Anyway, the point is that
#help-0
wild trail
alpine sable
Ah
wild trail
You need to know if you want pivot columns of original matrix or the augmented matrix
alpine sable
Augmented
alpine sable
Okay, thank you!
wild trail
Yeah, you count the last column also, you can look here for info - https://math.stackexchange.com/questions/1132929/do-entries-in-augmented-columns-count-as-pivot
lone heartBOT
@alpine sable Has your question been resolved?
austere copper
lone heartBOT
austere copper
i tried to add it together and factorise it
but couldnt factorise
did i do the wrong thing?
crimson totem
why are you factorizing it
crimson totem
you need the coeffecient of x not 1/x
austere copper
i got 60x^4+4x^2+9 what do i do next
outer swallow
you want the coefficient of x. so what number is x getting multiplied by?
austere copper
you want the coefficient of x. so what number is x getting multiplied by?
idk, i got a plus in the equation so how do i write that
i probably did it wrong hold on
crimson totem
i might be wrong but the answer should be ||Not telling ans cuz math|| since coefficient of x is being asked and that is the only option making sense to me
austere copper
what am i mean to with the squares and cubes here
serene junco
are you sure you sent the right picture?
austere copper
yeah
median oar
The coefficient of x is the constant that multiplied x
austere copper
is it just 1/3
outer swallow
yes
austere copper
💀
median oar
Yep
outer swallow
lmao
lone heartBOT
outer swallow
haha no coefficient just means what costant is getting multiplied
lone heartBOT
Available help channel!
high ether
we can always find an inf in R if we choose any set of numbers?
vale wigeon
yes, every subset of R that is bounded from below has an infimum.
tame tangle
Do you want to generalize for any set or intervals specifically?
high ether
for any sets not in R
idk..
what's the property we're using in R that allows us to find an inf
always
from any sets of ordered things
completeness?
tame tangle
completeness?
Yes, a corollary of that
high ether
So how do we justify that the natural numbers also have this property
ofc N isnt complete
or is it idk
high ether
yes, every subset of R that is bounded from below has an infimum.
And can we always find a seq that goes to the inf?
in {1,2,3} for example the seq would be just Un=1?
tame tangle
So how do we justify that the natural numbers also have this property
$\mathbb{N} \subset \mathbb{R} \ \mathbb{N} \neq \phi $
tame tangle
in {1,2,3} for example the seq would be just Un=1?
Yes
high ether
$\mathbb{N} \subset \mathbb{R} \ \mathbb{N} \neq \phi$
ocean sealBOT
dabble
tame tangle
From what i remember, completeness says that every non empty bounded subset of R has a sup (and thus inf) in R
high ether
yeah i see
so we have 2 choices, either the inf is in the set or we get arbitrarily close to it
tame tangle
Yes
vale wigeon
$\mathbb{N} \subset \mathbb{R} \ \mathbb{N} \neq \phi$
\emptyset or \varnothing but not phi
tame tangle
Here to help 😄
vale wigeon
And can we always find a seq that goes to the inf?
yes we can
high ether
wait but lets say we have a function defined on each element of a set
and it's constant 1
can i say that since theres a seq going to the inf
then f(inf)=1 also
if f continuous
tame tangle
Yes, I believe so
lone heartBOT
high ether
.reopen
lone heartBOT
✅
high ether
Yes, I believe so
one more, if we know a point is isolated from the set and we suppose it's the inf
do we know that the inf then is certainly reached?
meaning suppose x1 is the inf and we know that there is no element in A near x1
are we sure that x1 is in A
desert zephyr
I'm pretty sure infimum and supremum do not have to be in the set itself
high ether
yeah, i am saying if they're isolated
desert zephyr
Ah like that 🤔
high ether
then i think they have to be
otherwise there's certainly another element that can be the inf
raven haven
isolated points must be elements of the set
tame tangle
Actually, they have to be "very close" to the elements of A otherwise that will not be an inf
high ether
no i mean if we're not its in A
raven haven
if p not in A then it can't be isolated
high ether
we're just sure that the points in A are all isolated
lone island
ofc N isnt complete
Except it is
high ether
and A not empty
lone island
Which is quite interesting
raven haven
right
high ether
Which is quite interesting
are you srs
raven haven
$\original$
ocean sealBOT
DerpZ
high ether
now I'm interested
i definitely am
lone island
Since it challenges the usual intuition of a complete space
high ether
Since it challenges the usual intuition of a complete space
Well can you explain
lone island
Well
lone island
Every Cauchy sequence must eventually converge
And it must converge to a number in N
raven haven
if s = infA and s is an isolated point of A then s is in A
lone island
Which means it's complete lel
lone island
Yea
tame tangle
Which means it's complete lel
$\mathbb{N}$ doesn't converge KEKW
ocean sealBOT
Void Walker
lone island
N got an even stronger property actually
EVERY subset of N got a min
That's easy to see coz all or bounded below by 0
But still 
tame tangle
EVERY subset of N got a min
Nope, not in general
raven haven
dabble this is an analysis course?
high ether
Which means it's complete lel
So thats why it has the same properties as R?
high ether
Nope, not in general
what?
lone island
The property you're using in R is the least upper bound property
raven haven
it's wrong
high ether
dabble this is an analysis course?
