2d euclidean geometry is bad enough😭😭
#help-39
north talon
rotund ferry
Olympiad ahh 🥀
frank violet
Olympiad ahh 🥀
🥀
north talon
💔 💔
rotund ferry
I don't see any other way you would solve this problem tbh 
north talon
also quick question, how did you even make this
frank violet
also quick question, how did you even make this
Geogebra 
just like you usually do
Calculate where each point is in 3D space to make it precise
north talon
i see, thanks!
frank violet
i see, thanks!
pearl pondBOT
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shut flicker
would this be right, i feel maybe i have double counted a bit
shut flicker
naive zinc
Inclusion exclusion principle
Yours is correct
Wait
I don’t get a 6! in the numerator, let me check
shut flicker
thats from arranging the 1 2 3 4 5 6 that we want but i think may be the cause for double counting idk
naive zinc
Mine is (Σbinom(6, k) (-1)^k (6-k)^n)/6^n
iron basin
yeahh might have double counted a bit
naive zinc
So I don’t think yours is correct but I haven’t checked your steps
iron basin
for n = 7 for example there are two ways you could've counted in 1 1 2 3 4 5 6
shut flicker
ohhh yh
naive zinc
$\frac{\sum_{k}(-1)^{k}\binom{6}{k}(6-k)^{n}}{6^{n}}$
jolly parrotBOT
Cogwheels of the mind
calm maple
for n = 7 for example there are two ways you could've counted in 1 1 2 3 4 5 6
Idts.. the method fixes a set of {1,2,3,4,5,6}, permutes that in 6! and places it in 6 positions out of n and the remaining (n-6) slots can be filled in 6^(n-6) ways?
So ig its right
iron basin
Idts.. the method fixes a set of {1,2,3,4,5,6}, permutes that in 6! and places i...
ok then what about these two ways
- 1, _, 2, 3, 4, 5, 6 and fill in the remaining 1 later
- _, 1, 2, 3, 4, 5, 6 and fill in the remaining 1 later
shut flicker
nah buts its like ( one 1 two three four five six ) and ( 1 one two three four fix six ) are the same but counted twice, the letter numbers being the fixed ones
naive zinc
A_j is set of cases the sequence doesn’t contain j. Clearly sum of |intersection of k many A_j| is binom(6,k)(6-k)^n
naive zinc
**Cogwheels of the mind**
Which deduces this
calm maple
ok then what about these two ways
- 1, _, 2, 3, 4, 5, 6 and fill in the remainin...
ahhh i see
my bad
torn lodge
for part b, idk why i didnt get aln2 (where a is some rational constant)
toxic lichen
you've got that ln(6/8) which still can and should get some simplification
agile hedge
for part b, idk why i didnt get aln2 (where a is some rational constant)
break ln(6/8) into 3/4 and then use ln m/n = ln m - ln n property, add 9 ln 3 and12 ln 3
torn lodge
break ln(6/8) into 3/4 and then use ln m/n = ln m - ln n property, add 9 ln 3 an...
ohhhh
kk i'll try that
agile hedge
you can write ln 4 as ln 2^2 and then use property ln m^n = n ln m
so it become 2 * 12 ln 2
so a = 24/5 and b = 21/5 (can be wrong didnt use calc or sheet, calc is short of calculator btw)
agile hedge
kk i'll try that
bet bet
agile hedge
for part b, idk why i didnt get aln2 (where a is some rational constant)
btw which app? the handwriting is mindblowing
torn lodge
btw which app? the handwriting is mindblowing
haha tysm! im using onenote
agile hedge
haha tysm! im using onenote
ahh, thank you :3
torn lodge
so a = 24/5 and b = 21/5 (can be wrong didnt use calc or sheet, calc is short of...
ah i didn't know u could simplify 9ln(3) + 12ln(3) to 21ln(3)
tysm!
.close
pearl pondBOT
agile hedge
ah i didn't know u could simplify 9ln(3) + 12ln(3) to 21ln(3)
yes its like taking away common, best of luck
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wind lagoon
A median of a random variable $X$ is defined as any $m \in \mathbb{R}$ such that $$P(X \le m) \ge 1/2\text{ and }P(X \ge m) \ge 1/2.$$ I know of an example when the median is not unique, but now I'd like to give and prove a condition for when it is unique. I know of an MSE related answer (see below), but I fail to understand why the condition given is equivalent to unique median. The answer claims that the median is unique iff $\lambda(F_X^{-1}({0.5}))=0$, where $F_X^{-1}$ is the inverse image of the CDF $F_X$. Appreciate any help.
jolly parrotBOT
psie
pearl pondBOT
@wind lagoon Has your question been resolved?
pearl pondBOT
@wind lagoon Has your question been resolved?
wind lagoon
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pearl pondBOT
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safe prairie
What went wrong??
pearl pondBOT
What went wrong??
safe prairie
I gotta prove that there’s a double eigenvalue and a triple eigenvalue
bitter herald
I gotta prove that there’s a double eigenvalue and a triple eigenvalue
U messed up one of ur signs
Methinks
When expanding along the 5th column
safe prairie
Alr yeah 1st line 2nd term should start with -
pearl pondBOT
@safe prairie Has your question been resolved?
robust lichen
okay so
robust lichen
AE => m^3 - 3m^2 + 4m - 2 = 0
m = 1, 1+i, 1-i
so CF = e^x(C1 cos x + C2 sin x) + C3 e^x
got that
how can i guess the PI like
applying Method of Undetermined Coefficients to Find a Particular Solution
should i just do
Ae^x + Bcos x + C sin x cos x ?
or Ae^x + Bcos x + Csin x + D sinx cos x
waxen agate
You already have e^x in your CF, so you multiply Ae^x by x.
robust lichen
can take sin x cos x as .5 sin 2x
waxen agate
The guess for the term cos(x) is Bcos(x) + Csin(x), yes.
waxen agate
can take sin x cos x as .5 sin 2x
Correct.
robust lichen
No need for the 0.5 scaling
ill have to include it no?
these a, b, c, d arent arbitary constants
or are they?
robust lichen
Also where is your Ccos(x) term
wdym
waxen agate
They are constants that you have to calculate.
robust lichen
Axe^x + B cos x + .5C sin 2x + .5D cos 2x
is this correct tho
waxen agate
You can absorb any contants into C and D
waxen agate
Axe^x + B cos x + .5C sin 2x + .5D cos 2x
missing the sin x term
waxen agate
Yes
robust lichen
imma do this then come back
@waxen agate if in my CF there wasnt e^x then i would have written just Ae^x right
waxen agate
Yes.
