |f|^p d\alpha = 0$, then $\int_a^b |f| d\alpha = 0$.
final saddleBOT
Let $f \in \mathcal{R}(\alpha)$ on $[a, b]$ and $p > 0$. Prove that if $\int_a^b...
soft zealotBOT
Halex
regal hamlet
f is riemann-stieltjes integrable with respect to alpha on [a,b]
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
@regal hamlet Has your question been resolved?
rustic wedge
final saddleBOT
**Halex**
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
opaque ember
Let $f \in \mathcal{R}(\alpha)$ on $[a, b]$ and $p > 0$. Prove that if $\int_a^b...
what have you tried and where are you stuck?
final saddleBOT
@regal hamlet Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
rotund thicket
how do i find the area and perimeter of this trapezoid
final saddleBOT
how do i find the area and perimeter of this trapezoid
craggy plank
Is that 5, 4, and 8?
rotund thicket
yeah
solid notch
umbral steppe
do you know the formula for the area of a trapezoid?
craggy plank
rotund thicket
no, my school has issues of hiring math teachers so in the year i was meant to learn it, it didnt really happen
umbral steppe
the formula for the area of a trapezoid is (sum of length of parallel sides) * (perpendicular height of trapezoid) * (1/2).
(the perpendicular height is the 4m here.)
rotund thicket
can you show it visually please if it isnt too much to ask for
umbral steppe
given a trapezoid with these sides, the formula of the area of this trapezoid is $A = \frac{1}{2} (a+b)h$.
soft zealotBOT
Lute
rotund thicket
let me see if i can do this and ill show you how it turns out, but I just solve that right?
umbral steppe
yes.
rotund thicket
thank you
umbral steppe
the perimeter is a bit more involved.
rotund thicket
what do you mean?
umbral steppe
you need to find the length of the other slanted side.
you'll need a few steps to get there.
and before you ask, no, you are not allowed to assume the other slanted side is the same length as the one given if it's not explicitly stated.
(such an assumption is impossible on this trapezoid anyway, for reasons you shall see later.)
rotund thicket
Excuse me but may I ask a question about the equation for the area before we move onto perimeter
umbral steppe
you may.
rotund thicket
**Lute**
would I multiply what i get on the inside of the parenthesis with the 1/2 or h?
umbral steppe
with both.
rotund thicket
or am i doing this wrong
umbral steppe
it's 1/2 times a+b, times h.
rotund thicket
Oh i forgot that for a second
thank you it slipped my mind
I got A=2.5+4, do i multiply the 4 with the 4 now
umbral steppe
hm? where did the = sign come from?
umbral steppe
the left side is a capital A. it means the area, not the side a.
rotund thicket
Oh thank you
umbral steppe
that capital A is what you want to find. I apologize if it was unclear.
rotund thicket
no worries
rotund thicket
I got A=2.5+4, do i multiply the 4 with the 4 now
so do I do it like this then?
rotund thicket
1/2=0.5 no? I just kinda viewed it like that then multiplyed it with the 5 and the 8
umbral steppe
I see, sure, that would work (a tad bit harder though). but you forgot the multiplication by the height.
rotund thicket
its the 4 that i asked about, do i multiply it with the 4 i got or with the 2.5 and the 4
umbral steppe
once you've added the 2.5 and the 4 together, you can then multiply the height with the sum.
but first finish the sum.
rotund thicket
sorry I dont know how these things are slipping my mind, Im working at this at a late time so I might be a bit tired
umbral steppe
consider taking a rest and coming back at it some other time, if you have the luxury to.
rotund thicket
so the Area is 26? also unfourtanatly cant, this paper has 60% worth of my grade and its due later today since its technically the next day
umbral steppe
correct.
rotund thicket
How do I start for the perimeter now?
umbral steppe
you have three sides, which is a good thing.
the not-so-good thing is that the last side involves three steps.
let's label some additional lengths on the diagram.
we want to find y, our last missing side, but to do that we would need z, and we can only get z by getting x first.
so let's start by getting x.
rotund thicket
how?
umbral steppe
what shape do you recognize the right side as?
specifically, the shape with the sides labelled 4, sqrt(20), and x.
rotund thicket
the triangle?
umbral steppe
correct, but what kind of triangle is that?
rotund thicket
okay so funny thing is im actually really really bad with shapes
umbral steppe
i'll give you this for free. that shape is a right triangle.
(or a right-angled triangle)
rotund thicket
is it because of the 90 degree angle?
rotund thicket
I will remember as we go, chances are I do know them I just need a refresher
umbral steppe
maybe the name Pythagoras rings familiar?
rotund thicket
yes it sound familar
umbral steppe
do you recall that law?
rotund thicket
Sort of, its better showing me it. I have no doubt I can remember better as we go.
umbral steppe
this is Pythagoras in its entirety.
well, better known as the Pythagorean theorem.
umbral steppe
yes, but apply the theorem carefully.
consider which sides you have and which side is missing.
rotund thicket
Yes ma'am
umbral steppe
hint: you will need to rearrange this equation for the side you need.