Yeah kind of. Differential equations
lone island
Which is a corollary of completeness
raven haven
ah
lone island
Actually
high ether
tho i have some lacking in my knowledge
lone island
R is constructed specifically to have the least upper bound property lmfao
high ether
I meant his argument was wrong, conclusion is correct
why? every set bounded from below has an inf?
tame tangle
why? every set bounded from below has an inf?
But not a least element
raven haven
this is easy to see, consider (0, 1)
tame tangle
I assume he meant least element by min
lone island
R is constructed specifically to have the least upper bound property lmfao
I really want you to focus on this
high ether
Ah. Then ill go back to my question. if we're just sure that the points in A are all isolated and A not empty and bounded from below
is the inf in A?
high ether
I really want you to focus on this
Yeah i see, we took Q and completed it
lone island
Yep
raven haven
is the inf in A?
still not necessarily
lone island
Coz numbers that can't be rational kept appearing
lone island
Which was quite annoying
lone island
not necessarily
Take {1/n for all n in N}
tame tangle
What is meant by isolated?
lone island
high ether
Take {1/n for all n in N}
fuuck
raven haven
an isolated point is not a limit point
tame tangle
Okok
lone island
beat me to it
This is a very standard counterexample
high ether
What is meant by isolated?
if i take a point, there exists an r>0 such that the interection between my set and the [point-r,point+r] is point
raven haven
yeah I was right about to type it up :(
lone island
4/5 using this example worked lol
raven haven
[point - r, point+r] is wrong
lone island
What is meant by isolated?
Isolated means you can put an open set around it that contains only that point
high ether
[point - r, point+r] is wrong
mm.. why?
lone island
So for example
raven haven
not an open set
lone island
You can put (0.75, 1.25) around 1
high ether
why does it have to be open
raven haven
definition
lone island
And that only contains 1
high ether
thats fine lol for our purposes
lone island
Take {1/n for all n in N}
And no other from this set
raven haven
fun exercise is to prove that every point in that set is isolated
if you're interested dabble, read an analysis book
I shill understanding analysis but there's a few others
lone island
rudin 
raven haven
but rudin is great to take exercises from
raven haven
ooh
tame tangle
Yes please
lone island
raven haven
rudin chapter 3?
raven haven
for R it would be |p_n - q_n| converges
lone island
It's the outline for the Cauchy construction of the reals
tame tangle
I don't know metric spaces, so I'm out for this
raven haven
ah okay a metric space is just st d obeys the triangle inequality
lone island
ah okay a metric space is just st d obeys the triangle inequality
It's a set with a metric, more precisely
raven haven
wonder if we can do this in R and just replace
|pn - qn| with d(pn, qn) 
just gotta make p_m - q_n converge
ok 23 is not bad
lets see 24
we should rope grass in
lone island
Grass doesn't know Cauchy stuff yet
raven haven
nah we can shove it down his throat
lone heartBOT
@high ether Has your question been resolved?
static lion
Hello. I have a simple assignment but I don’t have confidence to consider it 100% correct
static lion
The problem is: Imagine we have a deck of 52 cards. How many ways of choosing 6 cards out of 52, so that 3 of them would be Kings and 3 other would be cards of different colors
C(4,3) is the number of choosing 3 kings out of 4
C(48,3) is number of choosing 3 cards out of 48 left
I multiply them and divide by 4, because there are 4 ways where 3 cards would be of 1 color
Is it right?
alpine sable
I multiply them and divide by 4, because there are 4 ways where 3 cards would be...
probability?
lone heartBOT
@static lion Has your question been resolved?
prime badge
it's not correct at the point where you divide by 4
but it's good up to that point
try to only multiply
static lion
If I only multiply then I include a moment where 3 cards are of the same color
C(48,3) does not Guarantee that 3 out of those cards will have unique colors
Now that I think of it, the division on 4 also doesn’t guarantee that we won’t have 2 of the same color cards
static lion
You mean I have to do C(4,3) once again?