robust lichen
okok
@waxen agate is there a better way to solve this than what im doing rn
too lengthy god damn
.close
pearl pondBOT
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arctic hazel
may i get some help on this
pearl pondBOT
may i get some help on this
sharp fractal
may i get some help on this
what have you tried? do you just not know where to start?
arctic hazel
yea im not sure where to start
sharp fractal
yea im not sure where to start
as the question directly asked for the midpoint rule, have you attempted using that?
arctic hazel
ye
sharp fractal
can you show your work/give your answer
arctic hazel
i did one for 2,4,6,8 etc
yea one sec
i got my answer to be 6.6
but its incorrect
sharp fractal
but its incorrect
have you noticed/kept in mind that the graph gives you it in seconds and not minutes like the question asked?
sharp fractal
what was the n value for the 6.6 answer? sorry for the many questions, im trying to see what went wrong here
arctic hazel
should be 8
sharp fractal
yeah 8 checks out
would it be possible for you to show how you got that 6.6?
sharp fractal
sorry I need to go for a sec. is this time sensitive? I can get another helper here for you, if needed
sharp fractal
<@&286206848099549185> if anyone could get this guy 'til I'm back
sharp fractal
ohh dude wait, can you write down your c(t) values?
like c(0)=0, c(2)=6, so on and so forth? perhaps its just that?
sharp fractal
*jesus sorry about that, your work is right, I got stuck in my method lol
arctic hazel
its all g LOL
are you getting the same answer i was? maybe it's just a rounding error icl
idk i only have 1 more try on it 😭
sharp fractal
I don't think it was a rounding error, no
arctic hazel
hmm okay
sharp fractal
c(1)=4, c(3)=7, c(5)=6, c(7)=5, c(9)=4, c(11)=3, c(13)=2, c(15)=1
is what you wrote yeah?
arctic hazel
yup
sharp fractal
I sent you something in dms, do check if possible
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quiet plover
hi
quiet plover
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cedar harbor
let $x[n]$ be a discrete time signal. $y_1 = x[3n]$. if $y_1[n]$ is periodic, is $x[n]$ periodic?
is saying that $$y_1[n] = y_1[n + T] = x[3n+3T] = x[3n]$$ enough to say that only x[3n] is periodic, not x[n]
jolly parrotBOT
thiccfetus
cedar harbor
and in the other direction, if $x[n]$ is periodic, is $y_1[n]$ periodic?
$$ x[n] = x[n+p] -> x[3n+ 3p] = x[3n] = y_1[n] $$ so y[n] is also periodic.
jolly parrotBOT
thiccfetus
cedar harbor
**thiccfetus**
i am also not sure that you can convert x[n] to x[3n] directly here
pearl pondBOT
@cedar harbor Has your question been resolved?
pearl pondBOT
@cedar harbor Has your question been resolved?
errant cedar
**thiccfetus**
assuming what you mean by a discrete time signal is essentially a sequence (so an indexed list of numbers) and that your definition of a period p is that x[n]=x[n+p] for any n, this is true imo
cedar harbor
assuming what you mean by a discrete time signal is essentially a sequence (so a...
yes
but i'm not sure if my proof is valid
like my process
errant cedar
for the x[n] periodic of period p implies the subsampled y_1[n]is periodic, you can use the period definition 3 times in a row to get what you want
cedar harbor
how about y_1 is periodic?
errant cedar
but the other direction like y_1[n] periodic does not imply that x[n] is periodic imo
to refute that you would have to produce a counter example
cedar harbor
for the x[n] periodic of period p implies the subsampled y_1[n]is periodic, you ...
so we can assume y is T periodic: y[n+T] = x[3n + 3T] = x[3n] = y[n]
cedar harbor
but the other direction like y_1[n] periodic does not imply that x[n] is periodi...
asumme x is P periodic: x[n+P] = y[(n+P)/3] = x[n/3] != x[n]
errant cedar
so we can assume y is T periodic: y[n+T] = x[3n + 3T] = x[3n] = y[n]
you assume x[n] is periodic then you get with that hypothesis that y[n] is, implicitly that’s what justify your middle equal there
cedar harbor
you assume x[n] is periodic then you get with that hypothesis that y[n] is, impl...
i thought x is given to be periodic. so we can hypothesise that y[n] is by using periodicity of x in the middle part
errant cedar
i thought x is given to be periodic. so we can hypothesise that y[n] is by using...
yes that’s how you start to prove an implication, but you can’t assume what you want to prove is true to prove it’s true if that’s what you mean by hypothesize. you have to start with x[n] = x[n+T] for each n and use that somewhere in your chain of equals
cedar harbor
yes that’s how you start to prove an implication, but you can’t assume what you ...
i'm not sure how this would work
to start with x[n+p]
errant cedar
so y[n] = x[3n] that’s the definition of y[n], then x[3n]=x[3n+p] because we use the periodicity on the index 3n of the sequence x
then can you see what you need to do to get to y[n]=y[n+p]?
cedar harbor
then can you see what you need to do to get to y[n]=y[n+p]?
i cannot
how can you say that x[3n] is periodic, with only given that x[n] is periodic
errant cedar
the property that the sequence x is periodic is applicable to each index of the sequence
maybe a drawing would help
cedar harbor
the property that the sequence x is periodic is applicable to each index of the ...
i see, but i still do not know how to get y[n] = y[n+p]
errant cedar
errant cedar
i see, but i still do not know how to get y[n] = y[n+p]
so we have y[n]=x[3n]=x[3n+p] but because the signal repeats each p time steps we also have x[3n+p]=x[3n+2p]=x[3n+3p]
does this make sense
cedar harbor
i'm not sure if this is true for all k*n
i think it's only for mod 3. since x[2(1) + p] != x[2(2) + p]
errant cedar
i'm not sure if this is true for all k*n
i’m still explaining the proof direction where we have that x[n] is periodic and want to show y[n] is, this will be good insight for the other direction
you have to separate the two proof directions in your head imo
errant cedar
i think it's only for mod 3. since x[2(1) + p] != x[2(2) + p]
this would not be true if we only had as an hypothesis that y[n] is periodic but again that’s the direction y[n] periodic implies (?) x[n] also periodic
cedar harbor
this would not be true if we only had as an hypothesis that y[n] is periodic but...
uh how would you do the other direction
errant cedar
i said earlier i think it’s not true all the time
to confirm this a counter example is enough proof
cedar harbor
asumme x is P periodic: x[n+P] = y[(n+P)/3] = x[n/3] != x[n]
can you say this ?
