#help-10
timid silo
hasty flint
royal pawn
Hello
royal pawn
is this true ? :
x/y = q/w , p/u = o/g => x+p/y+u = q+o/w+g
analog gale
Just substitute the values
q=kx
w=ky
o=kp
g=ku
This holds true if the coefficients are equal!
k is an arbitrary constant
river plank
we can ask questions besides the help section
?
sorry just saw this, connection problem ( 3rd world issues😅 )
compact shadow
Don’t worry
river plank
i was referring to this
the way you wrote this
doesn't seem at all like the def of cartesian product
compact shadow
(First glance I thought you said it was a 3-rd world problem, like hilbert 3-rd problem or something)
It is,bijection from S(123) product S(456) to S(1,,6) mapping (h,k) to g as I constructed
obtuse pebbleBOT
Available help channel!
river plank
like the way i understand this it says g from S6 that fix either 456 or those that fix 123
obtuse pebbleBOT
like the way i understand this it says g from S6 that fix either 456 or those th...
river plank
oh so it's saying that it permutes the elments of 123 among themselves
and 456 among themselves
is that right?
compact shadow
Yeah S(123) product S(456)—>g from S(1..6): {g fix {1,2,3} and {4,5,6}}
Mapping (h,k) to g as I defined
river plank
oh got it so
you took the product S(123) S(456)
defined a homorphism from this to a subgroup of S6
compact shadow
Np
river plank
river plank
Np
Also the same happened with this (connection stuff) but i understood what you said. Thanks for this as well! ( couldn't reply there as the channel is unavaiable to me)
river plank
Oh it was you
yeah
river plank
You can ping me next time you ask algebra problems
like pinging individual users
compact shadow
Idk, but who cares, I mean I personally allow and prefer it
river plank
ok Thanks i will!
compact shadow
As long as I don’t care, probably fine
river plank
You can ping me next time you ask algebra problems
i have more questions regarding burnside lemma
first i need to hit the notes
try to understan the questions somewhat
compact shadow
Number of orbits thing?
river plank
then i will post here
river plank
Number of orbits thing?
yeah
compact shadow
Okay
river plank
the questions are like finding the number of ways we can color polyhedra and stuff
compact shadow
Yeah, useful for those things
hybrid crescent
can someone help pls
tardy stratus
obtuse pebbleBOT
@river plank Has your question been resolved?
languid bone
15x+41y = 1.
(b) 1234x + 4321y = 5.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
native idol
obtuse pebbleBOT
native idol
Can somebody teach me how do i find B? but i know what to do but is just how can i make the question identifiable and specific . (A right circular cone is inside a cube).
im stuck reading with the question over and over
Do i make my own assumptions of the (s) and B?
obtuse pebbleBOT
@native idol Has your question been resolved?
timid silo
Can somebody teach me how do i find B? but i know what to do but is just how can...
subtract the volume of cone from the cube
native idol
Ahh
volume of cube - volume of cone = ? is that it
if so then
no matter what volume it is for example
so once i subtracted did i find B?
timid silo
so once i subtracted did i find B?
yes do that
native idol
Ok ok
fathom belfry
obtuse pebbleBOT
fathom belfry
Can someone help me with this question
timid silo
what is your definition of continuity
fathom belfry
one sec
Basically there are 3 conditions
the limit as x is approaching zero exists from both left and right
f(x) exists
and f(x) = the limit as x is approaching a certain value
rigid agate
Assume f is continuous then by your definition lim x->a f(x) = f(a). Now you need to show: lim h->0 f(a+h) = f(a).
Can you work from here?
Opposite direction: Assume lim h->0 f(a+h) = f(a). Now show: lim x->a f(x) = f(a)
fathom belfry
I have no idea how to do that
fathom belfry
Assume f is continuous then by your definition `lim x->a f(x) = f(a)`. Now you ...
I understand the first part
rigid agate
I think you would also need some definition of the limit, if you want to do it rigorously.
If lim x->a f(x) = f(a) is True then by definition of the limit [...] is True, and then try to satisfy the definition of limit for lim h->0 f(a+h) = f(a).
fathom belfry
So I need to go back to limit first?
rigid agate
Probably yes. Unless there is some easy trick or something
Best is to work with definitions
And also depending on how rigorous your proof needs to be. You kind of see that if f is cont. and h goes to 0, probably f(a+h) goes to f(a) but that's obviously not a proof.
rigid agate
Oh ok, then maybe don't go into too much detail I would say😅
outer hedge
help
outer hedge
oh shoot
anyways
so
0 and 1 => 0
0 and 2=> 1
1 and 0 => 2
2 and 0 =>3
i need to get the number on the right
from the numbers on the left
but i need a general formula that would work for the 4 cases
this is like my 3rd time asking the same question but sure
timid silo
ok so if 0 is written first number reduces
and 0 written in front number increases by 1
outer hedge
ok so if 0 is written first number reduces
and 0 written in front number increas...