C(4,3) * 2?
prime badge
i think that's what they mean, 3 different, is not the same as "not all the same"
static lion
i think that's what they mean, 3 different, is not the same as "not all the same...
Yeah, the difference should be mainly in color
Like for example: king of Hearts, King of diamonds, King of spades, 9 of spades, 9 of diamonds, 9 of crest
Also sorry if spades diamonds and stuff is not called „color“ I just don’t know another term for it
prime badge
ok yeah good
that's what i thought from the start cuz they are different colors when i played poker
static lion
Oh nice)
static lion
And why do I need to 12^3?
static lion
13 cards in a suit minus the king
Oh
prime badge
and you already chose the suit
static lion
So in the end: C(4,3) kings * C(4,3) suits * 12^3, because 13-1 we took the king and why in ^3?
Because 3 cards of different suits right?
prime badge
yeah
static lion
Okay thank you very much! I will try to Pass this assignment to my teacher, hopefully it’s correct this time. He is handing me back this assignment for 3rd time already
prime badge
a school teacher?
static lion
No, a university professor
The subject is a special cases of discrete maths or something like that
prime badge
i was like combinatorics in russian school чзх
static lion
i was like combinatorics in russian school чзх
No we had a simple combinatorics like exercise with black and white balls in a bin for example
But the advanced stuff started in Uni, also are u Russian?
prime badge
yeah
prime badge
xd
static lion
@lone heart close
prime badge
.close
lone heartBOT
lone heartBOT
Available help channel!
kindred jacinth
lone heartBOT
kindred jacinth
Did i do this right ?
and i was wondering what the second part wants me to do
jade dagger
I guess you have to find W_0 root the zeroth root as W starts from 0,1,2…
kindred jacinth
I guess you have to find W_0 root the zeroth root as W starts from 0,1,2…
so root2/2(cos 75+360n +iSin 75+360n) and sub in 0,1,2 for n?
jade dagger
so root2/2(cos 75+360n +iSin 75+360n) and sub in 0,1,2 for n?
Shouldn’t it be just (75 + 0x360) /n= 75 as we are finding the zeroth root?
kindred jacinth
ah yes since there is no power on the w
jade dagger
Also shouldn’t degrees be converted to radians? I usually write in radians
kindred jacinth
Also shouldn’t degrees be converted to radians? I usually write in radians
it normally would ask u to put in radians but i dont see it here
lone heartBOT
lone heartBOT
Available help channel!
icy coral
How did it go from 1 to 2
lone heartBOT
How did it go from 1 to 2
icy coral
icy coral
6a - 2a = 4a
Yes i got that part
icy coral
Righttt i do know that
main kraken
ln3a - lna = ln(3a/a) = ln3
.
icy coral
Yes thank you i just didnt think to do the opposite lol
icy coral
. Close
main kraken
.close
icy coral
.close
alpine sable
I need help with an arithmetic question
lone heartBOT
I need help with an arithmetic question
alpine sable
The question is
I have the formulae provided but it’s telling me that my answer is wrong
wind cloak
$\Sigma_n = \frac{n}{2}(2a + (n-1)d)$
raven haven
thats giving the answer tho
alpine sable
Yes, I have that formuale
raven haven
oh okay
alpine sable
I just don’t know how to use it
raven haven
find the difference and the first term and just plug
raven haven
$\Sigma_n = \frac{n}{2}(2a + (n-1)d)$
wrong, S_n is the group of permutations on n things
wind cloak
,calc 25(6 + 49*4)
ocean sealBOT
Result:
5050
I have the formuale and subbed in, my calc can’t solve it though
raven haven
er what
ocean sealBOT
NEONPerseus
lone heartBOT
raven haven
i love how you changed it because of my meme response
wind cloak
wind cloak
Didn't know that
raven haven
well I was doing algebra just now so
wind cloak
I always used P(a, b)
wind cloak
Well never used P(a, b) tbh
raven haven
what is P(a,b) anyway
wind cloak
Always did b!C(a, b)
raven haven
ahh
wind cloak
what is P(a,b) anyway
$\frac{a!}{(a - b)!}$
ocean sealBOT
NEONPerseus
raven haven
like $^n P _r$
ocean sealBOT
DerpZ
alpine sable
.reopen
lone heartBOT
✅
alpine sable
My calculator cannot do these equations
What is the command to calculate?
Sorry
I need to do
30(2x100+(60-1)6)
raven haven
.close
shut pelican
how do i solve this problem? the inverse is f(y) = (y^2)+2, but i don't know what to do with the domain and range
crystal mason
how do i solve this problem? the inverse is f(y) = (y^2)+2, but i don't know wha...
is it?
