yeah but i get a different answer 😅
#help-27
pulsar trellis
Wait I think I understand lol
sorry
I forgot that it can't be a negative when square rooting
.close
devout snowBOT
devout snowBOT
Available help channel!
pure stone
Given A and B are real, n x n matrices that satisfy AB = BA. Prove det(A^2 + B^2) >= 0
devout snowBOT
Given A and B are real, n x n matrices that satisfy AB = BA. Prove det(A^2 + B^2...
royal hatch
what have u tried ??
devout snowBOT
@pure stone Has your question been resolved?
devout snowBOT
@pure stone Has your question been resolved?
shell igloo
Given A and B are real, n x n matrices that satisfy AB = BA. Prove det(A^2 + B^2...
do you remember how matrix multiplication is done?
zenith lion
Hello helpers
devout snowBOT
Hello helpers
zenith lion
why is the output vector and input vector on the same plane?
its just for intuition right?
because 2d input vector and 2d output vector would be 4 dimensional
pseudo basin
if you were to graph a function R^2 -> R^2 in the literal same way as we do R -> R then yes that would require 4 dimensions
here though visuals-wise the output vector is attached to its corresponding input
zenith lion
right so if I just took two different 2d planes, what would the resulting output vector look like
would it also start at 0,0 ?
or at the input vectors coordinates
Im trying to understand where the output vector actually begins and ends
zenith lion
here though visuals-wise the output vector is _attached to_ its corresponding in...
because as you say its attached at the input
on its own 2d plane it would begin at (0,0) right?
pseudo basin
Im trying to understand where the output vector actually begins and ends
"where a vector 'actually' begins and ends" is a moot question
it doesnt 'actually' begin/end anywhere at all
zenith lion
So its generally normal to be confusing
because I always get it wrong considering this way
whatever not worth digging into it
the visualization is good
thanks ann
.close
devout snowBOT
devout snowBOT
Available help channel!
fair raft
could someone help me with this problem?
devout snowBOT
could someone help me with this problem?
@fair raft Has your question been resolved?
fair raft
anyone?
devout snowBOT
@fair raft Has your question been resolved?
carmine veldt
anyone?
I think we could apply the definition of ρ-length on the equality given for ρ-length being invariant for mobius transformations of H
once we subtract both integrals, we shd get somethings like integral from a to b of (ρ(γ(σ(t)))∣γ′(σ(t))∣−ρ(σ(t)))∣σ′(t)∣ dt = 0
setting f(z)=ρ(γ(z))∣γ′(z)∣−ρ(z) should immediately give you the answer after applying the thing given in the hint
Correct me if I'm wrong tho, idk what those transformations and all mean 😭
devout snowBOT
@fair raft Has your question been resolved?
dusky belfry
anyone?
I am not gonna be too much of a helper but after no one responds for 15 minutes
I read it on the rules
it's safe to ping them at @ helpers
once
only once
fair raft
I am not gonna be too much of a helper but after no one responds for 15 minutes
okoko tysm
.close
merry ivy
Is this the right method
devout snowBOT
Is this the right method
surreal zenith
when price is 700 + 100 * 0, number of occupied rooms is 72 - 2 * 0
when price is 700 + 100 * 1, number of occupied rooms is 72 - 2 * 1
when price is 700 + 100 * 2, number of occupied rooms is 72 - 2 * 2
....
when price is 700 + 100 * n, number of occupied rooms is 72 - 2 * n
daily income is (700 + 100 * n) (72 - 2 * n)
and x = 700 + 100 * n
merry ivy
when price is 700 + 100 * 0, number of occupied rooms is 72 - 2 * 0
when price i...