that's true but i need a general formula
i don't want to handle the 2 cases separately
something like 3a+b+7 or something
you can use whatever operations you wantr
@timid silo
timid silo
I'll inform you if I can think of any operation
timid silo
this is for a program right ?
timid silo
if its only got 4 cases, what's stopping you from hard coding it?
outer hedge
if its only got 4 cases, what's stopping you from hard coding it?
because those 4 cases also apply somewhere else in the code
and i don't want to hardcode it twice
maybe even more
my function has to be less than a certain number of lines 🙂
if i hardcode i'll go over that limit
timid silo
just define it at the beginning, then call the function lol
timid silo
I think they only care about the first four cases
outer hedge
I think they only care about the first four cases
yeah
gloomy valve
works for the first 4 cases as well
outer hedge
that wouldn't be a closed case formula tho
timid silo
'num of zeros' is kinda hard to program
outer hedge
'num of zeros' is kinda hard to program
yeah
timid silo
especially when theres leading zeros
gloomy valve
num zeros will just be the string length - 1 anyway
outer hedge
i need a one line formula 
gloomy valve
if we assume that only the first digit is non-zero
timid silo
i need a one line formula <:happy_cry_cat:636407813144576010>
are you using python?
outer hedge
are you using python?
yeah
ik i can use string.count("0)
but still like ...
there must be an easier way
warm canopy
I'm confused why you won't just hardcode a function you can then call in the future whenever you need it
gloomy valve
if its only 4 fixed cases it doesnt even matter to have a closed formula
timid silo
if a==0:
return b-1
else:
return a+1```Ah lol
outer hedge
```def myfunction(a,b):
if a==0:
return b-1
else:
return a+1```
honestly, i might just go with this....
tysm y'all
appreciate the help
.close
timid silo
honestly, i might just go with this....
actually, a(b-1)+b(a+1) works lmao
obtuse pebbleBOT
actually, a(b-1)+b(a+1) works lmao
timid silo
.close
obtuse pebbleBOT
outer hedge
actually, a(b-1)+b(a+1) works lmao
it does? 💀
outer hedge
it doesn't tho ...
outer hedge
0 and 1 => 0
0 and 2=> 1
1 and 0 => 2
2 and 0 =>3
i need to get the number on th...
.
if a=0 and b=1
timid silo
.reopen
obtuse pebbleBOT
✅
outer hedge
if a=0 and b=1
it would be 1 not 0
timid silo
if a=0 and b=1
oh sorry, I meant a(a+1)+b(b-1)
I think
oh wait
nvm
lmao
just use the hard code method
.close
obtuse pebbleBOT
outer hedge
oh sorry, I meant a(a+1)+b(b-1)
that fails for a=0 and b=2 lol
timid silo
yeah
outer hedge
just use the hard code method
i will
timid silo
I cant add in my head apparently
outer hedge
I cant add in my head apparently
same
obtuse pebbleBOT
Available help channel!
warm matrix
How do I find the degrees of freedom for a chi squared distribution matrix of a single row/column with any number for the other column/row? Using X^2cdf for the P-value I got the correct answer(according to the answer key) by using 3 degrees of freedom, when I thought it should have been 4. In another similar problem with 5 rows and a single column the correct number of degrees of freedom was 4.
obtuse pebbleBOT
How do I find the degrees of freedom for a chi squared distribution matrix of a ...
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
misty valve
obtuse pebbleBOT
misty valve
What is the best way to approach this problem?
misty valve
f(u)1/5du
kind hawk
from where to where?
misty valve
f(2)1/5-f(0)1/5
kind hawk
no
misty valve
From 10 to 0?
kind hawk
from 0 to 10
misty valve
Oh right
kind hawk
so we have $\int_0^{10} \frac15 f(u) du$
warm shaleBOT
Denascite
misty valve
Yes
kind hawk
now remember that u is just a variable and its name doesn't matter
so we could also rename it again to $x$ and get $\int_0^{10} \frac15 f(x) dx$
warm shaleBOT
Denascite
kind hawk
now how can we use the info we are given
misty valve
If we just evaluate we get 2
misty valve
10/5 -0/5
kind hawk
that's not how that works
the 1/5 is a factor
we can take it out of the integral and get $\frac15 \int_0^{10} f(x) dx$
warm shaleBOT
Denascite
misty valve
Yea -9
kind hawk
so when we plug this in we get -9/5
so we started with $\int_0^2 f(5x)dx$ and ended with -9/5
warm shaleBOT
Denascite
misty valve
If this is where we use algebra I'm lost
high lily
ur overthinking
misty valve
Oh
That's gonna be hard to remember
Wow it's actually really simple though
I used the same technique on the next question
Anyways
Ty
.close
native idol
obtuse pebbleBOT
native idol
A similar question before but even more complex .
i don't have advanced experience of doing the linear equation.
teach and give me some hints.