errant cedar
no because you are not sure n+P is a multiple of 3 and fractional indices on a sequence don’t make sense imo
cedar harbor
no because you are not sure n+P is a multiple of 3 and fractional indices on a s...
so a counter example would be that n+ P is not a multiple of 3
errant cedar
a counter example is a particular choice of x where y is periodic but x is not
errant cedar
so a counter example would be that n+ P is not a multiple of 3
no i’m afraid to say that i perceived what you wrote earlier as gibberish unfortunately
but again learning to prove things is hard imo
errant cedar
i think it's only for mod 3. since x[2(1) + p] != x[2(2) + p]
but this made some sense
cedar harbor
no i’m afraid to say that i perceived what you wrote earlier as gibberish unfort...
uh what i mean is that for x[n/3 + P/3] = x[n], it must be that n is divisible by 3. so you can come up with an x where x!=0 for n mod 3 != 0
errant cedar
yep, you can indeed cook up a sequence such that x[3n] = 0 for each n and the rest is free to be anything
cedar harbor
if that's correct, what i'm struggling with is knowing when to give a counterexample
cedar harbor
asumme x is P periodic: x[n+P] = y[(n+P)/3] = x[n/3] != x[n]
that means, this is enough for me to try to find a counter example?
errant cedar
a counterexample is a way to prove that a statement holding over many objects fail for one of the objects. Here the objects are sequence/signals and the statement is that for any signal, the periodicity of the downsampled one x[3n] imply the periodicity of the source signal x.
if the statement fails for some choice of x, it can’t be true for any x, it disproves directly the « for each/for all »
hence it disprove this whole proof direction
pearl pondBOT
scarlet dragon
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short fog
Hi, So my doubt is not for any math question right now, But I have Caclulus in my second sem of college and would like to know how should i go about learning it to gain full conceptual clarity. I had also learnt calculus to some extent in my high school but due to lack of conceptual clarity topics like AOI, AOD, Limits, Continuity etc used to trouble me while solving questions. So Could anyone suggest which topic should I start with and from where should I be doing it, because this time i want full conceptual clarity for all the topics. I am attaching the photo of the syllabus as well.
Thanks
short fog
If someone could guide me, It'll be very helpful.
I am in a B-School. Hence the topics have business applications mentioned in them, But again, we need the concepts anyway.
pearl pondBOT
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pearl pondBOT
@short fog Has your question been resolved?
short fog
No
pearl pondBOT
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safe ore
dusk willow
!done?
pearl pondBOT
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@flint wyvern Has your question been resolved?
void grail
pearl pondBOT
rotund ferry
slender viper
do you remember the definition of "preorder" and "product of preorders"
void grail
Γ = {Refl: ⊢ ∀x x≤x, Trans: ⊢ ∀x y z (x≤y∧y≤z→x≤z)}.
def ≤×:
⊢ (a≤×b ↔ π₁a≤π₁b ∧ π₂a≤π₂b).
Γ ⊢ Refl× via ⟨Refl₁,Refl₂⟩
Γ ⊢ (a,a)≤×(a,a) (Refl∧Refl)
Γ ⊢ Trans× via π₁,π₂ + Trans
Γ ⊢ (a≤×b ∧ b≤×c → a≤×c) (Trans×).
⇒ Γ ⊢ Preorder(P×Q) ⇒ Γ ⊨ preorder(P×Q)
void grail
do you remember the definition of "preorder" and "product of preorders"
Preorder ⇔ (Reflexive ∧ Transitive).
slender viper
so, if I get your notation, now all you have to show that "≤×" is such that "Refl×" and "Trans×"
hmm, or is that supposed to be some sort of closure
void grail
so, if I get your notation, now all you have to show that "≤×" is such that "Ref...
reflexive:
Refl× means ∀x, x≤×x.
take arbitrary x≔(a,b):
from Γ: Refl₁ ⊢ a≤ₚa, Refl₂ ⊢ b≤ᵩb.
∧-intro ⟨Refl₁,Refl₂⟩:
Γ ⊢ (a,b)≤×(a,b).
x≤×x ⇒ reflexive
transitive:
≤× is componentwise,
assume Γ ⊢ a≤×b ∧ b≤×c,
by π₁,π₂ (∧-elim):
- a₁≤b₁ ∧ b₁≤c₁
- a₂≤b₂ ∧ b₂≤c₂
apply Trans in P,Q:
- a₁≤c₁, a₂≤c₂
then ∧-intro ⇒ (a≤×c).
∴ Γ ⊢ Trans×.
∧-intro:
from Γ ⊢ φ and Γ ⊢ ψ, infer Γ ⊢ φ∧ψ
∧-elim:
from Γ ⊢ φ∧ψ, infer Γ ⊢ φ or Γ ⊢ ψ
π₁(a≤×b) = a₁≤b₁
π₂(a≤×b) = a₂≤b₂
pearl pondBOT
@void grail Has your question been resolved?
void grail
I think it is possible to reason about this statement using just this information, the definition of Preorder and Product of categories
preorder P:
objects (p),
arrows (p → p'),
≤ defined by existence of arrow
reflexive: (p → p)
transitive: (p → p' ∧ p' → p'' ⇒ p → p'')
product P × Q:
objects (a,b),
arrows (f,g) with
f: a→a' in P,
g: b→b' in Q
order:
(a,b) ≤× (a',b') ⇔ a≤_P a' ∧ b≤_Q b'
reflexive:
(1_a,1_b): (a,b)→(a,b)
transitive:
(f',g') ∘ (f,g) = (f'∘f, g'∘g)
P×Q inherit reflexivity & transitivity
→ preorder
ty
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eager jewel
pearl pondBOT
eager jewel
given this function derivative how to find the maximas and minimas
tropic saddle
of f or f'?
eager jewel
of f
split void
try to set $f'(x) = 0$
jolly parrotBOT
Annie Maqionde
split void
I can see quite a few linear factors there
split void
think if $f'' > 0$ its a minimum and if $f''<0$ its a maximum but there cud be a simpler way
jolly parrotBOT
Annie Maqionde
eager jewel
the change in sign of f'
ye its changing at x=0,1/2 2 and 5
but how do decide which is max and min
frank violet
If it's negative then positive it means that fx decreasing then increasing
So what it should be? down then up
eager jewel
If it's negative then positive it means that fx decreasing then increasing
ohk so i have to check at like for example x=2+ and x=2- sign of f'?
pearl pondBOT
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potent flax
pearl pondBOT
latent quail
solving for the inequality?
prisma kernel
Can you send the full question please
glass meadow
Are those really the only options? 
