For example the function that alternates between slopes 2a and 0 evenly has infinitely many spikes, has no limit to its derivative, its derivative doesn't ever get close to a, yet its asymptote is ax
#help-10
haughty coyote
grave halo
For example the function that alternates between slopes 2a and 0 evenly has infi...
that makes sense thanks
haughty coyote
So that's why you don't talk about derivatives
Also you have a bit more theory about asymptotic behavior that I think explains your intuition
In the case where f(x) / x -> a, you have a few different cases to consider
If f(x) - ax -> some constant b, then we can say ax+b is the asymptote of f, that's the nice case
If f(x) - ax -> + or - inf, we can't say it's an asymptote because the distance between f(x) and any ax+b is not going to 0, so we talk about a "parabolic branch" (at least in French, but I think it's the same name in English)
If there's no limit, then we can only talk about an asymptotic direction
grave halo
If f(x) - ax -> + or - inf, we can't say it's an asymptote because the distance ...
Je parle francais ducoup tkt pas d'utiliser des termes francais 🙂
haughty coyote
For example the function that alternates between slopes 2a and 0 evenly has infi...
That last case would be examplified by that example, because we only go in that direction, but we don't get closer to the line nor do we stray farther away from it towards an infinite distance
Ok
1 _ Derivation et integration, une première approche.pdf
cf 5, page 31-32
median mesa
obtuse pebbleBOT
median mesa
have to solve for t and the corresponding points (a,b,c) at which the lines intersects the plane
is this allowed given its= to r
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
.close
sturdy rune
Why is the thing highlighted in red always positive?
obtuse pebbleBOT
Why is the thing highlighted in red always positive?
kind arrow
simple question( x = 1)
is y=x-3, y=-4 or y=-2?
obtuse pebbleBOT
simple question( x = 1)
is y=x-3, y=-4 or y=-2?
stark ether
what is 1-3
timid silo
how do I correctly perform reverse chain rule on the following:
obtuse pebbleBOT
how do I correctly perform reverse chain rule on the following:
timid silo
ok in hindsight tbh its a disgusting integral i think id be better off using u substitution
robust sleet
just u sub x-1
timid silo
ye, i can do that
but i thought i could pull it off
in my head
using reverse chain rule
oh u could
it simplifies to 1/2(x-1)^3/2
doesnt it?
yh
.close
devout hatch
if i have f'(x, y) = 0 and f''(x, y) = 0,
does that just mean inflection point for f''(x, y)? (this is for the point 0, 0 for x,y)
soooo does that mean saddle point? i forget things with f(x,y) lol
obtuse pebbleBOT
if i have f'(x, y) = 0 and f''(x, y) = 0,
does that just mean inflection point f...
@devout hatch Has your question been resolved?
eternal bloom
if i have f'(x, y) = 0 and f''(x, y) = 0,
does that just mean inflection point f...
um no.
to show that a point (x,y) is a saddle point, show that grad f = (0,0) and the Hessian is indefinite
devout hatch
um no.
to show that a point (x,y) is a saddle point, show that grad f = (0,0) a...
so wait what does the derivative of 0 or double derivative of 0 represent
royal solar
so wait what does the derivative of 0 or double derivative of 0 represent
second differential?
eternal bloom
so wait what does the derivative of 0 or double derivative of 0 represent
f'(x,y) and f''(x,y) is unclear. are you differentiating wrt the first variable or second?
royal solar
if i have f'(x, y) = 0 and f''(x, y) = 0,
does that just mean inflection point f...
OH YEAH, partial derivatives and contour plots
royal solar
f'(x,y) and f''(x,y) is unclear. are you differentiating wrt the first variable ...