obtuse pebbleBOT
@native idol Has your question been resolved?
native idol
.close
ruby path
$\frac{2}{3} \times \frac{3}{2} = 1$
warm shaleBOT
NEONPerseus
ruby path
Also anything multiplied with 0 is 0
What are you comparing
2/3 into 3/2 is equals to into 2X3 and 3X3
What does this mean
uh
But there
Is no equation
:P
$\frac{a}{b} = \frac{c}{d} \implies a \times d = c \times b$
warm shaleBOT
NEONPerseus
ruby path
This is what cross multiplication is
How did $\frac{-7}{13} \times \frac{0}{1}$ become $-7 \times 1 = 13 \times 0$
warm shaleBOT
NEONPerseus
ruby path
This is where you went wrong I feel 😄
ruby path
**NEONPerseus**
You need to have an expression like this to cross multiply
What is the question @timid silo you just need to tell which number is greatest?
um
but what are we cross multiplying
all of those values equal 0
I honestly still don't know what this is trying to say ;-;
You are trying to find which fraction is greater by cross multiplying?
I'm sorry I couldn't help 😔
sharp crow
@timid silo this isnt like 7th grade answer but when you multiply negatives in comparision the sign gets reversed (the greater or less thing)
like
wait
ruby path
Ohh so that's what he was asking
sharp crow
Ohh so that's what he was asking
yes
he is asking inequalities
comparision
(and I cant elaborate further)
ruby path
If a, b, c, and d are positive numbers, then $-\frac{a}{b} > \frac{c}{d} \implies -a \times d < b \times c$
warm shaleBOT
NEONPerseus
ruby path
Can you see how the sign flips from > to <?
sharp crow
see below
ruby path
😛 Honestly this inequality flipping thing is something you'd only use and learn in high school
sharp crow
yes
ruby path
You shouldn't worry too much about inequalities
Until 10th Grade math is "do as you're told"
Harsh truth
sharp crow
cuz you aint in 10th
ruby path
You can probably ask your teacher
But we did give you the explaination
:( Well the concept is advanced for you
The inequality flips upon cross multiplying a negative quantity
Sorry I'm not sure, you can look them up yourself if you're curious 😄 I can't guarantee you'd understand everything though
go ahead
go ahead and try learning linear algebra
:P There's a reason you're taught in steps
ruby path
Derivatives and integrals are fun ngl
But I don't think I would be able to understand shit in grade 7 xd
sharp crow
they will understand why not to concentrate on high concepts
or
they will understand derivatives and integrals
:p
ruby path
If they manage to crack derivatives and integrals then tf you doing in 7th grade we have a prodigy
sharp crow
good luck
sharp crow
If they manage to crack derivatives and integrals then tf you doing in 7th grade...
prodigy coming soon lol
ruby path
$e = \sum^{\infty}_{n =0 } \frac{1}{n!}$
warm shaleBOT
NEONPerseus
ruby path
Just know this value before moving on to derivatives and integrals
sharp crow
lol
ruby path
**NEONPerseus**
This is beautiful btw
sharp crow
even I never knew this
ruby path
One whose derivative with a variable in the power is itself
I'm in love with Euler's constant
sharp crow
lol
ruby path
Also @timid silo close this channel xd
sharp crow
or make this general
merry peak
If they manage to crack derivatives and integrals then tf you doing in 7th grade...
I did it in 6th grade ez
ruby path
orz
timid silo
If they manage to crack derivatives and integrals then tf you doing in 7th grade...
it's not what standard of maths they do make them a prodogy
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
restive plinth
hi i was wondering how do u solve this limit?
obtuse pebbleBOT
hi i was wondering how do u solve this limit?
restive plinth
forest yacht
$0\leq 1+cos(\pi x)\leq 2$, so the limit is between 0 and $\lim_{x\to \infty}\frac{2}{(x-1)^2}=0$
warm shaleBOT
JellyShark
rigid agate
does this limit exists?
Which one?
forest yacht
$0\leq 1+cos(\pi x)\leq 2$, so the limit is between 0 and $\lim_{x\to \infty}\fr...
$0\leq\lim_{x\to \infty}\frac{1+\cos(\pi x)}{(x-1)^2}\leq\lim_{x\to \infty}\frac{2}{(x-1)^2}$
warm shaleBOT
JellyShark
restive plinth
this one?
grave oyster
does this limit exists?
yes it does it’s 0
grave oyster
no problem
violet sentinel
OH!!!