I would recommend setting up the equation first.
rotund thicket
gettin me nervous ma'am
umbral steppe
I'm no ma'am, please.
rotund thicket
sorry
rotund thicket
No worries you are doing well, also quick question when you said rearrange did you meant moving the B squared to where the C is at since thats the missing side or did you mean something else?
umbral steppe
you are on the right track in moving one of the two sides to join the c^2, and it could very well be the b^2, but in that case your missing side is then a, not b.
the idea is that we want the missing side to be alone.
rotund thicket
wait so do you mean it would be a^2=b^2+c^2?
umbral steppe
incorrect.
rotund thicket
sorry got lost on what you said
umbral steppe
from $a^2 + b^2 = c^2$, if we want to isolate, say, a, we want b on the right. \
therefore, we need to subtract $b^2$ from both sides: $a^2 + b^2 - b^2 = c^2 - b^2$.
soft zealotBOT
Lute
umbral steppe
on the left, the b^2 - b^2 cancel each other out, so you're left with a^2 = c^2 - b^2 (not a plus).
if you want to isolate b instead, subtract a^2 from both sides. it's the same concept here.
rotund thicket
so subract from both sides to isolate one of them
soft zealotBOT
Lute
umbral steppe
here, we want to isolate x, so there's only one way to do it.
rotund thicket
subtract the 4^2 from both sides?
umbral steppe
yes! well spotted.
after that, you will have x^2 = (a lot of stuff on the right). solve the stuff on the right first.
rotund thicket
how could I go on about for the 20 since i know the 4 is 16
umbral steppe
what do you think will happen to a square root when you square it?
rotund thicket
No clue, I haven't done it yet. I can't think of any instance when I have, and if I have then I must have forgotten.
umbral steppe
if I tell you that the square root is the "opposite" of a square, will you be able to do it?
(it's also slightly worrying that you claimed to not have encountered radicals before at this stage, but we'll save that for another time.)
rotund thicket
(my school is really not the best when it comes to math, I still havent met the teacher and its been weeks) also I can give it a go
umbral steppe
sure.
fallen heart
if I tell you that the square root is the "opposite" of a square, will you be ab...
are we not supposed to give them straight forward steps?
umbral steppe
are we not supposed to give them straight forward steps?
I'm not giving OP the straightforward steps to the original problem.
fallen heart
I'm just generally asking
rotund thicket
I couldnt tell it was straight forward, im tired its been a long day i barley remembered to add until they pointed it out. So no worries
umbral steppe
generally, if the straightforward step leads directly to the solution, then it would be frowned upon, I suppose.
if the higher-ups think that I have indeed violated this principle, I shall apologize and remove this.
fallen heart
generally, if the straightforward step leads directly to the solution, then it w...
No you've not done anything wrong I'm just asking because I'm kind of new to the channel so
please ignore me and continue
rotund thicket
unrelated but related to the math, would the square roots like cancel out and leave the number inside alone?
I think I remember something like that
umbral steppe
correct. the square root and square "undo" each other.
to understand why, we would need to go back to how exponents and radicals are defined, but that is a topic for another day.
rotund thicket
dont worry you can trust Ill be back
my teacher will probably appear only 5 weeks like they did last school year so I will appreciate any help
rotund thicket
isnt the x still squared?
rotund thicket
yes I have x^2
umbral steppe
what is it?
rotund thicket
i got it equals 4
umbral steppe
so x^2 = 4.
rotund thicket
yes
umbral steppe
remember how we said that the square root "undoes" a square?
rotund thicket
yes
umbral steppe
now we're going to put that to use.
take the square root on both sides.
rotund thicket
like you want the set up to be: x multiplied by x= 4 multiplied by 4, or do it only to the fours? sorry just a little confused
umbral steppe
x^2 = 4
sqrt(x^2) = sqrt(4)
rotund thicket
oh
umbral steppe
that's it.
rotund thicket
so x=2?
umbral steppe
correct.
umbral steppe
let's label some additional lengths on the diagram.
now let's revisit this diagram. the bottom length is 8m, 2m of which belongs to x. can you find z?
rotund thicket
how do i start it off
rotund thicket
is it technically 4 too?
rotund thicket
are you talking about the 8?
umbral steppe
no.
the 8m is the length of the entire bottom line segment.
we want just the section in between z and x.
rotund thicket
6? also sorry i took a second, my laptop was about to die
plucky rover
Do we know x already
umbral steppe
yes.
rotund thicket
its 2
umbral steppe
yes to Xavier.
no to Bonnie.
focus on the shape in the center. what does it remind you of, and what conclusions can you draw regarding the line segmnet between z and x from the shape?
rotund thicket
WAIT WAS IT 5
umbral steppe
absolutely.
rotund thicket
I forgot it was on top.
umbral steppe
so now you have that line segment, and x. can you now find z?
rotund thicket
is z=1?
umbral steppe
correct.
so now you have two sides of the right triangle on the left side.
finding y is now straightforward.