^^
which one are you doing it with respect to,
devout hatch
i thoughttt f'(x, y) was equivalent to f(x, y) derived with respect to x PLUS f(x, y) derived with respect to y
eternal bloom
i thoughttt f'(x, y) was equivalent to f(x, y) derived with respect to x PLUS f...
no
that's div f
devout hatch
whats div f
obtuse pebbleBOT
devout hatch
.reopen
obtuse pebbleBOT
✅
devout hatch
hm, its just this question is saying i need to use the 'second derivative test' to classify the point at the origin... (it says the procedure doesnt work though)
so i guess the second derivative test just doesnt exist? cos how do you find f'(x, y) and then f''(x, y), because ur saying you can only differentiate with respect to one variable, but i'd wanna differentiate for both i thought
robust sleet
u can differentiate for x then for x again, or for y then for y again, or u can diff for x then for y or for y then for x
devout hatch
yeah i know of that but i don't know where to go from there really. the question doesnt tell me what to derive with respect to, thats why i suggested
obtuse pebbleBOT
@devout hatch Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
median mesa
Up to part b, haven't got to much experience using mat lab. I tried coping it in with the xyz value but it was giving errors
obtuse pebbleBOT
Up to part b, haven't got to much experience using mat lab. I tried coping it in...
@median mesa Has your question been resolved?
obtuse pebbleBOT
Available help channel!
lucid sluice
obtuse pebbleBOT
lucid sluice
please can anyone help me
timid silo
Ok so the question needs you to put the triangle in the circle and label the sectors and segments
steel socket
the cubic formula is so large, is there any mapipulation i can do to make it smaller but keep it the cubic formula
obtuse pebbleBOT
the cubic formula is so large, is there any mapipulation i can do to make it sma...
steel socket
the cubic formula is so big i had to write it across two separate lines
the plus in the middle connects the two terms
civic zealot
most versions I've seen use substitutions
steel socket
yes
civic zealot
that trinomial and binomial are the same, so set them equal to p and q
steel socket
im trying to do it without substiution
ik about the substitutions ppl do with p and q, the only difference between the two giant terms is the middle operation sign in each of the cube roots
it just seems like there is a form of notation, or something that could allow me to shorten it without substitutions
If you know a lot about mathematical notation itself pls lmk
civic zealot
then probably not. If there was a simpler way to write it, then it'd be written that way
steel socket
then probably not. If there was a simpler way to write it, then it'd be written ...
i was just wondering if there was an obscure way to do it, some form of notation or a sign that isn't used often, idk
obtuse pebbleBOT
@steel socket Has your question been resolved?
lucid falcon
.close
woeful folio
Hi! How could this be done being both together?
obtuse pebbleBOT
Hi! How could this be done being both together?
woeful folio
Like this i mean (ik best representation lol)
obtuse pebbleBOT
@woeful folio Has your question been resolved?
woeful folio
<@&286206848099549185>
daring rock
What do you mean "both together"?
woeful folio
What do you mean "both together"?
Uh, I can't really explain it in english since its not my first language, but it's like the first exercise combined with the second
Like the first one divided with the parallel lines like in the second one
daring rock
You mean, could you solve for all the individual segments if there were more parallel lines in the first problem?
woeful folio
yeah
i think I'll be fine if I know how to do the first one tho
Should it be 60/40 = x/36?
daring rock
Yes
And I think the answer to your question is yes. The triangles would still be similar and each trapezium would be similar as well
daring rock
I don't know it by that name, but you just have to use the fact that the side lengths are proportional
daring rock
Should it be 60/40 = x/36?
like you did here
woeful folio
I don't know it by that name, but you just have to use the fact that the side le...
yeah I get it
thanks!
daring rock
You're welcome
woeful folio
.close
plush axle
obtuse pebbleBOT
plush axle
Hi I have a question about this hypothesis test
as i dont really know how to approach it
and where to start
especially for my H_0 and H_A
data^
obtuse pebbleBOT
@plush axle Has your question been resolved?
plush axle
<@&286206848099549185>
kindred fractal
Ignore my trash eraser
“A polynomial function with rational coefficients has the follow zeroes. Find all additional zeroes.”
I have to write it in function form
How do I factor these numbers?