I love this question
it has to do with logic
basically
take the statement if f'(x) > 0 and f''(x) < 0 for all x with a < x < b then ...
this means that if the condition above is true, then it implies the the statement is true. BUT it's not the same backwards. In other words:
For all x within a < x < b, if f'(x) > 0 and f''(x) < 0, then the trapezium rule produces and overestimate for the integral Is a true statement
For all x within a < x < b, if the trapezium rule produces and overestimate for the integral, then f'(x) > 0 and f''(x) < 0 is not necessarily true
yep exactly
if and only if is A <=>B
which means B=>A and A=>B
you can't have one without the other
but in A=>B, B does not necessarily imply A
does that make sense?
that's not to say that it doesn't ever happen! It's just not a necessary and suffiicent condition
Only If simply creates the reverse statement as if you used “IF”
it's a way to re-write an if statement
for example
"if it's raining, I will bring my umbrella" and "I'll bring my umbrella only if it's raining" are equivalent statemetns
if you see an If and only if, then that's biconditional
you got it
I got a resource one second
this is all the ways to say "if A then B"
don't get too wrapped up in memorizing them, but it's a good tool to have in case you're reading a statement and you're not sure what it's saying
yep no problem
timid silo
Hello, I was looking for an answer to this, I'm thinking its AB // CD, didn't get much information from my teacher's lessons so I'm looking forward to a better explanation!!
obtuse pebbleBOT
Hello, I was looking for an answer to this, I'm thinking its AB // CD, didn't ge...
timid silo
.close
raw relic
obtuse pebbleBOT
violet sentinel
hmmm well I dont think the tree will work out here. Since there is not an evenly distributed number of primes
raw relic
so how would you do it?
violet sentinel
so the max value we can get is 6 + 5 = 11, and that's IF we dont roll the 4 sided die
the lowest value we can get is 1 + 1 = 2, either die
so our possible rolls are 2 to 11
of which 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
so
...huh
wait
it is even chances to get a prime number lol
nvm
yeah I guess your approach works
violet sentinel
I could be wrong, but then the tree is fine here. Yep I think you're on the right path
except for I wouldn't start with "4 sided die"
start with a *
here let me draw it out
wait actually no
tulip kestrel
Its ok im just burn out from trying to solve this
I have a different tree in mind that might work better
violet sentinel
@tulip kestrel please go ahead!
tulip kestrel
@raw relic how many situations do you have (dice wise)?
raw relic
As in?
tulip kestrel
like what choises can you make
i kinda need to sleep now so start with a tree that has 3 branches first (4,5) (5,6),(4,6) and the rest would be the same
and I think the rest would be just applying formulas
give that a thought
good night
raw relic
Aite ill try thx alot
obtuse pebbleBOT
@raw relic Has your question been resolved?
raw relic
But what about the prime numbers?
tulip kestrel
But what about the prime numbers?
you can just use branch of with prime numbers and no prime numbers
and than apply conditional probability
obtuse pebbleBOT
@raw relic Has your question been resolved?
obtuse pebbleBOT
@raw relic Has your question been resolved?
timid silo
What am I doing wrong?
Do I need to use L and is the range -pi,pi correct or should I be using range 0 to 2pi?
obtuse pebbleBOT
Available help channel!
timid silo
Channel open
obtuse pebbleBOT
Channel open
timid silo
Do I need to use L and is the range -pi,pi correct or should I be using range 0 ...
<@&286206848099549185>
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hidden fable
I actually have two questions bc I don't understand how to do either..
obtuse pebbleBOT
I actually have two questions bc I don't understand how to do either..
hidden fable
Channel open
spiral pebble
what
visual onyx
.close
obtuse pebbleBOT
hidden fable
.close
visual onyx
it's closed already
obtuse pebbleBOT
Available help channel!
mellow halo
Hi
mellow halo
Part a was relatively easy
I don’t understand part b i.
I got 43 by adding a box on each side of diagram 3
Like u know
Diagram one has 1
Diagram 2 has 3 boxes around 1
Diagram 3 has 5 boxes around 3
So I assumed that diagram 4 would have 7 boxes around 5
Then I counted the lines and got 43
Is there another way that would confirm my answer?
obtuse pebbleBOT
@mellow halo Has your question been resolved?
sharp crow
the image is not clear
sharp crow
its clear now
mellow halo
W
So uh
My nth term formula for part b (number of 1 cm lines) is a whole equation
2n^2 + 3n - 1
sharp crow
lol
mellow halo
Yup
sharp crow
then solve the quadratic
sharp crow
*will
sharp crow
Ye I was just writing down the steps for part i
ok
mellow halo
I WILL
sharp crow
yes
mellow halo
Hmm quadratic formula time
mellow halo
I’m doing it rn
sharp crow
lol
sharp crow
I’m not using middle term break
I do neither I was just typing ol
sharp crow
Quadratic ez and more fun
yes
sharp crow
lol
mellow halo
So diagram 7 would have 118 lines
sharp crow
ig yeah
sharp crow
..
mellow halo
Cough
sharp crow
coughs
mellow halo
sharp crow
funny ngl
sharp crow
wc
mellow halo
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lyric granite
There's a question on my homework that is asking me to approximate values of y(x) based on a given value and a direction field. The lecture video did not go over this in any meaningful detail so I am stuck.