Wait...what
merry ivy
and x = 700 + 100 * n
Hello?
devout snowBOT
@merry ivy Has your question been resolved?
merry ivy
<@&286206848099549185>
merry ivy
<@&286206848099549185>
merry ivy
<@&286206848099549185>
devout snowBOT
@merry ivy Has your question been resolved?
errant tapir
hello
I am taking algebra 2 this summer
should I get any textbooks
or rely on the normal curriculum work
unique crown
I need help learning elimination and substution
devout snowBOT
I need help learning elimination and substution
devout snowBOT
@unique crown Has your question been resolved?
silk rock
which method do you want to use for this question first?
unique crown
which method do you want to use for this question first?
Elimination, sorry
devout snowBOT
Elimination, sorry
unique crown
Had dnd on
upbeat forge
so do you know what you need in both equations to use elimination?
unique crown
Subtract
upbeat forge
before you do, you need to make sure you have a term in each equation that will cancel itself out when added to or subtracted from the second equation.
that's why the whole process is called elimination - you're eliminating one variable from consideration.
as of now, though, using your question, there's no direct elimination possible. a naive subtraction here will still see both x and y.
to start using elimination in a situation like this, you should first match the coefficient of one variable in one of the two equations to its coefficient in the other one by multiplying.
in this case, the x terms are easy to match here.
hint: multiply the second equation by a number to get the x coefficient to the same as the one in the first.
can you do this step first?
unique crown
Appreciate it
strange vale
yall know about quadratic equations like finding roots and vertex??
upbeat forge
yall know about quadratic equations like finding roots and vertex??
!occupied, sorry. please open another channel for your question, like #help-49.
devout snowBOT
yall know about quadratic equations like finding roots and vertex??
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
upbeat forge
it does.
you want the 5x to turn into 15x so that when you subtract the two equations, the 15x from the first equation and the 15x from the second cancel each other out.
lost tide
you want the 5x to turn into 15x so that when you subtract the two equations, th...
What grade are u in 😭?
upbeat forge
that's the whole idea behind matching coefficients: multiply one of the two equations by a specific number to get either the x/y-cofficient to match that of the other equation's, then add or subtract them to eliminate that variable.
upbeat forge
What grade are u in 😭?
I don't think we should be chatting in another OP's channel, but if it helps you somehow, whatever grade corresponds to age 15.
lost tide
I don't think we should be chatting in another OP's channel, but if it helps you...
U are in grade 9
Nice
unique crown
So 75x + 75y = 300
upbeat forge
how did that happen?
unique crown
I multiplied 15 by the bottom equation
upbeat forge
15 is overkill.
you want the 5x to turn into 15x, not multiply the whole thing by 15.
unique crown
The 3 is negative though
upbeat forge
we're eliminating x, not y. if you want to eliminate y, you'd have to scale both equations.
unique crown
Would it be easier to use substitution?
upbeat forge
for this one, using elimination kills the problem right away.
crystal dawn
upbeat forge
in that case, write the entire equation after you've multiplied by 3.
don't do anything else with it yet - just write out the equation as a whole.
unique crown
15x + 15y = 60
upbeat forge
right side?
there we go.
now, we see that we have a 15x in this new equation and a 15x in the first equation.
at this step, you can now subtract the two equations. the order doesn't matter.
(by the two equations, I mean the original first equation and the new second equation, by the way. don't use the original second equation for this.)
upbeat forge
ok see, let me line up the two equations top to bottom.
15x - 3y = -30
15x + 15y = 60
oh, wait, never mind then. your 18y is correct, but not your right side.
a 60 and a 30 don't make an 80.
unique crown
-30-60=90
upbeat forge
18y = 80
after fixing this mistake, you're now on the right track to getting the value of y.
one minor tidbit though: if this was a free-response section, ensure you say which way you're doing the subtraction to result in this new equation.
unique crown
So i plug 5 into y
upbeat forge
why do that though?
I know y = 5 fits, but if you didn't know that, you're going to have to show how you got it.
upbeat forge
90/18
you should make this step clear, in my opinion.
in this case, yes, you can solve for x now, but the question didn't really ask for the value of x.
unique crown
Oh wait I realize that now
upbeat forge
is there anything else you'd need help with?
unique crown
Nope, thank you
unique crown
8th
Im taking algebra 1 honors and ive been absent for 1 week and now we have a quiz 😭
crystal dawn
so is there anything OP still wants to ask?
unique crown
Not as of right now no
upbeat forge
!done, if you're done then.