potent flax
yes
my tests are some of the most braindead ones so i cant tell if the answer isnt flip coin based
glass meadow
Well, sorry but the answer to what you posted is none of these four options
prisma kernel
Kinda close though
glass meadow
Unless the question isn't exactly "what is the set of solutions"
Kinda... I guess they meant for it to be 4+x >= 7
potent flax
so umm which answer i have the best chance with?
prisma kernel
which do you think
light helm
potent flax
i doubt the teacher cares
prisma kernel
Well first of all, what's the answer you're getting?
potent flax
i will tell once i finish the test
prisma kernel
sure
verbal whale
Mmh how?
potent flax
well thanks for help
pearl pondBOT
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wintry anvil
hi i am learning about logical notation i want to write this sentence in logical notation
stray canyon
yeah
wintry anvil
great
stray canyon
you can
wintry anvil
or do i use that fancy arrow
final shore
$\forall M \in \textbf{R}, \exists x \in \textbf{R}$ s.t.$ |x| \geq M$
jolly parrotBOT
holo_morph
stray canyon
not write anything
autumn fossil
**holo\_morph**
it can be either with the comma, or with nothing
definitely not arrow
cloud willow
∀ M ∈ ℝ, ∃ x ∈ ℝ : |f(x)| ≥ M
final shore
$A \implies B$
jolly parrotBOT
holo_morph
stray canyon
but if A is not true you cant say anything
autumn fossil
it's a binary connective, so it's the same kind of thing as e.g. AND and OR (∧ and ∨); u dont use it to connect 2 quantifiers
stray canyon
thats just a mistake
wintry anvil
oh ok
cloud willow
but why is absolute value of f(x) just |x|
∀ M ∈ ℝ, ∃ x ∈ ℝ : |f(x)| ≥ M
stray canyon
yes
cloud willow
and there isnt a symbol for "such that"? that seems like a common one
{ x ∈ ℝ | x > 0 }
Or ,
;
viscid shale
{ x ∈ ℝ | x > 0 }
Or ,
this is mostly for set construction tho
wintry anvil
ohh right i remember |
viscid shale
youre probably fine using st.
wintry anvil
but ; feels cool
stray canyon
basically, if you add commas between your quantifiers (forall, exists), you can use ":" and "|"
and if not, you can also use comma
cloud willow
so this is fine?
Yea
stray canyon
yea
pearl pondBOT
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odd tundra
I don't really understand why the symbolization of this english sentence into First-Order Logic didn't work
odd tundra
I've also posted the symbolization key on the 2nd image
My statement says: "For all x, if x likes cory, then x is a dog"
I don't get how that isn't logically equivalent to "Only a dog can be heavier than Cory"
oh wait, I used the wrong predicate lmao
I just needed to change L(x,c) into H(x,c), then it would be correct
glass meadow
Uh... so "for all x, if x is heavier than Cory, then x is a dog" ?
autumn fossil
Uh... so "for all x, if x is heavier than Cory, then x is a dog" ?
whats wrong with that?
glass meadow
Just asking for confirmation
odd tundra
Uh... so "for all x, if x is heavier than Cory, then x is a dog" ?
yea, that's the right answer
I just wrote "For all x, if x likes cory, then x is a dog"
but i should've written "if x is heaver than cory"
instead of "if x likes cory"
glass meadow
What's the exercise? Writing the sentence with logic symbols?
odd tundra
What's the exercise? Writing the sentence with logic symbols?
yea, translating english sentences into First Order Logic sentences
but yeah, I just did a silly mistake lol
have any of you helpers heard of the Fitch proof system?
I may have some questions on that later on
glass meadow
No
To answer your question, "only a dog can be heavier than Cory" is logically equivalent but I'm not sure where that sentence came from, so...
odd tundra
oh, that sentence you put under quotes is the sentence we have to translate into FOL
glass meadow
(as long as the domain is the same, that is, animals)
odd tundra
we're given english sentences
and our job is to write that into FOL
glass meadow
Not sure what the issue is then
Also I have to leave, feel free to ping helpers if no one else is around
odd tundra
there's no issue anymore, it's resolved as I posted my issue
cuz I realized my issue halfway as I wrote the request
.close
pearl pondBOT
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rare holly
hello in this why dont we convert the % into decimals
pearl pondBOT
hello in this why dont we convert the % into decimals
toxic lichen
i mean, what happened here is essentially that QR was taken as length 60 and PR was taken as length 100
you could do the same thing with PR = 1 and QR = 0.6 if you wanted; you would get the same value of sin(PQR) this way
(for the record, i don't think PR=100 and QR=60 is the nicest way to do this)
pearl pondBOT
shut wren
pearl pondBOT
Available help channel!
carmine juniper
Is it possible to simplify it?
pearl pondBOT
Is it possible to simplify it?
warped violet
,rccw
jolly parrotBOT
warped violet
What in the world is written here
You've got equals sign = in the denominator
with random floating fractions
hint: you've got a whole blank page - go to a new line
warped violet
,rccw
jolly parrotBOT
warped violet
great, another equals sign randomly appeared
viscid shale
I like to believe the original problem is $$\frac{(16x^2y^2)^{\frac 14}}{\sqrt{xy^4}}$$
jolly parrotBOT
carmine juniper
Correct
warped violet
I like to believe the original problem is $$\frac{(16x^2y^2)^{\frac 14}}{\sqrt{x...
Yes, and in the second step the fraction and denominator simply disappeared
carmine juniper
You just copy and pasted
viscid shale
yes the solution is right.
viscid shale
I am sorry but I have no clue what this means
Distributed the fourth root on the numerator, the sqrt in the denominator, and the next part is just the next stage, where hes cancelling terms
warped violet
Distributed the fourth root on the numerator, the sqrt in the denominator, and t...
Yeah I know I was just exaggerating
But my point still stands
viscid shale
lmao
warped violet
Please
Go to a new line
Don't cram things together
and also
more importantly
don't just leave stuff out
carmine juniper
,w y^-3/2
jolly parrotBOT
warped violet
Because $\frac{(16x^2y^2)^{\frac 14}}{\sqrt{xy^4}} \neq \sqrt[4]{16x^2y^2}$
jolly parrotBOT
USS-Enterprise
carmine juniper
@viscid shale i have 2 * y^-3/2 now
How do you change y^-3/2 into positive power
Like
5^-1 is 1/5
warped violet
$a^{-m} = \frac{1}{a^m}$
jolly parrotBOT
USS-Enterprise
jolly parrotBOT
USS-Enterprise
carmine juniper
Ah i get it
jolly parrotBOT
USS-Enterprise
warped violet
uh
what
how did
Why y^2 at the end
Also why is 1 1/2 written on top of everything
sudden tangle
Hello, I'm in 8th grade and i have about 5 hours till my math's exam, i need someone to help me learn basic maths like propotion, Nth term etc
pearl pondBOT
@carmine juniper Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
ruby wharf
Can someone please help explain horizontal stretch about a vertical line PQ to me? I know about dilation and I know about horizontal stretch for linear, quadratic, and exponential functions but I don't know how this is done here in this question, how am I supposed to visualize this?
ruby wharf
This was a test that I had earlier and I picked D and that was correct, their explanation was that it wasn't a rigid transformation nor was it a dilation.