-1 + i, -1 - i, √5, -√5
obtuse pebbleBOT
Ignore my trash eraser
“A polynomial function with rational coefficients has th...
kindred fractal
I can figure out the -1 + i, -1 - i part simply because I already did a question like that
But I don’t understand how to factor the square root of 5’s
brave bramble
Factor these numbers?
kindred fractal
Yeah
brave bramble
That's all the zeroes that such a function would have
kindred fractal
Or rather, just write them as (x +3) or the such
I’m not great at wording things
Don’t wanna leave this open while I go sleep so
.close
sage plover
obtuse pebbleBOT
sage plover
thoes answers are wrong!
sage plover
No they are correct
they were marked as wrong
crimson horizon
IJK is inscribed to the diameter
sage plover
180/2
sage plover
90
sage plover
90?
sage plover
157
crimson horizon
Yes
sage plover
now how about IKL
crimson horizon
Arc JK + arc JI = arc KJI (semicircle)
You know a semicircle is 180 degrees
And it’s given that JK is 112
fierce lagoon
No they are correct
You know what, I think you applied them incorrectly
It seems I can't do division in my head lmao
It hit me that you wrote 67 and not what I thought of
sage plover
And it’s given that JK is 112
it says 68 is incorrect although
sage plover
multiply by 2?
crimson horizon
Divide
sage plover
34?
crimson horizon
Yep
sage plover
(1, -2)
sage plover
Gonna go eat lunch now
👋🏻
crimson horizon
Oh btw sorry I said vertex not center
dapper bloom
The radius extends from the center to either of those diameter pts
So you just gotta use the distance formula
sage plover
i hate distanceeee
dapper bloom
Yeah, it's a pain lol
You can skip some of it I guess.
You want to use the general equation for a circle
That equation uses the center of the circle and the square of the radius (so you can try to be clever and avoid the sqrt)
sage plover
is it -2?
dapper bloom
Mmm, the radius will never be a negative length
sage plover
0?
dapper bloom
That also seems wrong
So, for A=(a_x,a_y) and B=(b_x,b_y) the distance between A and B is d(A,B)=sqrt((a_x-b_x)^2 + (a_y-b_y)^2 )
And for a circle to compute the radius you need to find the distance from its center point to any point on the circle
You just found the center and either of those two given diameter points are on the circle, so pick either and use them with the center point in the distance formula.
sage plover
wha-
dapper bloom
Hmm. You remember the distance formula right?
dapper bloom
Mmm. Why two? Did you just use both diameter points in the distance formula?
Pretty sure that's what you did lol.
Ask yourself this: what's the difference between the length of a diameter of a circle and the length of the radius of a circle? How are they related?
What you found is not the length of the radius, but you can use it to find the length of the radius.
From there you will have everything you need. The general equation of a circle centered at (a,b) with radius r is (x-a)^2 + (y-b)^2 = r^2 and you will have just found the center point and radius length.
obtuse pebbleBOT
@sage plover Has your question been resolved?
fierce schooner
toxic harbor
obtuse pebbleBOT
toxic harbor
Is it correct to find the domain after you simplify here, or do you find the domain before you simplify?
Because simplified you get one answer and not simplified you get a different answer.
obtuse pebbleBOT
@toxic harbor Has your question been resolved?
dapper bloom
Do it before
toxic harbor
Is this like common practice, or is there a specific reason?
dapper bloom
Stuff like f(x)=(x-1)/(x-1) for example. It's the line y=1 with a gap at x=1 because it is undefined at x=1.
toxic harbor
Oh I see
Why do we get two different results when you simplify though?
That's verty strange
dapper bloom
Because the functions f(x)=1 and g(x)=(x-1)/(x-1) are defined in two different ways that lead you to two different functions I guess. 
toxic harbor
I don't think so cause even if it was one function you would still have the same problem
right?
dapper bloom
Like, when you simplify (x-1)/(x-1) you're assuming it's defined in the first place i.e. that x is not 1. (Or else it would just be 0/0)
dapper bloom
I don't think so cause even if it was one function you would still have the same...
What do you mean?
toxic harbor
Like f(x) = ((1)/(sqrt(x))^2 - 4
This would just be the same problem
Even though it's not composite
dapper bloom
Mmm, that's still a composition of several functions.
dapper bloom
Yeah, like there's a way to write that as a composition of a bunch of functions.
dapper bloom
Lets do a less complicated one
toxic harbor
Sure sure
dapper bloom
Iike f(x)=abx
Even though we haven't specified it above we could let g(x)=bx and h(x)=ax so f(x)=h(g(x))=h(bx)=abx.
toxic harbor
Oh I see
Hm, fair enough
So before simplifying?