I trust you can finish this yourself.
rotund thicket
thank you very much Lute
umbral steppe
none necessary. I'm glad to help.
rotund thicket
towards the end i got to the point where i have to square 17, just to be sure am i still doing okay or did I over look something?
umbral steppe
what do you mean?
rotund thicket
x^2 = 4
sqrt(x^2) = sqrt(4)
something like this
umbral steppe
so what is the equation you have at the moment?
I know a 17 is eventually involved, but I need to see your steps to confirm.
rotund thicket
sqrt(c^2)=sqrt(17)
umbral steppe
correct.
rotund thicket
is the 17 going to turn out as a decimal?
umbral steppe
unfortunately yes, as the square root of 17 is irrational.
as is the square root of 20 on the other slant, but for that you can simplify the 20 inside to get a smaller number.
not that it helps much if you need a number as a final answer.
rotund thicket
wait ill be back, give me a second
okay im back
also may you explain further please
umbral steppe
what do you need an explanation of?
rotund thicket
on how to simplify the 20, do you mean getting it down to something like a 10 or a 5, or do you mean when its a decimal?
umbral steppe
do you need a numerical answer?
if you do, this simplification matters not, as in the end you'll still need to use a calculator.
if not, factorize 20, and notice that one of its factors is a perfect square. you can move that perfect square out of the square root.
rotund thicket
i do need a numerical answer
umbral steppe
then ignore this simplification and use a calculator.
rotund thicket
so just put it in a calculator?
umbral steppe
yes.
rotund thicket
the same for the 17?
rotund thicket
ill see what else i have to do, if i need help ill try to come back but i also need rest
umbral steppe
good call. enjoy your rest, and remember to close the channel when done.
rotund thicket
how do I close it?
umbral steppe
!done
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
craggy plank
.solved
final saddleBOT
final saddleBOT
Available help channel!
uneven ginkgo
final saddleBOT
pliant shore
what have you tried?
ah yes, so u = 2 and v = 7, that's correct
then you should recall that slope $= \frac{y_2 - y_1}{x_2 - x_1}$
soft zealotBOT
south
uneven ginkgo
So 2+1/5-7=-3/2?
pliant shore
you need brackets
pliant shore
yep!
uneven ginkgo
So y=-3/2x + 9.5?
pliant shore
So y=-3/2x + 9.5?
yep!
final saddleBOT
@uneven ginkgo Has your question been resolved?
harsh solstice
Prove that if p and p^2 + 8 are prime, then p^p^2 + p^2 - p! + 1 prime.
runic tulip
bro make up your mind
harsh solstice
Done.
worldly mesa
just be clear you mean
if $p$ and $p^2+8$ are prime then $p^{p^2} + p^{2} - p! + 1$ is also prime?
soft zealotBOT
ExpertEsquieESQUIE
small zodiac
i think u can find p from p and p^2 + 8 (and make sure its a prime) and sub it into the p^p^2 + p^2 - p! + 1 and test if that number is a prime or not
stuck juniper
Also the given expression is not said to lie between p and p^2+8
stuck juniper
maybe p^2 + 8 and p cannot be prime except a few small cases
Not like this is not valid
U have to prove it for every given case
And we have no idea how many cases are there
worldly mesa
yep
harsh solstice
There is something unnatural about p^p^2 + p^2 - p! + 1
worldly mesa
if p is an odd prime then p^2 + 8 is divisiable by 3
small zodiac
Thats not a proof tho
😭 my mistake
stuck juniper
This shi is sum imo level ahhh
harsh solstice
p = 2?
stuck juniper
stuck juniper
yeah because I ruled out every other one
🗣️🗣️solved the prime conjecture
harsh solstice
p = 2 does not satisfy the original conditions.
worldly mesa
any for p=3
p^p^2 + p^2 - p! + 1 is 3^9 + 4 = 19687
harsh solstice
Funnily, p = 2 and p = 3 both satisfy that p^p^2 + p^2 - p! + 1 is prime.