But I don't know what a horizontal stretch about a vertical line is actually doing for any transformation of any object.
To clarify, this is for geometry on Khan Academy.
stuck spoke
Can someone please help explain horizontal stretch about a vertical line PQ to m...
a horizontal stretch about a vertical line means points move horizontally away from the vertical line but stay at the same vertical position. it changes distances but not angles. it’s not a rigid transformation or dilation. only angle measures are preserved, not segment lengths.
hope that helps
ruby wharf
Ah nevermind I get it now, thank you so much 🩷
stuck spoke
Ah nevermind I get it now, thank you so much 🩷
kinda late...
ight girl have a good one
ruby wharf
a horizontal stretch about a vertical line means points move horizontally away f...
a horizontal stretch about a vertical line means points move horizontally away from the vertical line but stay at the same vertical position
What vertical line are we talking about though?
Where does this exist?
Is it parallel to the y axis?
Is it arbitrary?
Is it just any 2 points that form a line segment on any shape or function in a 2d grid?
I don't understand.
stuck spoke
> a horizontal stretch about a vertical line means points move horizontally away...
good question
let me break it down for you
ruby wharf
Thank you
stuck spoke
the vertical line is the line around which the stretch happens
it’s parallel to the y-axis, and points move horizontally away from it. it’s not random; the problem will tell you which line it
is
ruby wharf
it’s parallel to the y-axis, and points move horizontally away from it. it’s not...
Where is this line though?
stuck spoke
wait wdym
ruby wharf
because for example if it's here then it's going to be different than if it were here right?
It will transform the shape differently, no?
stuck spoke
im not sure 
ruby wharf
Does it matter where it is?
ty anyway 🩷
I know what a vertical stretch is now though
i think?
idk
safe prairie
Sth like this?
stuck spoke
we need help
safe prairie
Horizontal stretch along some vert
ruby wharf
Horizontal stretch along some vert
That is, but I'm taking geometry and I don't think horizontal stretches were introduced in this course yet, they probably were in algebra 1 on the website but not on the course
so i'm pretty confused
safe prairie
wait this isnt about graph transformation?
ruby wharf
wait this isnt about graph transformation?
No
It's about sequence transformations in geometry and what's preserved and what isn't
In terms of angles and line lengths
ruby wharf
wait this isnt about graph transformation?
I suppose that it falls under this
I would love to be able to generalize the statement that "a stretch about line PQ transforms any given shape to where the angles and lengths do not match the original shape" but I don't know how to visualize that or show-case it on a graph or something like how I know how to do that with other transformations like dilations, rotations, reflections, and vertical and horizontal translations.
safe prairie
i mean stretching a square to a rhombus does that
ruby wharf
i mean stretching a square to a rhombus does that
Does stretching dilate a shape but not for all vertices?
safe prairie
Ah nevermind I get it now, thank you so much 🩷
i was watching this vid and idk if its him drawing things badly and not making the stretching up to scale, or if hes just moving AB away, parallel to its original. i hope its the former
ruby wharf
i was watching this vid and idk if its him drawing things badly and not making t...
But either way i don't remember him doing that before
In that geometry course at least
so idk how he devised that
ruby wharf
Does stretching dilate a shape but not for all vertices?
Is this considered a dilation?
safe prairie
Does stretching dilate a shape but not for all vertices?
i think for the definition of "dilate" in ur chapter, it means growing/shrinking the entire thing, with a "point", which in art would be called a vanishing point
ruby wharf
Is this considered a dilation?
By moving b and c one to the right?
ruby wharf
i think for the definition of "dilate" in ur chapter, it means growing/shrinking...
I see
safe prairie
i dont think this is what they mean, this type of transformation requires a matrix no?
ruby wharf
i think for the definition of "dilate" in ur chapter, it means growing/shrinking...
Omggg i love vanishing points
ruby wharf
i dont think this is what they mean, this type of transformation requires a matr...
Well I haven't learned matrices yet
safe prairie
yeah
ruby wharf
Is this considered a dilation?
Is this a horizontal stretch about line BC?
safe prairie
more like horizontal translation "of" line BC
stuck spoke
Is this considered a dilation?
this isn't a dilation. it looks like the shape has been... smudged
ruby wharf
this isn't a dilation. it looks like the shape has been... smudged
B and C have been moved 1 unit to the right.
stuck spoke
if you're speaking obt dilation
ruby wharf
if you're speaking obt dilation
i'm wondering if dilation is like stretching
stuck spoke
no...
stuck spoke
dilation is like stretching or shrinking a shape
stuck spoke
also
it changes the size of the shape but keeps the same proportions
ruby wharf
also
it changes the size of the shape but keeps the same proportions
Yea
The angles stay the same, but the lines aren't the same length as the pre-image
stuck spoke
How about stretching?
i said that already...
stuck spoke
all points of the shape move away from or towards a fixed point (called the center of dilation). The shape doesn’t change its form, just its size. So, it's like uniformly scaling the entire shape
stuck spoke
dilation is like stretching or shrinking a shape
there
ruby wharf
I think expanding is a better term btw
ruby wharf
Dilations are not the same thing in this lesson
safe prairie
so we moved to expanding
no like, replace ur use of "stretching" with her "expanding"
ruby wharf
There's stretching, and also dilation
and also rotations, and translations
and reflections as well
Stretching is not dilation
I don't know what stretching is though
stuck spoke
no like, replace ur use of "stretching" with her "expanding"
oh so she needs help with differentiating between those terms?
ruby wharf
I know how to use stretching say in a linear equation like y=2/3x+9
safe prairie
imagine this same thing happening to a shape on a gridless paper maybe
stuck spoke
wait igu
safe prairie
oh so she needs help with differentiating between those terms?
yes because stretching is a standalone action now
ruby wharf
imagine this same thing happening to a shape on a gridless paper maybe
Tysmmmmm!!!!!!!!!!!!!!! I see now why the angles and segment lengths aren't the same as the pre-image, I have another question though if you don't mind, does this apply to a line that's being stretched about that has any slope? Or is it just vertical lines? In other words, do angles and length segments stay the same for a line that isn't a vertical one? Or is it only vertical lines where this is the case?
ruby wharf
imagine this same thing happening to a shape on a gridless paper maybe
the angles clearly change, for example look at angle ABC, it's clearly bigger than the image of triangle ABC's respective angle A prime B prime C prime
safe prairie
if u dont have a coord system, if its just a shape on blank paper, then yeah the line can be in any direction. u can stretch a square diamond like 45 degrees topleft to make a slanted rectangle
safe prairie
if u dont have a coord system, if its just a shape on blank paper, then yeah the...
this preserves angles but it generally doesnt, cuz i can do the same to a circle, then nothing is preserved
ruby wharf
if u dont have a coord system, if its just a shape on blank paper, then yeah the...