,w graph y^2+2
,w graph 2-sqrt(x)
placid swallow
how do i solve this problem? the inverse is f(y) = (y^2)+2, but i don't know wha...
Dom(inv_fn) = range(fn)
crystal mason
,w graph x^2+2 and 2-sqrt(x)
ocean sealBOT
flint pecan
how do i solve this problem? the inverse is f(y) = (y^2)+2, but i don't know wha...
I don't think that's the invers
crystal mason
looking at the graphs it doesn't seem like its mirrored on f(x)=x
shut pelican
wait i found it its (-y+2)^2 haha
crystal mason
mhm?
stiff tree
lone heartBOT
stiff tree
How to do
flint pecan
translate first
stiff tree
But
flint pecan
oh nvm
stiff tree
Theres english
flint pecan
yeah, sorry
what's the hypotenuse, opposite, and adjecent for triangle NKL when the reference angle is x?
flint pecan
oof i'm sorry
flint pecan
KL is 67.5
yeah you're right
stiff tree
How do i find <z
flint pecan
you can find tan(z) since you know tan(y)=1
flint pecan
good
flint pecan
a right triangle with a tanjent value of 1 is a isoceles right triangle
flint pecan
nice
stiff tree
How is that 3 marks
flint pecan
lol i have no idea
stiff tree
By any chance is this correct
lone heartBOT
@stiff tree Has your question been resolved?
lone heartBOT
@stiff tree Has your question been resolved?
flint pecan
How do i find y
god i'm so sorry
you can find angle SOR since its the half of the cantral angle SOQ
so y would be 90-SOR
dim vine
Where have I made a mistake/ what should I do next? Not sure how to progress with that e^w being sat there
violet swift
What would be angle ADM in this question?
pliant cedar
What would be angle ADM in this question?
u must get ur own channel
violet swift
How?
pliant cedar
read #❓how-to-get-help
dim vine
Where have I made a mistake/ what should I do next? Not sure how to progress wit...
sorry for using k as well. That may go against certain peoples' principles
Where have I made a mistake/ what should I do next? Not sure how to progress with that e^w being sat there
spare moss
Hi
last ether
Does your log default to base e
spare moss
Can someone explain how to solve this problem
last ether
dim vine
Does your log default to base e
U mean like it could be log base 10? I'm pretty sure it means log base e
last ether
U mean like it could be log base 10? I'm pretty sure it means log base e
I mean I'm hoping it's not the default log, so I'm treating it as ln
Oh I see the issue
The denominator shouldn't even be there
The derivative of ln(u) is 1/u du
dim vine
The derivative of ln(u) is 1/u du
Just seen. Stupid mistake
Have a good day
👍
.close
smoky fulcrum
is it possible for a function to have 2 or more max/min point?
plain flame
smoky fulcrum
but is this possible?
echo socket
Like heavy said, yes
fiery reef
A ticket machine in a car park takes $1 coin and $2 coin. A ticket cost $3. The probability that the machine will accept a particular $1 coin is 0.9 and that it will accept a particular $2 coin is 0.8.
Pritam has one $1 coins and two $2 coins. Find the probability that Pritam will get a ticket.
modern sedge
A ticket machine in a car park takes $1 coin and $2 coin. A ticket cost $3. Th...
Well so the $2 coin can fail at most once, and the $1 coin cannot fail (By failing I mean not being accepted)
fiery reef
Well so the $2 coin can fail at most once, and the $1 coin cannot fail (By faili...
how can you say that that $2 coin can fail at most once?
lone heartBOT
@fiery reef Has your question been resolved?
alpine sable
$25x^2 +4$
lone heartBOT
$25x^2 +4$
ocean sealBOT
AllUtility
mortal trellis
over C or over R
rare gale
alpine sable
you cant either over C assuming you want some integers
oh wait you can i am just blind oops
alpine sable
over C or over R
what does this mean
mortal trellis
do you want to factor it into a product of real polynomials
alpine sable
do you want to factor it into a product of real polynomials
sure
mortal trellis
or are you ok if they are complex polynomials
alpine sable
factor completely
alpine sable
ok
mortal trellis
so usually R or C
if you want to factor it over R, you can't factor it further
over C you can
alpine sable
over C you can
ok how
mortal trellis
you can factor a^2+b^2=(a+bi)(a-bi) over C
alpine sable
you can factor a^2+b^2=(a+bi)(a-bi) over C
what is a and b here
alpine sable
5x^2 + 2
mortal trellis
no
mortal trellis
no
alpine sable
alpine sable
(5x+2)(5x+2)
would be 25x^2 +20x+4 try again
mortal trellis
so 25x^2 + 4 = (5x)^2+2^2 which is now in the form a^2+b^2 with a=5x and b=2
so now we can use the formula from before
and factor it as (5x+2i)(5x-2i)
alpine sable
what is the i ?