The first of these problems states: "For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following: y(1) and y(-1)"
obtuse pebbleBOT
There's a question on my homework that is asking me to approximate values of y(x...
lyric granite
I am given only the graph of the direction field, with no differential equation to go with it, hence approximation. I have a guess that what I am attempting to do is estimate the output half of the ordered pair, but without an equation this is difficult.
rigid pine
Show us the original question so we can see the information.
rigid pine
Between x = 0 and x = 1 there's four line elements. I think the aim of the exercise is to approximate sketch the integral curve in your head. The integral curve must be tangent to the line elements.
lyric granite
Indeed. But my question is what exactly am I approximating?
rigid pine
Imagine drawing a line segment to the next line element which is tangent to the current line element.
Well the direction field is overlaid on the xy-plane. We only know the slope at the sites where there's line elements.
lyric granite
Indeed.
rigid pine
At y(0) = 0, the origin, the slope is horizontal so the integral curve must also be approximately horizontal.
lyric granite
Hmm, let me try something, you might've created an epiphany.
Okay, yeah, I wasn't putting two and two together.
I was thinking it was more involved, but as it turns out I'm just following the line to where it goes.
Thank you for your time.
rigid pine
Thank you for your time.
Glad you see the idea now. 🙂
obtuse pebbleBOT
@lyric granite Has your question been resolved?
river bronze
p is "x > 30"; q is "x < or = 40". Write as simply as you can:
obtuse pebbleBOT
p is "x > 30"; q is "x < or = 40". Write as simply as you can:
river bronze
I am stuck at c, a and b are done
upbeat island
in classical logic you can cancel double negatives
river bronze
so its x > 30?
sullen cobalt
If something has a 10% chance of happening what is the odds of it happening 2 or more times out of 7
obtuse pebbleBOT
If something has a 10% chance of happening what is the odds of it happening 2 or...
sullen cobalt
Im having an argument with my friend about this lmao
He somehow thinks its 0.9^5
Which I’m 100% sure its wrong
But idk the exact answer
Nvm i got the answer alr
.close
obtuse pebbleBOT
haughty coyote
0.9^5 is the odds of it not happening in 5 attempts. Here you have a more complicated problem.
2 out of 7 has a probability of 0.1^2 * 0.9^5 * 21 (odds of getting 2 * the number of positions for these 2 wins) according to the binomial distribution
= 2 is 1 - 0.9^7 - 7 * 0.9^6 * 0.1
obtuse pebbleBOT
Available help channel!
timid socket
why does this function look this way?
obtuse pebbleBOT
why does this function look this way?
ruby path
infinite divided by anything is still infinite
timid socket
but why is it only negative?
ruby path
that doesn't seem right
proper forum
What mathematical operation do we perform while shifting exponents?
obtuse pebbleBOT
What mathematical operation do we perform while shifting exponents?
warm canopy
Exponentiation
ruby path
What mathematical operation do we perform while shifting exponents?
This is in essence taking the (n+1)th root of the RHS
proper forum
This is in essence taking the (n+1)th root of the RHS
you mean both sides, correct?
ruby path
you mean both sides, correct?
Ah yes
sage trail
Hi
sage trail
I’m not sure about how to do this
I know it has to do with similar triangles but I can’t figure out how I need to set it up
ruby path
Can you see how $\Delta LQP \sim \Delta LMN \text{ (AA similarity)}$
warm shaleBOT
NEONPerseus
sage trail
Yeah
ruby path
Great!
sage trail
Cause they share the same line in the middle right?
ruby path
Well
QP || MN
Since angles S and R are right angles
And since those lines are parallel, angles LQP and LMN are equal, and so are LPQ and LNM
sage trail
Would LSP and LRN be similar
sage trail
Ok ok I get why they are similar now
sage trail
but we're not bothered about it
Could you please help me find LMN
celest gorge
Hello everyone could someone help please
obtuse pebbleBOT
Hello everyone could someone help please
celest gorge
Hello everyone could someone help please
D) 37
celest gorge
He's given that A and b are rational numbers we should find value of a^2 + b^2
tardy stratus
And is there absolutely no other information on the question?
celest gorge
And is there absolutely no other information on the question?
No
tardy stratus
OK well you're not answering, so I will simply say: this question is impossible. There are no rational numbers a,b that satisfy the equation.
tardy stratus
Good point Ramonov, I realised my small error
Question for you, @celest gorge: is sqrt(5)b rational or irrational?
celest gorge
Good point Ramonov, I realised my small error
Sorry i didn't realize anything
tardy stratus
you didn't have to.
celest gorge
Question for you, <@897235309488635944>: is sqrt(5)b rational or irrational?
If b=sqrt5
tardy stratus
No
celest gorge
It is irrational
tardy stratus
This is not what I was asking
tardy stratus
b cannot be sqrt 5, because you are given in the question that b is rational
I am asking you
is $\sqrt 5 \times b$ rational or irrational?
warm shaleBOT
Boytjie (Plutonic Relations)
celest gorge
**Boytjie (Plutonic Relations)**
It could be both
tardy stratus
Can you explain when it's rational and when it's irrational?