So (0, infinity) for ((1)/(sqrt(x))^2 - 4
dapper bloom
Yeah p sure
dapper bloom
You can double check this with stuff like desmos too
dapper bloom
Compare the graph of 1/x and (1/sqrt(x))^2 for ex
toxic harbor
Yeah?
dapper bloom
God damn it no I'm still mixing it up
Other way sqrt(x^2 )=|x|
Eh, either way (1/sqrt(x))^2 only takes positive real inputs when you graph it
toxic harbor
What's the difference between these two?
dapper bloom
sqrt(x)^2 is undefined at x=-1 (assuming we stay in the reals)
But sqrt(x^2) just works out to be |x|
It's never undefined because squaring a negative gives a positive
toxic harbor
shouldn't the squarte be outside the root?
dapper bloom
I'm saying the diff between inside the root/outside the root gives two different functions
toxic harbor
Oh okay
fiery juniper
Why is there a difference
toxic harbor
Why is there a difference
Difference between?
fiery juniper
The power being in the root and outside the root
It shouldn't matter what power you apply first
dapper bloom
It dows matter what power you apply first if we're sticking with real numbers
toxic harbor
Because in the root means you do the square first, outside means you do the root first.
Right?
dapper bloom
sqrt(x)^2 is undefined at x=-1 but sqrt(x^2) is defined at x=-1
fiery juniper
but don't we have sqrt(x^2) = (x^2)^1/2 = (x^1/2)^2 = sqrt(x)^2
toxic harbor
Inside gives negatives too, while outside gives positives and negatives
dapper bloom
but don't we have sqrt(x^2) = (x^2)^1/2 = (x^1/2)^2 = sqrt(x)^2
Not if sqrt has a domain which only consists of the positive reals.
The analogy earlier was simpler x/x=1
But only if x is not zero
Because 0/0 is undefined
fiery juniper
yeah, it makes sense, I just can't get over the fact that I always though there is no difference
I remember being told they are the same
but probably we weren't that concerned with the domain back then
toxic harbor
This is so interesting
dapper bloom
You just have to be a little careful is all.
We could define the sqrt on all real numbers, we'd just need to send negative values to numbers involving i
toxic harbor
Btw, why is sqrt of a negative not real?
dapper bloom
Mmm, so let x<0, consider y=sqrt(x), by definition this value satisfies y^2 =x, but if y were real then y^2 would be at least zero, and x is in fact less than zero like we said earlier.
fiery juniper
because there is no number sqrt(x) such that sqrt(x) * sqrt(x) = x if x is negative
toxic harbor
Mmm, so let x<0, consider y=sqrt(x), by definition this value satisfies y^2 =x, ...
That's so kewl
fiery juniper
any number to an even power is a non-negative number
toxic harbor
That's so kewl
And a little scary
toxic harbor
any number to an even power is a non-negative number
right
I see
interesting
ty guys
dapper bloom
This is where complex numbers come from btw.
Worth looking into if you find it interesting.
fiery juniper
You introduce an imaginary unit that is i = sqrt(-1) and then there exists sqrt(x) such that sqrt(x) * sqrt(x) for any x
toxic harbor
Wait sorry sorry
fiery juniper
for example if x = -4
toxic harbor
Mmm, so let x<0, consider y=sqrt(x), by definition this value satisfies y^2 =x, ...
why can't we have sqrt(0)?
dapper bloom
why can't we have sqrt(0)?
sqrt(0) is just 0 and I was trying to show examples of a number x where sqrt(x) can't be real.