mortal trellis
do you know what complex numbers are
alpine sable
do you know what complex numbers are
nno
lone heartBOT
@alpine sable Has your question been resolved?
steady salmon
is it right way to apply comparison method?
lone heartBOT
is it right way to apply comparison method?
merry depot
no.....
steady salmon
why
merry depot
What you showed isn't what you think it is.
$\frac{2^n+3^n}{3^n+2^n} = 1$\
So $\sum \frac{2^n+3^n}{3^n+2^n} = \sum 1 \to \infty$
ocean sealBOT
Zybikron
steady salmon
every term of second series is bigger than first ones yes?
merry depot
sure
steady salmon
graph of this will be y=1 straight line yes?
then why it cant be right way to apply this method
it will always be under 1
merry depot
1/2 is always under 1 too
tacit arch
,w int from 0 to inf of 1 dx
ocean sealBOT
merry depot
if I add 1/2 to itself infinitely it doesn't converge
you basically showed your series is 'bounded' by infinity, which is basically always true.
You got no information about the convergence/divergence of your original series.
steady salmon
ohh yeah got the point
then which method can i use to find the divergence or convergece for the left series
merry depot
it's the right idea. you want to find a series that is larger than yours term by term, but then show that your larger series converges.
That gives you that your oroginal series converges.
What happens if you just drop the 3^n in the denominator?
final depot
Help
tacit arch
try using quotient rule for g'(x) first
final depot
I know the quotient rule but where is the other value?
tacit arch
I know the quotient rule but where is the other value?
what "other value" ?
you just need x=2
final depot
I thought quotient rule requires a numerator and denominator
merry depot
yeah. x is in the numerator, f(x) is in the denominator.
tacit arch
When I differentiate them they both become 0
you don't plug in the number BEFORE differentiating
g'(x) is a function
final depot
so 2/g'(2)?
I'm sorry I get confused easily
Sorry for some reason my maths book only has examples of quotient rule questions involving sin and cos
tacit arch
so 2/g'(2)?
your answer for g'(x) shouldn't have g itself
$\frac{d}{dx} \left( \frac{x}{f(x)}\right)=$
ocean sealBOT
riemann
tacit arch
your answer should be in terms of $f, f'$
ocean sealBOT
riemann
final depot
I think I see my mistake
I think I followed the formula wrong
Where am I going wrong?
tacit arch
you don't plug in the number BEFORE differentiating
.
maybe separately write $u'(x), v'(x)$ first
ocean sealBOT
riemann
final depot
tacit arch
what's $x'$
ocean sealBOT
riemann
ocean sealBOT
riemann
rapid prairie
Hello I am stuck on this problem, not sure where to start
lone heartBOT
Hello I am stuck on this problem, not sure where to start
rapid prairie
alpine sable
what is the domain of f(x)=|x|?
rapid prairie
All real numbers?
rapid prairie
what would be g(x)?
Nvm lol I got it thank you for your help !! Really appreciate it. Have a good day !
.close
tight thunder
lone heartBOT
tight thunder
is this true?
candid mantle
indeed it is
tight thunder
very nice
candid mantle
🤠
candid mantle
yep
tight thunder
sarrus rule nice
candid mantle
so true
celest stump
whats sarrus rule
candid mantle
linear alg
candid mantle
sum of normal diagonal - sum of antinormal diagonal
idk if antinormal is the right word but it makes sense to me
celest stump
what math is this?
candid mantle
it make death to all
lolol
tight thunder
hey
candid mantle
my first linear alg prof always called it killing
tight thunder
please give me tips
candid mantle
for making matrices rref
tight thunder
woah
candid mantle
now we KILL this row
tight thunder
😄
candid mantle
with his vietnamese accent
tight thunder
drama obama
candid mantle
funny
tight thunder
give me professional tips
wary stream
give me professional tips
Don't fail
tight thunder
i need to learn from matrix to integrals
what is best stratgy?
solve every single online homework I have archived?
If i didnt start doing this i would try apply laplace progression on 3x3 matrix
candid mantle
best way to learn math is to try and fail
wary stream
Practice is good
tight thunder
yes
candid mantle
ie practice
tight thunder
i tried to solve 3x3 determinant with laplace
and now i learned sarrus rule
artifical inteligence say this
wary stream
That's using 2 x 2 minors
tight thunder
wtf
wary stream
It's a fairly easy method
tight thunder
I already tried solve with minors
candid mantle
🤠
wary stream
wary stream
its like laplace progression no?