How about with a coordinate system
safe prairie
then i wouldnt know the math needed to do such a thing
but visually its possible ofc
ruby wharf
this preserves angles but it generally doesnt, cuz i can do the same to a circle...
Then how are they teaching me proofs after this when this isn't true?
safe prairie
what aint true
ruby wharf
then i wouldnt know the math needed to do such a thing
For example the line PQ with a slope of 1
ruby wharf
what aint true
That it preserves angles
safe prairie
it indeed doesnt preserve angles
ruby wharf
for that case
safe prairie
it occasionally does
ruby wharf
this preserves angles but it generally doesnt, cuz i can do the same to a circle...
You're saying for a square diamond it will preserve the angles?
ruby wharf
which means theres no theorem that says it preserves anything
So then this is only useful for like any object that I'm just gonna normally be using in this course or proving with but not all then?
Like to say "Because of such and such"?
in a proof maybe?
safe prairie
ngl i never had a course in highschool talking about manipulating shapes
ruby wharf
or double column proof?
ruby wharf
ngl i never had a course in highschool talking about manipulating shapes
oh
i'm doing this for fun
safe prairie
we transformed graphs
ruby wharf
we transformed graphs
same in High School
ruby wharf
Tysm for helping me 🥺
ruby wharf
what course then?
Algebra 1 we transformed all kinds of functions
@stuck spoke Tysmmmmmmmm too i really appreciate you both
safe prairie
So then this is only useful for like any object that I'm just gonna normally be ...
i mean this course
stuck spoke
<@914216765553254420> Tysmmmmmmmm too i really appreciate you both
have a good one
safe prairie
Like to say "Because of such and such"?
i think at the very least you can identify that sth is "stretched"
maybe for those khan academy questions idk i didnt do a single course of theirs
ruby wharf
maybe for those khan academy questions idk i didnt do a single course of theirs
thats fair tysm anyway! ❤️
ruby wharf
i think at the very least you can identify that sth is "stretched"
Mhm!
safe prairie
"because nothing is preserved" yeah
they arent gonna show you irregular transformations that straight up is just smudging the shape into sth else
(right)
ruby wharf
Yea!
safe prairie
there you have it!
pearl pondBOT
plush bramble
!15m
pearl pondBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
Please do not ping individual helpers unprompted.
ancient valley
Sorry I might be a bit late but I’ll check I just need to plot it real quick
Well it sucks on phone bro 😭
I’ll switch to my pc right quick
It is indeed correct twin 👍
@flint wyvern
If you need anything I can try and help
pearl pondBOT
@flint wyvern Has your question been resolved?
pearl pondBOT
@flint wyvern Has your question been resolved?
pearl pondBOT
✅ Original question: #help-39 message
Please do not ping individual helpers unprompted.
pearl pondBOT
@flint wyvern Has your question been resolved?
ancient valley
Sure thing
wild vigil
why was the exponent dropped for the denominator
pearl pondBOT
why was the exponent dropped for the denominator
cinder flower
hm nothing was really dropped
this process is starting from something else
not exactly what’s given in the problem
wild vigil
can you elaborate? i assume we're trying to go from the form a/1-r to sum ar^n
cinder flower
what is the relation between f and 1/(1+4x)?
wild vigil
nnnnnnevermind i should've watched further in
the instructor creates a separate series that's functionally equivalent and then we just do some fiddling to make it look like f(x) somewhere
.close
pearl pondBOT
cinder flower
yea something like that
pearl pondBOT
Available help channel!
fading nexus
If k said horizontal transformation, translate 4 units. , over x axis, then up 3 is rhag also correct
dense jasper
If k said horizontal transformation, translate 4 units over x axis, then up 3 is rhag also correct
in what direction
did you mean to write "Translate 4 units left, then reflect over the x axis, then translate up 3 units"
because it looks like you're missing words here
dense jasper
did you mean to write "Translate 4 units left, then reflect over the x axis, the...
if this is it, then no
that would give you $3-\frac{1}{x+4}$
jolly parrotBOT
Civil Service Pigeon
fading nexus
What’s wrong with it?
dense jasper
but you want $3-\frac{2}{x+4}$
jolly parrotBOT
Civil Service Pigeon
fading nexus
Oh yea I forgot the Vertical transformation of 2 I put that as the first step on my paper
dense jasper
then yes
pearl pondBOT
If you are done with this channel, please mark your problem as solved by typing .close
@fading nexus Has your question been resolved?
bitter herald
.close
fading nexus
Where did the -x come from
random ermine
role well deserved
fading nexus
Sorrry I thought the other one got closed automatically I thought I read that 😭
toxic lichen
close your prev girl 😭
fading nexus
Which is why I went to a new one
crystal dew
closed it for you
toxic lichen
the x in the numerator gives you that x intercept at 0
toxic lichen
the -1 factor seems to be vertical scale adjustment
random ermine
Sorrry I thought the other one got closed automatically I thought I read that 😭
also do 1 question at a time, from a learning pov
toxic lichen
you know the eq is y = kx/((x+2)(x-2))
fading nexus
We haven’t done vertical scales for these types
toxic lichen
so take any point on the graph and use it to find k
ah they say k could be anything <0
fading nexus
But there’s no concrete points
None of them ever go exactly on top of a grid line corner
So how would I know what point to do since I don’t know how to find the decimals
fading nexus
so take any point on the graph and use it to find k
The only point is (0,0 but I don’t think we can use that point
toxic lichen
(1, something positive)
toxic lichen
ah they say k could be anything <0
the image says that you aren't expected to say anything about k except its sign
fading nexus
the image says that you aren't expected to say anything about k except its sign
but it says it has to be negative and how do I know that without plugging a point in
and I also don’t see the difference the - is making
I don’t understand how we got all this information some of it is missing from the given info
toxic lichen
and I also don’t see the difference the - is making
vertical flip
toxic lichen
but it says it has to be negative and how do I know that without plugging a poin...
the closest thing you have to that is (1, something positive)
fading nexus
I just don’t UNDESTAJD what I should do on my test
because now it seems like any of them could have a - without me realizing so how do I know which ones do and which ones don’t
How am I supposed to write the equations if I am not given the y and x intercepts
<@&286206848099549185>
fading nexus
I don’t understand how we are supposed to make and write the equation for this graph because we are not given the x intercepts s
fading nexus
How am I supposed to write the equations if I am not given the y and x intercept...