It's just the negative reals for x that make sqrt(x) not a real number basically.
supple pumice
draw the subgroup lattice for the group generated by a,b,c each of order 2
supple pumice
the group <1,a,b,c>
compact shadow
gilded needle
aren't <a,b>, <b,c> and <a,c> just G?
compact shadow
No
gilded needle
then what are they?
compact shadow
They are isomorphic to (Z/2Z)^2 while G is isomorphic to (Z/2Z)^3
gilded needle
<a,b> contains a and b by definition and it contains 1 since it's a group
so it has at least 3 elements
by lagrange it must have all 4
oh right
compact shadow
Like I said, (Z/2Z)^2, Klein group
gilded needle
i misinterpreted what G is
compact shadow
I see
gilded needle
and assumed it was the Klein group
supple pumice
i was thinking about <ab> etc
compact shadow
I was dumb, why did I assume they are abelian… nvm
gilded needle
seems there's not really enough info
i mean the group could be the klein group or it could be (Z2)^3
depending on the assumption about multiplication
compact shadow
I thought it was <a,b,c|a^2=b^2=c^2=1>
supple pumice
yeah, the group i have could be generated like so
compact shadow
It is this group? Okay
supple pumice
its also abelian
compact shadow
?
So free abelian group generated by a,b,c
Quotient
Smallest subgroup containing a^2, b^2, c^2?
supple pumice
huh
compact shadow
Then this is correct
compact shadow
So which one it is?
Free group generated by a,b,c over a^2,b^2,c^2 or free abelian group generated by a,b,c over a^2,b^2,c^2?
Or you give us the galois extension
warm shaleBOT
please request a new nickname
compact shadow
I see
supple pumice
Ive shown that its galois already
compact shadow
Then this is correct
supple pumice
and i have eight automorphisms
oh ok
but Im still confused why <ab> doesnt show up for instance
compact shadow
Yeah I wonder the same… what went wrong…
supple pumice
because <ab> is a subgroup of order 2 and its not contained in any of the smaller subgroups so it should show up somewhere, right?
compact shadow
Strange… a maps sqrt(2) to -sqrt(2),doesn’t change other roots. b maps sqrt(3) to -sqrt(3), c maps sqrt(5) to -sqrt(5). Then Inv(<a,b>)=Inv(<ab>)=Q(sqrt(5)) right
supple pumice
Inv is the field fixed by these right?
supple pumice
i forgot about <a,bc> and stuff
compact shadow
I will try to give the corresponding intermediate fields
supple pumice
ok ill use it to check my own
gilded needle
isn't <ab> a subgroup of <a,b> as well? (since ab is an element of <a,b>)
compact shadow
Yeah
compact shadow
Yeah several lines
supple pumice
its ok though i was mainly concerned about the subgroups
supple pumice
also would you say that
<a,b,c|a^2 = b^2 = c^2 = 1, ab=ba, ac=ca, bc=cb> is a sufficient presentation
compact shadow
Yes
compact shadow
Forgot to draw lines connecting Q(sqrt(30)) though
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stark ether
anyway to say this is 0 using det properties and without expanding?
obtuse pebbleBOT
anyway to say this is 0 using det properties and without expanding?
kind hawk
add first column to second and then compare second and third column
royal basin
this matrix multiplied from the right by [1; 1; -(a+b+c)] gives 0 so it is singular
kind hawk
(or just generally show the columns are lineraly dependent)
stark ether
.close
toxic harbor
obtuse pebbleBOT
toxic harbor
What parent function is this?
The -3 throws me off
It looks like a quadratic function but then -3 happens
So I'm kinda confuzzeled
pallid flame
it really don’t matter what f(x) is
you’re just writing the other functions in terms of f(x)
@toxic harbor
also it looks more like a line with a point discontinuity than a quadratic if you’re trying to classify it
but that’s not really relevant
obtuse pebbleBOT
@toxic harbor Has your question been resolved?
toxic harbor
@pallid flameHow do I write the function if I don't know what the parent function is?
obtuse pebbleBOT
<@635245771318493193>How do I write the function if I don't know what the parent...
timid silo
can you spot any difference between f(x) and g(x)?
toxic harbor
Yeah I can spot the differences by just looking at it
But I want to know if it's possible to figure out the parent function of a function.
toxic harbor
What does toolkit function mean?
obtuse pebbleBOT
What does toolkit function mean?