I think it's that way
tight thunder
so i just do minor + minor + minor
each minor multiplied by value of that element?
wary stream
What?
tight thunder
because AI told me i cant use laplaces method for this
wary stream
tight thunder
is this how to solve determinant of 3x3 using minors?
wait
he was using sarrus rule for the 3x3 matrix
he can only use laplace expansion for 4x4 right?
wary stream
he was using sarrus rule for the 3x3 matrix
That's a different method
wary stream
he can only use laplace expansion for 4x4 right?
No, you can use it for any size matrix, I believe
lone heartBOT
Show your work, and if possible, explain where you are stuck.
wary stream
You can't do this to find the determinant, it's only rows or columns, not diagonals
wary stream
The reason why this is wrong, is the signs are wrong
tight thunder
yes i didnt do that
i did for second row
the diagonal circles were my wrong understanding of sarrus rule
wary stream
i did for second row
The sign chart for the second row is different compared to the first row
wary stream
If you look up Laplace expansion, part of the formula is (-1)^(i + j)
And that's the sign for that coefficient
tight thunder
hmm
but i always thought its unncesary
i can just apply the
and so on?
is it as such?
wary stream
So because you used the second row, that element in the second row, first column is (2, 1) so (-1)^(2 + 1) = (-1)^3 = -1
wary stream
So the sign of that, when using Laplace expansion, is negative, but you made it positive
lone heartBOT
@tight thunder Has your question been resolved?
twilit cypress
lone heartBOT
twilit cypress
can anyone give me a hint as to how to tackle this one?
alpine sable
use the binomial distribution
twilit cypress
Is there a way to do this one without binomial distribution? I know we will cover binomial distribution, but we haven't covered it yet, which makes me think that he wants us to use a different strategy. I am thinking the instructor can choose from 4/10 questions, then 3/10, then 2/10, so multiplied together would be 3/125.....but I am not sure if this is even a valid process
alpine sable
yes that's fine
exotic ridge
So far, I've inserted the basis vectors inside of a matrix, then row reduced. I'm not entirely sure how to proceed from here, especially because I don't want to guess and check to see if I can stumble into a correct linear combination
exotic ridge
.close
alpine sable
Hi! So I'm trying to help a friend of mine with her math homework, but for some reason, I never learned absolute value graphs properly😅
Basically, I'm asking about a particular integral of an absolute value of x^2-1. Like I said before, I never really learned absolute value domains & ranges properly. I know what the graph itself looks like for the absolute value of x (the parent function) only, but I don't know anything when it comes to mixing up with other types of functions (linear, quadratic, cubic, exponential, trig like sine, cosine, or tangent with AN ABSOLUTE VALUE) & finding their domains/ranges (this also includes the parent function of |x|). So my friend's question, which also turned out to be a good question for me as well since I also struggled with this before, is....."From only an equation, like |x^2-1| in this case, how do you find that domain of x-values that that graph becomes positive in (since the graph itself doesn't pass through the x-axis due to the absolute value.........look at the 2 Desmos graphs from before + after with the absolute value & see how it changed things.......like how the 2nd one matches that of the example purple paged problem with the graph to the right) where it would usually become negative (in terms of behavior passing the x-axis normally)? Like how do they know that for x^2-1, it's domain is 1 <= x <= 2?
/ Like how they know that it's x^2-1 for 1 <= x <= 2? The same goes for the other. Like how do they know that for -x^2+1, it's domain is 0 <= x <= 1? / Like how they know that it's -x^2+1 for 0 <= x <= 1? So like how do you know for each one (x^2-1 vs. -x^2+1) are between those specific domains/values? Is it really just by looking at the graph to the right or is there some mathematical pathway explanation? To me, it looks mathematical because I don't get what they're doing that part in red all the way at the end with their explanation versions for both? Adding on to that, why are all the inequality signs "= to" as well?
Rather than me continuously asking back & forth, I think the best way to explain this to me all in one go is to start from the parent graph of |x| (analyze everything about that & in order to integrate explicitly, explain how these representations from the parent graph correlate to everything in this problem specifically). I'm a visual learner, so if you can either write out everything on a piece of paper/iPad (like parent graph of |x| vs. integral of an absolute value of x^2-1) or make a short video talking about everything step by step, that would honestly be great & end with a summary response to our question, we would greatly appreciate it.