,w factor 19687
soft zealotBOT
worldly mesa
(p-1)! not p!
tired walrus
i think u can find p from p and p^2 + 8 (and make sure its a prime) and sub it i...
as in you think there's only a finite number of primes that make this happen?
yeah actually it's already been said
stuck juniper
This proof gonna be tedious af
tired walrus
if p is an odd prime then p^2 + 8 is divisiable by 3
this kills it @stuck juniper
what exactly were you claiming as invalid earlier?
stuck juniper
I did not see that but yea took me some time to even think that 
final saddleBOT
@harsh solstice Has your question been resolved?
harsh solstice
Thank you y'all.
quartz flame
can there be a equation of a line that is parallel to 2 non-parallel planes?
quartz flame
like it is parallel to each plane
ornate tree
You mean two planes that are not parallel to each others, asking if there is a line that does not touch any of them?
bleak granite
yeah that's just the line of intersection, no? 
quartz flame
now that you word it like that i fucked ip
ornate tree
now that you word it like that i fucked ip
I'm not sure what you're looking for, this is a mere speculation
potent mauve
sup yall how do we do solve equationsn by completing the square
quartz flame
I'm not sure what you're looking for, this is a mere speculation
i had an exam yesterday
and it said to find the equation of the line that is parallel to plane 1 and plane 2
the planes were not parallel to each other
:( i think i messed up on it now
ornate tree
and it said to find the equation of the line that is parallel to plane 1 and pla...
There indeed exist such line
ornate tree
and there are multiple of them
quartz flame
this is a cruel world
ornate tree
how
First of all, do you agree that when two planes are not parallel, you always get an intersection line between them?
quartz flame
yeah
ornate tree
So the lines that fulfill this requirement is parallel to this line
quartz flame
damn i see it now
ornate tree
That's how it works
quartz flame
maybe i still did it correctly
ornate tree
Anything else you wanna ask?
quartz flame
nope that was all
ornate tree
maybe i still did it correctly
perhaps :))
glgl
quartz flame
.close
final saddleBOT
glossy zephyr
can there be a equation of a line that is parallel to 2 non-parallel planes?
Yeah, you can, it has to do with the fact that you have a lot more "freedom" on what is a parallel line to a plane compared to a plane to another plane
quartz flame
Yeah, you can, it has to do with the fact that you have a lot more "freedom" on ...
would i have gotten this line by doing the cross product of the planes' normal vectors
and using the point they gave me
this is a beautiful world no longer cruel
wow
glossy zephyr
That specific line is in reality the intersection curve tangent*, for planes it happens to be a straight line
quartz flame
gotcha
i will remember this now
i just didnt know it was parallel
and i wrote on my exam i thikn you mean perpendicular 
final saddleBOT
Available help channel!
ivory island
Can someone explain to me when lnx is plausible when integrating
final saddleBOT
Can someone explain to me when lnx is plausible when integrating
polar wyvern
integration of 1/x is lnx
and integration of 1/(ax+b) is (1/a)ln(ax+b)
for x/(x^2+3) u can use substitution method
ivory island
so integration into lnx wont work if its not just 1 in the numerator?
glossy zephyr
would it be lnx^2+3?
lmao. Yeah, sadly you cant just plug in the value of the denominator into it
ivory island
😔
glossy zephyr
For fractions involving polynomials, you have a few methods which vary case to case
1 / x is a really neat case
ivory island
if I see a problem asking me to integrate something, and I dont know how to start it, should I just try u substitution
ivory island
For fractions involving polynomials, you have a few methods which vary case to c...
can you expand
glossy zephyr
if I see a problem asking me to integrate something, and I dont know how to star...
If we are talking of early college or late years in HS, you usually should be fine with either u-sub or by parts
maybe a trig-sub
ivory island
I had a problem on homework where it was integration by parts but it was like 3 IBP deep and then it was basically repeating
so you had to just multiply the integral and then cancel them?
something like that
junior token
would it be lnx^2+3?
whenever you want to check an answer to an integral problem, you can always differentiate the answer to check it
ivory island
whenever you want to check an answer to an integral problem, you can always diff...
this is true but if I don't know how to differentiate it
then not helpful ig
glossy zephyr
can you expand
Suppose we have some function P(x) which is a polynomial: aka a function of form: $ax^n + bx^{n-1}+... mx^1 + Cx^0$
For functions that are $\frac{P(x)}{P_1(x)}$ where P1 is a different polynomial
You usually end up having to do some sort of polynomial division / simplification
ivory island
like long division?
soft zealotBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
glossy zephyr
Not really, because you are integrating a division
You cant just "divide" them and do multiple integrals because the denominator would be distributed to all fractions anyways.
Integration / Antiderivatives are a lot more strict on the rules you have to follow, thats usually why they are harder.
ivory island
It's not too bad
but im in bio, chem, physics, and calc 2 right now
so I don't spend as much time as I
would like doing calc
makes it a bit harder
vague anchor
5th
1st
bold zenith
,rccw
soft zealotBOT
vague anchor
I made a quadratic in tanx/2