warm canopy
You'll have to be more specific, what's the context
toxic harbor
high lily
parent
toxic harbor
hm alright
obtuse pebbleBOT
@toxic harbor Has your question been resolved?
shadow marlin
i need help with iv please 🙂
obtuse pebbleBOT
i need help with iv please 🙂
eternal bloom
i need help with iv please 🙂
Plug in the values into the formula you got in (iii)
leaden shoal
how do i find phase shift?
obtuse pebbleBOT
how do i find phase shift?
leaden shoal
leaden shoal
how
forest sinew
algebra
leaden shoal
=0?
forest sinew
what is attached to x
leaden shoal
pi/5
forest sinew
this is what u need to factor
leaden shoal
leaden shoal
a(x+b
leaden shoal
ik?
forest sinew
or factoring the expression
leaden shoal
bro
i know whats factor
but i dont know how to factor that
do u understand what im saying??
leaden shoal
im saying that i dont know how to factor that
leaden shoal
im just confused about what you are hung up on i guess
do u understand english?
forest sinew
you wanna factor pi /5 right
leaden shoal
yes
forest sinew
lol dont be mean
leaden shoal
no its just annoying
ur just repeating
factor! factor! factor!
like bro i know but how?
forest sinew
$\frac{\pi}{5} \qty( x - a)$
warm shaleBOT
jan Niku, Researcher in LinAlg
forest sinew
u wanna find a such that this is equal to what you have above
$\frac{\pi}{5} \qty( x - a) = \frac{\pi}{5} x - \frac{2 \pi}{5}$
warm shaleBOT
jan Niku, Researcher in LinAlg
forest sinew
what is a
leaden shoal
2pi/5
leaden shoal
u cant cause u dont have x
forest sinew
huh?
leaden shoal
is there any other ways to find the phase shift other than this?
forest sinew
if you are allowed to graph it
you can get it by visual inspection
the phase shift is always found it factored form
leaden shoal
bro what is the formula
forest sinew
if your argument isnt factored, then you have to factor it first to get it
leaden shoal
i just want to know the formula to find the phase shift
i remember that there was a formula
like a/b
or something
forest sinew
yea
forest sinew
the same?
leaden shoal
whats the difference?
forest sinew
i dont understand, difference? what do you mean?
difference between what
its just the same argument but in a different form
so you can extract phase shift
forest sinew
i do not understand why you want to set it equal to 0
and you arent solving for the correct thing
x is like
you arent solving for x
this is what you should be solving
for a
leaden shoal
hmm but i get the same answer
forest sinew
your algebra is bad
you just added pi/5 to one side?
you arent allowed to do that
so i think it's coincidental
forest sinew
hmm but i get the same answer
i can show you the way i factor in my head
im just worried its gonna make it seem more confusing
forest sinew
okay
leaden shoal
u can pollute my brain
forest sinew
$\frac{\pi}{5} x - \frac{2 \pi }{5}$
i guess note that there is no equals here
its just an expression
warm shaleBOT
jan Niku, Researcher in LinAlg
warm shaleBOT
jan Niku, Researcher in LinAlg
forest sinew
i rewrite 1
i guess lets stop for a second like
its okay to multiply by 1, right?
as long as you add 0 or multiply by 1 you wont change anything
leaden shoal
then why multiply 1?
warm shaleBOT
jan Niku, Researcher in LinAlg
leaden shoal
u got to find the lcm tho
forest sinew
this is still 1, right
leaden shoal
if the denominator isnt same u gotta cross multiply
forest sinew
im not doing anything like
no lcm or anything
im just multiplying by 1
nothing fancy
leaden shoal
1 of what?
leaden shoal
1 of pi/5 or 2pi/5
forest sinew
i guess i could just say i mean i know youre mad i keep saying it but
factoring is worth learning and getting comfortable with
leaden shoal
factoring is worth learning and getting comfortable with
wait how
which is the phase shift?
hello?
oh ok
so this is correct
forest sinew
okay sure
yea
this is more or less what i seeing in my head when i said just factor
leaden shoal
ok
coarse flare
obtuse pebbleBOT
stone solstice
the top one you should do
stone solstice
coarse flare
obtuse pebbleBOT
timid silo
why did you take 1/4 out?