^
compact sinew
part a?
fading nexus
Yea and part b in a way
compact sinew
Ok
fading nexus
i mean you have one, others are uhh guess work
Wdym
fair creek
like you could also have h(x)*(x-6) and it would still not change much
fading nexus
I’m so confused
fair creek
so its the bare minimum of an equatiob from the given data
fading nexus
There are set x intercepts those can’t be changed
compact sinew
just properly set the x and y asymptotes
fair creek
for example the x+2 can be aby other x-a me thinks
fair creek
for example the x+2 can be aby other x-a me thinks
because the second root is not given, you can make one up and it would lie under yohr given criteria
fair creek
i hope you understood what i meant
fading nexus
Kinda but I don’t know if I would if I did not know the x intercepts from the answer key if thag makes sense
pearl pondBOT
@fading nexus Has your question been resolved?
wind lagoon
The correlation coefficient is defined in terms of the covariance and variances of two random variables (it is the covariance divided by the square root of the variances). Can there be a situation where the covariance equals 0 (or simply finite) whereas the denominator is infinity?
pearl pondBOT
The correlation coefficient is defined in terms of the covariance and variances ...
@wind lagoon Has your question been resolved?
pearl pondBOT
@wind lagoon Has your question been resolved?
wind lagoon
.close
pearl pondBOT
pearl pondBOT
Available help channel!
carmine juniper
"Fill in the right column of the table with T if the statement is true, and F if it is false. Note that you do not need to provide justification here."
pearl pondBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
naive zinc
They are asking for answer checking not answer provided
hot viper
Sorry
autumn fossil
F
T
T
T
T
F
T
T
F
T
F
F
T
I cant see the last word in 1st pic
2nd pic seems mostly wrong
naive zinc
I cant see the last word in 1st pic
Defined
naive zinc
Please rewrite it this way: picture 1: FTT… picture 2 :… picture 3:…
west vault
By subset do you mean proper subset?
toxic lichen
The function f(x) = sqrt(2x-6) is defined at x=3
you wrote that this is false. you are wrong about that
toxic lichen
The domain of f(x)=1/(x^2-9) is all x except x=3
you wrote that this is true. you are also wrong about this. the domain also excludes x=-3
carmine juniper
> The domain of f(x)=1/(x^2-9) is all x except x=3
you wrote that this is true. ...
Ik I said that 7th is wrong
bitter herald
can you answer jewels' question as well
naive zinc
6 7 8
carmine juniper
What?
toxic lichen
yeah looks like those are your only 3 mistakes
autumn fossil
The 2 ones after the sqrt one are wrong
carmine juniper
It’s 0..
toxic lichen
It can’t be defined…
what's "it".
carmine juniper
The 2 ones after the sqrt one are wrong
Which ?
Sqrt one
Can’t you just tell me
toxic lichen
it would be really convenient if these were numbered
carmine juniper
@autumn fossil are those only wrong?
warped violet
The one right after is also incorrect (the statement)
naive zinc
<@951190447185874994> are those only wrong?
And 6th
carmine juniper
Why is 6th wrong?
warped violet
I doubt this is beneficial to you in any way
carmine juniper
It’s turning into 0…
naive zinc
sqrt(0) is well defined
carmine juniper
Why is 8 wrong?
warped violet
The one right after is also incorrect (the statement)
Oh my bad
carmine juniper
No…
warped violet
I wasn't aware I had to match all those letters to unnumbered statements here
naive zinc
Leading coefficient isn’t 0
carmine juniper
It can be
a>0
a=0
a<0
bitter herald
is this about the b^2 - 4ac = 0 question?
carmine juniper
Then you are correct if you use this definition of yours
Gosh that was so bitchy…
carmine juniper
a = 0 turns a quadratic into a linear function so...
a>d = 2 solution
a=d = 1 solution
a<0 = 0 solutions
hybrid ivy
so, not only have you turned two of the 0s into ds, but now a is supposed to represent the discrim??
warped violet
Why are you complaining about literally everything 😭
bitter herald
Gosh that was so bitchy…
Yeah, uh, <@&268886789983436800> this person has been repeatedly and excessively rude to the people helping them. Can you give this a look?
pastel umbra
"Tonight, on 'What does Attitude mean?'..."
carmine juniper
Yeah, uh, <@&268886789983436800> this person has been repeatedly and excessively...
Are you kidding me?
hybrid ivy
Gosh that was so bitchy…
I mean if you dislike that people are pointing out definitions to you, you can always, not ask.
nobody here owes you time.
naive zinc
There isn’t such a thing, t=b^2-4ac, when a doesn’t equal 0, t>0 two, t=0 one, t<0 zero, a=0 infinite (presume you are talking about that over R)
bitter herald
He wasn't, though
carmine juniper
THAT WAS CRASS
hybrid ivy
trolling? I don't think so? in a general quadratic ax^2 + bx + c, if a = 0, it indeed turns into a linear function
naive zinc
He says I am trolling. I say I am the one who blocks him
hybrid ivy
the fuck you on?
pastel umbra
That's not a trolly response; he's implying your definition's wrong.
pastel umbra
a>d = 2 solution
a=d = 1 solution
a<0 = 0 solutions
Namely, that this is wrong.
carmine juniper
Namely, that _this_ is wrong.
Why
merry carbon
HE WAS TROLLING JN THE RESPONSE
How exactly was the response trolling?
pastel umbra
You should know how the discriminant test works
carmine juniper
How exactly was the response trolling?