Remember: you are given that b is rational
Let me know when you're ready to continue. I'll be waiting for a ping
tardy stratus
No...
celest gorge
Or sqrt5
tardy stratus
No need to apologise
OK, so let's take it again
We know that b is rational
We also know that sqrt 5 is irrational
floral garnet
Remember: you are given that b is rational
it can only be irrational then
tardy stratus
When is b * sqrt 5 irrational, and when is it rational?
tardy stratus
it can only be irrational then
Not quite, but I would like Coal_Bond to work this out
tardy stratus
When is b * sqrt 5 irrational, and when is it rational?
To be clear, when I say "when..." I mean "for what values of b..."
celest gorge
When is b * sqrt 5 irrational, and when is it rational?
Never?
floral garnet
To be clear, when I say "when..." I mean "for what values of b..."
φ
tardy stratus
Never?
Ok this is an important thing to recall. It's true that the product of a rational and irrational number is usually irrational, however: if b = 0, then the result is a rational number. This is the only case where an irrational multiplied by a rational is also rational.
tardy stratus
It means null set
No, phi is not the null set symbol.
Please let me work with Coal_Bond. Thank you.
celest gorge
Ok this is an important thing to recall. It's true that the product of a rationa...
Yeah i am understanding
tardy stratus
Ok this is an important thing to recall. It's true that the product of a rationa...
So just to explain this a bit further @celest gorge: sqrt(5) * b is irrational exactly when b is nonzero, and rational (in fact, it is 0) when b = 0
All good with that?
celest gorge
So then a=5?
celest gorge
Yeahhh get it thank you a lot
tardy stratus
Wait hold on a moment! We should make sure you get this
celest gorge
Input the value of b
celest gorge
Thank u a lot
celest gorge
So a^2 + b^2 = ?
25
celest gorge
Thank u a lot
For being so kind
tardy stratus
It's an interesting question isn't it!
junior pond
hi, can somebody please help explain as to why the answers are different when antidiff this? thank you!
obtuse pebbleBOT
hi, can somebody please help explain as to why the answers are different when an...
haughty coyote
the difference is between ln(u) and ln(2u) (with u = x - 3/2), but ln u and ln 2u differ by ln 2, a constant. So both are correct
junior pond
does it justt mean their c values are different?
haughty coyote
yes
for the same initial condition, both will be correct, but for a different value of C
junior pond
ahh ok
the weird thing is when i put it into my classpad it only shows the top answer
haughty coyote
it shows one correct answer, which is expected
obtuse pebbleBOT
junior pond
.reopen
obtuse pebbleBOT
✅
high lily
use + 3/4 ln(2)
instead of ln(2)
vale canopy
does anybody know how to factor -6x^2+25x-25 with the following method?
obtuse pebbleBOT
does anybody know how to factor -6x^2+25x-25 with the following method?
vale canopy
vale canopy
link's here if needed https://www.youtube.com/watch?v=YtN9_tCaRQc
timid silo
If your quadratic is as follows...
$$ax^2+bx+c$$
Then you factor it by figuring out a possible way that you can add two factors of $a\times c$ so you can get $b$
warm shaleBOT
idecanymore
timid silo
Like in your quadratic,
$$a = -6, b = 25, c = -25$$
So it's
$$-6x^2+25x-25$$
So we figure out $a\times c$ first. That is $-6 \times -25$ which is $150$
So now you will try to figure out some factors of this product, $150$ that can add up to $b$ which is $25$ in your case.
\
You know that $10+15=25$ and $15\times 10 = 150$ so you can write your quadratic as
$$-6x^2+25x-25$$
$$= -6x^2+10x+15x-25$$
You can take $-2x$ and $5$ as common factors and re-write your expression as
$$-2x(3x-5)+5(3x-5)$$
So you can write it now as
$$(-2x+5)(3x-5)$$
warm shaleBOT
idecanymore
timid silo
@vale canopy hope that's helpful for you
Also this doesn't work always just so you know that
But you'll be fine dw
obtuse pebbleBOT
Available help channel!
vocal tree
Hello they got the same truth table but I don't manage to prove it algebraically
vocal tree
If two statements have the same truth table does it's always possible to prove it algebraically?
obtuse pebbleBOT
@vocal tree Has your question been resolved?
warm shaleBOT
ΣAC
noble flower
Hi, could someone help me with some probability? I feel like I'm missing a formulae to use in order to work this out.
obtuse pebbleBOT
Hi, could someone help me with some probability? I feel like I'm missing a formu...
noble flower
<@&286206848099549185>
obtuse pebbleBOT
@noble flower Has your question been resolved?