coarse flare
why did you take 1/4 out?
why not? i think it makes the equation simpler
timid silo
before u do that
log_b(b)+log_b(x^1/4)
then do it
yes, taking out like that doesnt work
if it was (bx)^1/4 then you could have taken out
coarse flare
yes, taking out like that doesnt work
what log rule is this? i didnt know bout this
timid silo
log_a(bc) = log_a(b) + log_a(c)
coarse flare
so if its like log_b (bx^2) , then i cant just take out the 2?
timid silo
yeah cuz x is only squared
timid silo
yes
cinder hull
Why did my teacher give me a 0/15??????
obtuse pebbleBOT
Why did my teacher give me a 0/15??????
@cinder hull Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fallow plume
obtuse pebbleBOT
fallow plume
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Does
xˆn = a
only have one root when
- n is odd
- a >= 0
obtuse pebbleBOT
Does
xˆn = a
only have one root when
- n is odd
- a >= 0
steep harness
On the reals, yes
snow latch
For a>0 it is x=+- nth root of a
For a=0 ot is x=0
And for a<0 x isnt real
2 4 6 etc are odds right?
steep harness
No, those are even
xⁿ has n unique roots in the complex plane if x≠0
And at least 1 real root
timid silo
So it’s impossible to factorize x^3 - 27
nocturne sun
Does
xˆn = a
only have one root when
- n is odd
- a >= 0
are we meant to show that x^n = a has only one root when n is odd and a >= 0 or do we have to show there are other conditions when it has only one root?
steep harness
So it’s impossible to factorize x^3 - 27
Any difference of powers aⁿ-bⁿ, n as a natural number, is factorable
feral swallow
obtuse pebbleBOT
royal shard
yes
feral swallow
When do we calculate it as hrs?
frosty river
1 m/s = 60 m/min = 3600 m/h = 86 400 m/day
1 m/s = 60 m/min = 3600 m/h = 86 400 m/day = 86.4 km/day
20 000 m/s = 20 000 * 1 m/s = ... km/day
Conversion factors are the best 😄
royal shard
you normally never calculate with hours in an equation
you can do that if you have to solve something like $t_1/t_2$
warm shaleBOT
~Martin
royal shard
there you could write t1 and t2 in hours
obtuse pebbleBOT
@feral swallow Has your question been resolved?
lyric totem
Hey
warm shaleBOT
dopediscorduser
warm shaleBOT
dopediscorduser
haughty coyote
,w log_10 (x) + log_10 (5) = 1
warm shaleBOT
haughty coyote
As you can see, yes
lyric totem
I didn't even know you could do that
haughty coyote
If you just want to check your result, you can go to Wolfram Alpha or Desmos
magic portal
I need help
obtuse pebbleBOT
I need help
magic portal
I dont get what to do for this question
how to find one side of a triangle when you're given all 3 angles
haughty coyote
You need a length as well
pine sail
Sine rule.
magic portal
k
brittle blaze
Basic trig yeah
magic portal
what do you put as the bottom?
pine sail
Side length, opposite to angle A.
magic portal
What
pine sail
Name them whatever you want.
magic portal
Ok
obtuse pebbleBOT
@magic portal Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
@proper coyote Has your question been resolved?
meager swift
Testing 123
Hi i just joined the server and got no clue what I'm doing but i can try to help
f'(any number) is equal to c
Yeah f is linear, and that's why the derivative is constant
proper coyote
Pretty cat in your profile header btw
proper coyote
Yeah f is linear, and that's why the derivative is constant
Ah okay
meager swift
But it seems like you got the correct numbers
Don't really see how your friend got b = -1/3
meager swift
Damn I misread. Yeah it's late over here
proper coyote
Oh how late
meager swift
11:40 pm
meager swift
In twenty minutes i think
proper coyote
Alright
If u need help with a math problem u can scroll to available help channels and then choose one btw
proper coyote
Oh
proper coyote
Nicee did ur exams go well
proper coyote
Yay good job
meager swift
Tyty
proper coyote
Thnx for helping me btw
Now im done with homework
Im gonna close this channel, sleep well for later 😴
.close
obtuse pebbleBOT
meager swift
gn
obtuse pebbleBOT
Available help channel!