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
unique crown
!done
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
granite fractal
i'm confused on how to get the vertex with -b/2a
devout snowBOT
i'm confused on how to get the vertex with -b/2a
supple knot
which line in there is confusing
granite fractal
how do i get the y
supple knot
f(3)
supple knot
yes that's what f(3) means
granite fractal
sorry brain farting rn thank you 😭
supple knot
all good
granite fractal
.close
devout snowBOT
devout snowBOT
Available help channel!
blissful gorge
hi im a little confused where did the -e^-x come from?
devout snowBOT
hi im a little confused where did the -e^-x come from?
blissful gorge
this is my teachers asnwer key
heavy current
hi im a little confused where did the -e^-x come from?
in the dy/dx?
if that's what you mean, then it's because the derivative of e^-x is -e^-x
and the reason we're getting that is because of the product rule
blissful gorge
if that's what you mean, then it's because the derivative of e^-x is -e^-x
how does that work?
heavy current
chain rule!
blissful gorge
i know that the derivative of e^x is e^x
heavy current
devout snowBOT
heavy current
blissful gorge
.reopen
devout snowBOT
✅ Original question: #help-27 message
blissful gorge
okay so i fear im still confused
blissful gorge
if that's what you mean, then it's because the derivative of e^-x is -e^-x
can you quickly walk me through this
its breaking me
heavy current
can you quickly walk me through this
let $f(x) = e^x$ and let $g(x) = -x$. then $e^{-x}$ is $f(g(x))$
woven radishBOT
higher!
heavy current
what is it's derivative? the chain rule says that it's $f'(g(x))g'(x)$
woven radishBOT
higher!
blissful gorge
okay got it
wait hold on
so why is f(x) e^x?
the -x isnt outside of the ^x, is it?
novel python
so why is f(x) e^x?
as in, why is f(x) e^x?
that is given in the question, the essence of doing f(g(x)) is putting the expression g(x) as the term for x
anothher example for constants would be f(3), this means you evaluate as x=3 in the equation, or if you do f(x^2) then you replace x with x^2, similarly this means that for composite f(g(x)) it just indicates that the x term in your f(x) now becomes whatever g(x) is
blissful gorge
i see
i fear im still a little foggy but i have a basic understanding and i gotta keep pushing through
thank you!
.close
devout snowBOT
heavy current
devout snowBOT
Available help channel!
ebon saddle
I don't get this. Why both of them are = to x.
Here is my evaluation,
For the first one, f-1(x)=x(domain), then f(x)=y(range)
For the second one, f(x)=y(range), then f-1(y)=x(domain)
novel python
do you mean the expression? or do you mean the range and domain
because correct me if im wrong, the doman and range of f operated on f^-1 and the method of f^-1 operated on f is diffferent
with regards to expression
you can think of f^-1 as an undo button, essentially if i have the result of f(x), doing f inverse takes the output of f(x) and gives you the original value
the undo button f inverse is similar to f^-1(y) =x and therefore i will explain it as such
since f(x) =y, then applying f^-1f(x) is essentially conducting f^-1(y) which returns x
ebon saddle
for the first one, if i use f-1(x), i can get the x in the f(x) right? then, i plug the x into f, that just f(x), so it equals to y. That's what i think of.....
novel python
okay... let me think of an intuitive way to understand this yeah
long pasture
My first thought is that x is a dummy variable.