drifting wraith
you want to add both "positive" together
you can find "positive no cancer" e.g. by subtracting "negative no cancer" from 0.99
noble flower
you want to add both "positive" together
So adding probability of positive test and cancer and positive test and not cancer?
drifting wraith
yeah
you don't know either one
positive test and cancer is one step to find
the other is like 2
noble flower
P(M|C) = 0.9, P(M|¬C)= 0.101, that would mean probability is above 1?
drifting wraith
i think so
warm shaleBOT
TopGAkhi
noble flower
Yeah it seems more sensible
obtuse pebbleBOT
@noble flower Has your question been resolved?
quiet vigil
obtuse pebbleBOT
quiet vigil
Not sure how I would go about doing this
quiet vigil
hm I think still lost
timid silo
using the triangle inequality we have |a|=|a-b+b| <= |a-b| +|b| therefore |a|-|b| <= |a-b|
similarly |b| <= |a-b| + |a|
so |a-b| >= |a|-|b| and |a-b| >= |b|-|a|
it follows |a-b| >= | |a| - |b| |
for b) which version of cauchy schwartz ?
obtuse pebbleBOT
@quiet vigil Has your question been resolved?
fading birch
wait what is this [] supposed to mean
obtuse pebbleBOT
wait what is this [] supposed to mean
ruby path
Greatest integer function usually
It should say in the question generally; something along the lines of "[.] denotes the greatest integer function"
golden onyx
wait what is this [] supposed to mean
It is the greatest integer smaller or equal to x
Sometimes also denoted by $\floor{x}$
warm shaleBOT
Yuese
fading birch
Hmm this is an old class, but what I remember is that the teacher made several integrals from 0 to 1, 1 to 2, 2-3, etc and then cancelled out each of them?
this was last year so I really have no idea how to do it now
ruby path
Hmm this is an old class, but what I remember is that the teacher made several i...
Yes
In technical terms we call that "pain"
fading birch
wonderful
so hmm, lemme just write something and send it over and hope I it makes sense from what little memory I have of that day
Hmm so if I made an integral from 0 to 1, [x] would represent 1, conversely if I made an integral from 1 to 2, [x] would represent 2?
forest sinew
Hmm so if I made an integral from 0 to 1, [x] would represent 1, conversely if I...
its greatest integer function, so down one
fading birch
i never used this symbol before so please bear with me
And if I wrote the first integral right, this should make a telescope function which cancels out a whole bunch of things?
forest sinew
maybe something like $\int _0 ^2 (x - \floor{x} ) \dd x = \int _0 ^1 (x - \floor{x}) \dd x + \int _1 ^2 (x - \floor{x}) \dd x$
warm shaleBOT
jan Niku
forest sinew
then note for each of the bounds $(a, a+1)$, that $\floor{x} \equiv a$.
warm shaleBOT
jan Niku
forest sinew
i cant tell, i think you're sort of there? its not clear if you stopped writing
,w graph floor function from x=0 to x=5
fading birch
What I'm confused on it's if in the [x] I ought to be putting 0 or 1
warm shaleBOT
forest sinew
oh its a minus 
fading birch
Like, if I can get the integral from 0 to 1 right, I'm all good to go
But I don't know what values to put orz
fading birch
Wait then what is the [x] supposed to do!? I thought it affected which values were being used
I'm just a Neanderthal and I discovered this fancy bracket
forest sinew
\begin{align*}
\int _0 ^9 (x-\floor{x})\dd x &=
\int _0 ^1 (x-\floor{x})\dd x + \dots + \int _8 ^9 (x-\floor{x})\dd x \ &=
\int _0 ^1 (x-0)\dd x + \dots + \int _8 ^9 (x-8)\dd x \ &=
\sum _{i=0} ^8 \int _i ^{i+1} (x-i) \dd x
\end{align*}
right?
,w graph (x-floor(x)) from x=0 to x=5
forest sinew
i think so but i may be insanely wrong 
either way you can think that floor(x) is just like
removing the foot of a large rectangle with a triangular cap
think of $\int _a ^b x \dd x$
warm shaleBOT
jan Niku
forest sinew
but for every 1 distance you go in x
you remove the largest vertical rectangle you can
idk if that visual helps
,w graph floor(x) and x from x=0 to x=5
warm shaleBOT
forest sinew
leaves a bunch of triangles
forest sinew
**jan Niku**
now im thinking this is wrong but oh well
fading birch
Ehhh I’ll follow suit for now
I literally saw this only once the entire year and did such a acute chronic avoidance of it I would very much diagnose myself with something
If we could have a second voice to double confirm it’d be nice tho
forest sinew
ah, the integration works out okay
fading birch
Thanks!
forest sinew
it ends up as $\int _0 ^9 (x -\floor{x}) \dd x = \sum _{i=0} ^8 \frac{i^2}{2}$
warm shaleBOT
jan Niku
forest sinew
the area of a triangle
😌
if you integrate under the sum
it telescopes a bit i think
well theres a lot of cancelation
fading birch
I’ll double read everything you messaged since I have to go now, would it be alright if I DMed you if I run into an issue?