He neglected me
pastel umbra
Actively responding to you isn't neglect
warped violet
@carmine juniper if you want assistance from anyone in life, not just from people giving their time for free on Discord, you should be at least respectful to them.
pastel umbra
That's actually the opposite of that
hybrid ivy
Nenni, I'm not a mod, but with all due respect, you have a history of not exactly having a nice personality to helpers.
so, here's a quick and friendly reminder that narcissism won't get you too far here, especially towards people who are trying to help you for free.
now, where was I
merry carbon
Gonna ditto the two above comments 
unborn abyss
a quick scribbled T / F on each question in mspaint would go so hard
carmine juniper
I am trying to learn and he just comes with comments “oh it’s correct if you think that, but everyone else will know that you’re wrong”
That’s impudent
radiant terrace
Not every class uses the same definitions.
pastel umbra
In fairness that's cos multiple ppl had already told you otherwise
If you have a discriminant D = b^2 - 4ac of an equation ax^2 + bx + c = 0 (and we assume here that a != 0, because otherwise this is not a quadratic), then
- D > 0 means the equation has 2 distinct solutions
- D = 0 means the equation has 1 distinct solution
- D < 0 means the equation has no [real] solutions.
radiant terrace
These kinds of statements are not always a matter of rudeness.
warped violet
pastel umbra
If you have a discriminant D = b^2 - 4ac of an equation ax^2 + bx + c = 0 (and w...
Can you see how this differs from the justification you'd provided?
warped violet
Let's not forget the emoji spamming incident with you 10 days ago
carmine juniper
These kinds of statements are not always a matter of rudeness.
It is cause he stated that he doesn’t want to help and I should think what I think
carmine juniper
Let's not forget the emoji spamming incident with you 10 days ago
Because you were provoking me?
radiant terrace
People don't owe you help and it's not rude to say "under that assumption you are right, but that is not a common assumption"
warped violet
Because you were provoking me?
Feel free to read through the entire channel from the start and correct your sentence when you are ready.
carmine juniper
People don't owe you help and it's not rude to say "under that assumption you ar...
Neglection
radiant terrace
Okay cool
pastel umbra
One - the noun is "neglect"
Two - I've pointed out that that's the opposite of neglect
radiant terrace
Neglection
Take a day off to consider how to interact civilly with people trying to give you free help.
pastel umbra
Even if you think it's rude, and it's been argued why it isn't, it's not the same as neglect
radiant terrace
.close
pearl pondBOT
hybrid ivy
also, to tie up loose ends
pearl pondBOT
Available help channel!
eager jewel
pearl pondBOT
eager jewel
how to do this integration
west vault
Divide the top and bottom by x^2
In the denominator, one x to divide (1 + x^2), and the other goes inside the square root
eager jewel
o
west vault
complete the square inside the root and sub x + 1/x
pearl pondBOT
pearl pondBOT
Available help channel!
latent glen
Given a circle (O) with A outside. Draw tangent AB (B belongs to (O)) and draw BE perpendicular to OA (E belongs to (O)). Prove that AE is a tangent to (O).
Can someone explain this to me? My brain just short-circuited all of a sudden.
pearl pondBOT
pearl pondBOT
Available help channel!
bitter herald
just testing
distant folio
This channel will close soon, could you move to one of the available ones?
sorry ofc
jolly trout
This is an example from discrete structures. We defined a ternary operator:
[
\Lambda(p,q,r) = (\neg p \implies q) \ \lor \ (r \land q)
]
I need to prove that ${\Lambda}$ is not a functionally complete set.
I simplified the operator to
[
\Lambda(p,q,r) = p \lor q
]
I understand that ${\lor}$ (and therefore ${\Lambda}$) is not a functionally complete set as you can not express $\neg$.
I know it can be proven using the monotonic property in Boolean algebra, but I am wondering if there is another way?
jolly parrotBOT
squared_apple
toxic lichen
i mean, i dont think there would be a different way for your problem unless you have a different way of proving {or} isn't a functionally complete set
jolly trout
i mean, i dont think there would be a different way for your problem unless you ...
i was just wondering
because I don't fully understand how to prove it that way...
know was meant I know it's proved that way
but not that i know how to
toxic lichen
OR is monotonic, therefore so is anything you build from nothing but ORs. NOT is... not.
jolly trout
OR is monotonic, therefore so is anything you build from nothing but ORs. NOT is...
Yes. is it enough to write that? and conclude that therefore it is not a funct. complete set?
toxic lichen
failure to express even one function means failure to be functionally complete so yeah
pearl pondBOT
pearl pondBOT
Available help channel!
white mountain
Let f be a real smooth function with f(0)=1,f(1)=0,f'<0 and F(x,y,z)=f(x²+y²)exp(-z). I have shown that F is submersion and preimage of F for every c on R is a normal submanifold woth dimension 2. I have to show that preimage is diffeomorphic with: R², if c>0, unit circle, if c<0. How?
pearl pondBOT
Let f be a real smooth function with f(0)=1,f(1)=0,f'<0 and F(x,y,z)=f(x²+y²)exp...
@white mountain Has your question been resolved?
pearl pondBOT
@white mountain Has your question been resolved?
pearl pondBOT
@white mountain Has your question been resolved?
rugged leaf
hi
summer imp
summer imp
Just post your question whatever it is with pictures and someone will try to help.
warped violet
If you labeled the points correctly, then this is correct yes
GeoGebra 💪
There is no domain and range to be seen though
Also F is unnecessary
Also, I don't know what "equation of the axis" is supposed to mean
x = 0 and y = 0??
Also, I don't really see the point in this. You just typed the expression in the example in GeoGebra
But the graphs definitely are correct
pearl pondBOT
@rugged leaf Has your question been resolved?
warm elbow
pearl pondBOT
warm elbow
is the best way of solving this is putting Q(x,y,z) into matrix form then perform a regular diagonlization?
with eigenvalues
pearl pondBOT
@warm elbow Has your question been resolved?
warm elbow
Prove that if a matrix $A$ satisfies $A^5 =I$, then $A$ is diagonlizable
jolly parrotBOT
toast
warm elbow
how do you approach this problem
prime bramble
Prove that if a matrix $A$ satisfies $A^5 =I$, then $A$ is diagonlizable
is A a real matrix or a complex matrix? 
if it's a real matrix, I don't think the statement is true
but if it's a complex matrix, consider the minimal polynomial of A
prime bramble
is this theoreom particularitly usful?
mhm!
prime bramble
hm, it's not going to be enough to conclude I don't think 
I don't see a way to get around the minimal polynomial
have you seen that before?
warm elbow
not really haha
prime bramble
not really haha
ah well, it's just the "smallest polynomial" q such that q(A) = 0, i.e. q divides every polynomial p for which p(A) = 0
warm elbow
and A is the matrix right
prime bramble
a useful fact is that q has the same roots as the characteristic polynomial of A, so A is diagonalizable iff q splits into linear factors
prime bramble
and A is the matrix right
yup
prime bramble
if you choose an appropriate p, you can apply your theorem to find out what the eigenvalues of A must be