noble kindle
Suppose G is a cyclic group and it has at least one element of infinite order. Show that every non-identity element in G has infinite order
obtuse pebbleBOT
Suppose G is a cyclic group and it has at least one element of infinite order. S...
warm shaleBOT
Kurama
noble kindle
So if G is cyclic, that means $\exists a \in G$ such that $\langle a \rangle = G$. Then take $x \in \langle a \rangle$ so that $ x = a^m$ for some integer m. Then for any integer k, $x^k = a^{m^{k}} = a^{mk} = e$ iff $mk = 0$ following the definition. So only when $k = 0$ do we get the identity. Meaning no positive power k makes $x^{mk}$ equal the identity, which means $|a^m| = \infty$.
warm shaleBOT
Kurama
stone solstice
If the sum of the 3rd and 5th terms of the arithmetic sequence equals to the 10th term. Then what is ratio of the sum of the first two terms to the sum of the first nine terms of the arithmetic sequence?```I tried $$U3+U5=U10$$
warm shaleBOT
ItzAine
warped agate
do u know general term of ap
stone solstice
making it $$a+2b+a+4b=a+9b$$
warm shaleBOT
ItzAine
stone solstice
yes
warped agate
find the sums then
stone solstice
so it asks the ratio of the sum of the first two terms to the sum of the first 9 terms
warped agate
first 2 terms sum will be a+a+b = 2a+b
first 9 terms sum will be
9/2(a+a+8d)
take ratio and use a=3b u get the answer
stone solstice
yea so then it should be $$6b+b= 7b$$
warm shaleBOT
ItzAine
warm shaleBOT
ItzAine
stone solstice
how is it 1:9?
warped agate
npnp
stone solstice
.close
stone solstice
If matrix A has an Inverse of :
obtuse pebbleBOT
If matrix A has an Inverse of :
stone solstice
How do I find the original Matrix?
nocturne minnow
Find the inverse of that matrix
stone solstice
I inverse it again?
timid silo
(A^-1)^(-1) = A
stone solstice
so it would be $$:\begin{pmatrix}1&1\ -\frac{1}{3}&-\frac{2}{3}\end{pmatrix}$$?
warm shaleBOT
ItzAine
nocturne minnow
Show work
timid silo
Is A times that the identity, and is that times A the identity as well then yes it’s the A inverse
stone solstice
I didnt work on it, I just stuffed it in a calculator, I was looking for the theory itself
thank you
.close
hidden bronze
obtuse pebbleBOT
hidden bronze
having a bit of trouhble with this one
mabye i drew it out wrong
idk
<@&286206848099549185>
can someone look at this
nocturne minnow
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
hidden bronze
oops mb
ornate moss
i need help with this question
stark ether
i need help with this question
create a new channel
stark ether
what have you tried?
hidden bronze
what have you tried?
this formula
but
the thing is
i think i drew it out wrong
could u help me draw it out
stark ether
stark ether
what did you do after that
stark ether
no?
stark ether
cross wind velocity + initial velocity = final velocity
hidden bronze
hmm
stark ether
no?
stark ether
using vector subtraction
.
hidden bronze
so how would i do tht
stark ether
that gives you the magnitude
hidden bronze
okat
so
now the angle
uh
sinx
sina/a =sinb/b
ohh
wait
cant i just use cosine rule again?
stark ether
sin rule works too I think
stark ether
cant i just use cosine rule again?
yes
hidden bronze
leme try sin rule
then
okay
yeah
i got the angle
lol
bruh, this isnt even related to the chapter tho
the whole chapter was useing this rule
weird
stark ether
oh I see
you get the x component of the wind by using rcost-a
and y component of the wind is rsint
then find mag by sqrt(x^2 + y^2)
and you can find the angle by sint' = rsint/mag
@hidden bronze got it?
obtuse pebbleBOT
@hidden bronze Has your question been resolved?
strong vale
obtuse pebbleBOT