Please & Thank you!
alpine sable
last ether
What in gods name
Get your friend in here
And ngl we ain't gonna read all that
Tell me in a single sentence what's the issue
alpine sable
Yeah can u make a tldr
alpine sable
Tell me in a single sentence what's the issue
Look at the last picture then
And my friend doesn't have Discord. Long story why she doesn't, so I decided to ask it here.
last ether
Well okay the thing about $x^2-1$ is that it has a region that's negative. Using analysis and function behavior it's easy to tell that from $x \in (-1, 1), x^2 - 1 < 0$. The absolute value will make it behave like $1-x^2$, but only for that interval.
ocean sealBOT
Umbraleviathan
alpine sable
What's that E symbol? It looks familiar from the bot. Uhhhhhhhhhhh, explain it in different words
Here is the idea: @alpine sable
last ether
Ngl it'll be a lot easier if your friend got discord
alpine sable
She can't. Parent restrictions. Don't ask.
An absolute value function can be represented like this
[
|x| = \begin{cases} \hphantom{-}x, &\quad x \geq 0 \ -x, &\quad x < 0 \end{cases}
]
In its most basic form. This basically tells us that an absolute value function is just a collection of multiple functions 'sewn' up together in a sense. Aka piece wise functions.
\vspace{5 mm}
Those piecewise representations of the absolute value function can be determined by their 'roots'. Since we are looking at when exactly the insides of the absolute value function are going to be positive and negative
ocean sealBOT
Lixera
alpine sable
For your case, for example
You have |x^2 -1|, x^2 -1 will always be positive for values of x larger than 1 right? Since 2^2 - 1 = 3 is positive for example
While a value lesser than 1 is in fact negative such as (0.5)^2 -1
This helps because our goal is to turn the absolute value function into its piecewise form
We are considering values of x greater than 0 since the lower bound of the integral is 0. So we can disregard the other root of -1
alpine sable
All in all, we split the bounds for 0 to 1 and 1 to 2 because 1 is one of the roots of the absolute value in your integral
It being a root makes us able to split it into cases of where the function is either positive or negative for the interval surrounding it
Also are you here or am I just talking to myself
Okay I'm talking to myself so I will stop
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Also are you here or am I just talking to myself
I'm here. I was waiting till you were finished.
Let me read it all now
Yeah it's really hard to just write a lot of stuff at once and expect you to get it instantly so just tell me what you don't understand
alpine sable
You have |x^2 -1|, x^2 -1 will always be positive for values of x larger than 1 ...
Don't you mean larger than 0, not 1? Like x^2-1 >= 0?
No I'm just talking about when x^2 -1 is positive
It will get positive for values lesser than -1 and greater than 1 , but again we disregard the -1 here because your integral starts from 0 to begin with
By any chance, is there a way to voice call about this problem, that way it'll be easier to talk it out & understand this type of problem?
Uh sure yeah
Idk how to set it up unless you want to do it individually outside of the server....
Oh yeah they disabled vcs in the server
Okay well
I will just call u normally
ok
south stream
i need help with this question. A farmer has 200 meters of fencing and wants to fence off a rectangular fence that borders a
straight river. What dimensions of the field will give the maximum area? Be sure to define
the variables
south stream
.close
bronze helm
Looking at the y-axis
It’s the total amount of rain over the time period
D is a slower increasing graph compared to the rest the other graphs increase faster meaning that as time increases the total amount of rain increases
still condor
lone heartBOT
still condor
hm ok
so in this scenario would it be 4 then since its its 4 approaching from the left?
.close
willow brook
Any hints on how to solve this conics problem
lone heartBOT
Any hints on how to solve this conics problem
willow brook
I see there is some symmetry witj the parabolas with their vertex and points coinciding
But idk how to exploit it
They alao want us to only have the intersection between x=0 and x=1 but idk how to restrict that
lone heartBOT
@willow brook Has your question been resolved?
willow brook
(if someone replies, can you ping me)
lone heartBOT
@willow brook Has your question been resolved?
timber wyvern
(if someone replies, can you ping me)
hi
it seems you found the right equations for the parabolas
i believe you made a mistake on this step
but its the right thing to do, even though it seems ridiculous to have x^4
quaint elbow
I have zero clue how I do this
jagged violet
lone heartBOT
jagged violet
What do the d and p variables represent
dusty prairie
i need help with question 2 of https://cdn.artofproblemsolving.com/attachments/b/a/26f2119e4d1d603c222cc3ee64c4e07ba8bb37.pdf
pliant cedar
i need help with question 2 of https://cdn.artofproblemsolving.com/attachments/b...
you must get your own channel
dusty prairie
how?