forest sinew
sure
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dry egret
obtuse pebbleBOT
kind hawk
where is a t+2 ?
dry egret
well, there is (t-2)t + (t-2)2
kind hawk
there is a -(-2) hidden
dry egret
where is that coming from
kind hawk
-[(t-2)t-(t-2)2] = -(t-2)t + (t-2)2
gilded needle
don't forget there's a minus sign that applies to both terms when you apply the distributive law
to -(t-2)(t-2)
the minus sign out in front
dry egret
-[(t-2)t-(t-2)2] = -(t-2)t + (t-2)2
this cant be right
glacial mica
Can someone explain me why the second derivative can be used to determine extrem points?
dry egret
-(t-2) + (t-2)2 will not even give you a quadratic
kind hawk
what kind of weird questions are that
dry egret
what kind of weird questions are that
the SAT
kind hawk
yeah dunno. super weird question. I don't really know what they want. seems like they want something of the form 8+ (factored thing)
so with the factors you can easily see that if s=1.5 then d(s)=8
hexed blaze
That's truly odd question
How distance is represented in velocity but not time
obtuse pebbleBOT
@dry egret Has your question been resolved?
dry egret
yeah dunno. super weird question. I don't really know what they want. seems like...
how do I do this question?
kind hawk
do you know how to factor the sum of cubes?
dry egret
do you know how to factor the sum of cubes?
ive forgotten
kind hawk
otherwise you could just multiply out the RHS and then compare
dry egret
wait i know how to factorize
dry egret
otherwise you could just multiply out the RHS and then compare
yeah Ive forgotten, could you show me?
kind hawk
do you know how to multiply out brackets?
dry egret
Yes
kind hawk
then do that
dry egret
then do that
done
kind hawk
and what did you get?
dry egret
x^3-bx^2+9x+bx^2-xb^2+9b
kind hawk
and simplify
dry egret
x^3+9x-xb^2+9b
kind hawk
now compare coefficients
dry egret
now compare coefficients
wdym bro
kind hawk
what is the coefficient of x on the LHS
what is the coefficient of x on the RHS
they need to be equal
hexed blaze
x^3+9x-xb^2+9b
Now think
The LHS is just x³+b³
While the RHS is x³+9x-xb²+9b²
So something must cancel to each other right
hexed blaze
What should be cancelled you think?
dry egret
i dont know, but i've figured it out anyways
hexed blaze
lol
dry egret
what is the coefficient of x on the RHS
i took this guys advice
they have to be equal to each other
hexed blaze
Yes
kind hawk
two polynomials are equal if and only if all of their coefficients are equal
hexed blaze
That's why to make them equal, you must cancel 9x and xb²
So 9x=xb² or b=3
They say b>0 so remove b=-3
dry egret
yeah
dry egret
two polynomials are equal if and only if all of their coefficients are equal
how can you tell if this is the case
kind hawk
if you factor out the x you get x^3+(9-b^2)x + 9b^2 on the RHS. on the LHS the coefficient of x is 0, so we get 0=9-b^2
hexed blaze
Also aren't you supposed to memorize a³+b³=(a+b)(a²-ab+b²)?
kind hawk
yeah but they forgot so what are you gonna do
dry egret
Also aren't you supposed to memorize a³+b³=(a+b)(a²-ab+b²)?
probably
hexed blaze
I think it depends on country
dry egret
but i didnt learn that
In my school
i dont go to an american school, so the logic itself is new
kind hawk
you could also just use polynomial division on x^3+b^3 divided by x+b to get the factorization again
hexed blaze
Now you should memorize them
Would be helpful dealing limits many years after for you
dry egret
Also aren't you supposed to memorize a³+b³=(a+b)(a²-ab+b²)?
what about a^5+b^5
dry egret
and a^4+b^4 is (a+b)^2(a+b)^2 then
hexed blaze
No
Well first you must learn that (a+b)²≠a²+b² (only exception is when either a or b is 0)
Certainly a⁴+b⁴≠(a+b)⁴
dry egret
ah
kind hawk
a^4+b^4 has no nice factorization. similar to how a^2+b^2 has no nice factorization
hexed blaze
If you want to factorize them for literally no reason then you must learn more
dry egret
where do I learn this my guy
hexed blaze
You don't learn now
dry egret
but I must
sleek mantle
I "simplified" the problem to this...
dry egret
how do I factorize a^2+b^2
sleek mantle
i have no idea lol
dry egret
i have no idea lol
we figured it out
dry egret
what level is that for
hexed blaze
Not really the level matter but the purpose
dry egret
I may need it
hexed blaze
Nah
dry egret
this test has tricky asf questions
dry egret
okay
sleek mantle
is this algebra 2?
obtuse pebbleBOT
@dry egret Has your question been resolved?