pliant cedar
please read #❓how-to-get-help
pliant cedar
do u go to help forum?
you must post your question in one of the unoccupied channels
pliant cedar
What do the d and p variables represent
it says integrate 1/p^2 wrt p, as p varies from 4 to x^3
and differentiate that result wrt to x
jagged violet
But why is the d there
ocean sealBOT
SilverSoldier
pliant cedar
**SilverSoldier**
this stands for the integral of the function f(p) wrt p
unique torrent
long axle
alpine sable
help please
alpine sable
lone heartBOT
carmine reef
eh i kind of feel for him that one got buried
fallen verge
ah
carmine reef
but ig he can repost the problem screenshot there too
fierce prairie
yeah you may want to .close and .reopen the old one
fallen verge
my apologies
alpine sable
so not here
lone heartBOT
Available help channel!
sterile rover
f(x)=xsin(1/x) does the function have limiting point 1 or 0, is it discontinous at x=0, or it has no limit?
lone heartBOT
f(x)=xsin(1/x) does the function have limiting point 1 or 0, is it discontinous ...
@sterile rover Has your question been resolved?
pseudo ice
What do you mean by limiting point? As in does the limit exist as you go to zero? For that I’ll say 🥪
As for continuity, as it is, it isn’t defined at x=0 currently
unborn crane
lone heartBOT
unborn crane
How would I solve this here
lone heartBOT
@unborn crane Has your question been resolved?
lone heartBOT
@unborn crane Has your question been resolved?
unborn crane
<@&286206848099549185>
exotic belfry
What can you say about LN and LM?
manic rune
Simplifying square roots—
I have the final answer. I know how to set up the problem, know how to navigate through it a couple of steps, but I don’t understand how the final answer was gotten.
rocky grove
Hmm
Good step is that you divided up 512 into 64*8
Then you applied $\sqrt{ab} = \sqrt a \sqrt b$
ocean sealBOT
VulcanOne
manic rune
Step 3 answer wrong though
Yeah it is weird.. now that I look at it
That’s fine, I don’t have to use that way. I just need to know a good reliable way of simplifying sqrts 😅
rocky grove
$\sqrt{64} \times \sqrt 8 = 8 \sqrt{4 \times 2}$
ocean sealBOT
VulcanOne
rocky grove
**VulcanOne**
This is how you break down root 8
last tendon
If you work with computers enough you should just know that 512 is a power of 2 and you don't need to do this iterative factorization
rocky grove
$\sqrt 8 = \sqrt{4 \times 2} = 2\sqrt 2$
ocean sealBOT
VulcanOne
somber peak
anyone know how to approach question 24
lone heartBOT
anyone know how to approach question 24
flint pecan
It shouldn't be much different from 23
Are you having trouble with seperating the domain?
somber peak
yes
flint pecan
Can you show your work first?
I want to know what you've figured out so far
somber peak
i don't understand how to get started
flint pecan
Then can you show your work for 23?
somber peak
i was only assigned 24 😭
flint pecan
Whattttt 😭
f(|x-5|+2) basically means you subb in t=|x-5|+2
Can you do that and show me what you got?
somber peak
Can you do that and show me what you got?
flint pecan
You're not wrong, but for these kind of questions, writing the domain is very important
somber peak
You're not wrong, but for these kind of questions, writing the domain is very im...
where do i go from here
ocean sealBOT
flint pecan
This would be a more accutlrate expression
somber peak
ouhhh ok where do I go from there
flint pecan
You need to simplify it
Can you simplify these two first?
All you need to do is expand
(Don't expand the thing in the absolute value, though)
somber peak
How do I do that 
somber peak
uhhhh
somber peak
.close
modern lotus
I was thrown off by this sentence for an entire day struggle to understand what it means
modern lotus
I assume it's referring to the equation a≡b(mod m), so when a(mod m)≡b(mod m), a is reduced modulo m? But that doesn't make any reference to the number b?
lone heartBOT
@modern lotus Has your question been resolved?
modern lotus
<@&286206848099549185>
lone heartBOT
@modern lotus Has your question been resolved?
modern lotus
.close
wheat isle
How do I express 2^3(2^n) x 9^3 / 2^4 x 3^n+8 as a prime factor?
rocky grove
I found a better way to phrase your question
"How to simplify until reaching the factors"
Anyways
$\frac{2^3 (2^n) \times 9^3}{2^4 \times 3^{n +8}}$
Is this right?
ocean sealBOT
VulcanOne
rocky grove
Like that?
wheat isle
yea
wheat isle
3^2
rocky grove
So 9^3 = ???