The x in first line belongs to the range, while the x in the 2nd line belongs to the domain.
if you doesn't feel safe about both using x, you can rewrite the x's in the first line into y's
ebon saddle
so, they are not the same thing? 😨
The problem is, when I apply to the inverse+composite function, i feel weird....
btw i'll come back later after my class
long pasture
so, they are not the same thing? 😨
Let's pick an example
Let f:A→B, be bijective, hence inverse of f exists, lets call the inverse function g.
suppose x in A and y in B, and f(x)=y
Since f is a bjiection, g(f(x))=g(y)=x
and f(g(y))=y
But what if A=B?
then x in A also means x in B, therefore we can use x (in A)
to say g(f(x))=x
and we can use x (in B)
to say f(g(x))=x
devout snowBOT
@ebon saddle Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
sharp laurel
Hey guys, I have a question about how i start with matthematics I am now in 11t grade and my knowledge of math is pretty poor: fuctions, basic logarithm's ect... But i want to learn way more math and i really want to learn and understand everything well but i searched about how i should start with math online and there where so many different ways and fields that i came to the conclusion that i really just need someone that has some decent expirience to talk with them about it, so if anyone wants to start a little conversation with me about the most efficient ways on starting math im all ears! (sorry for bad english its not my main language).
devout snowBOT
Hey guys, I have a question about how i start with matthematics I am now in 11t ...
late scaffold
I'd say that the first move is to find a syllabus to structure your learning from this point forward
one sample syllabus I like to use is in the Bookshelves of Math LibreTexts, which covers you all the way to abstract algebra adequately
then, instead of focusing entirely on just reading, always do practice problems! you are only as good in math as the problems you understand and can solve, so consider spending some time trying out some problems after each topic
also, don't hesitate to ask when stuck! it would be nice if you tried the problems at least as much as you could first, but if you're stuck, someone could give you a tiny hint that could be enough for you to make progress.
and sometimes, while waiting for an answer (or even when voicing out the question for your helpers/teachers/tutors) you hit upon an idea you've never thought of
the last tip I can offer is to understand why formulas are what they are (i.e.: understand where they come from, why they work and how they apply)
sharp laurel
I'd say that the first move is to find a syllabus to structure your learning fro...
Hello, I have searched on the internet for math libre texts and i have found the website wich looks good to me, i just don't understand what you mean with finding my sullabus?
late scaffold
https://math.libretexts.org/Bookshelves
if you go to this part of the site specifically, notice that each field is laid in order
the fields start at Arithmetic, then Pre-Algebra, then Algebra, Geometry, Precalc/Trig, Calculus, etc.
up to and including calculus, this is more or less the suggested study order for most people
after that, you can sort of jump around depending on what field you plan to major in
sharp laurel
Ah ok its like a road map for the basics?
late scaffold
yes!
sharp laurel
And do you suggest that i learn all of them?
late scaffold
not necessarily, but if you are going into pure math, you will see a lot of them
sharp laurel
Alright thank you so much you are wonderfull
I finially have some good structure now
Thanks
sharp laurel
No that was all for now, i will close this channel
late scaffold
aight, see you around, and welcome to the server!
cold haven
sharp laurel
Hey i am now learning my math trough math libretexts but as i am going trough the excercises i just can't seem to find any solutions to the excercises so i can't know 100% if my answer is right or not. Is it just like that or does the Solutionpage stand anywhere that i can't seem to find?
late scaffold
the channel is closed btw. if you want to ask your question, please grab another channel
sharp laurel
Oh ok
devout snowBOT
Available help channel!
humble siren
prove that x=2 is the only solution
devout snowBOT
prove that x=2 is the only solution
gloomy aurora
what are your steps so far? where have you reached?
humble siren
I found that a=0 and x=2 is a solution
gloomy aurora
what is a here?
gloomy aurora
prove that x=2 is the only solution
its not mentioned in the problem statemenet
humble siren
the full statement is find a then find all solutions (all x)
gloomy aurora
I found that a=0 and x=2 is a solution
yes, so where do you get stuck when you need to prove x = 2 is the only solution? try to see if the same logic works
pure stone
I found that a=0 and x=2 is a solution
you've already found cbrt(3x^2-11) + sqrt(2x-3) + 4 - x^2 - x <= 0
so a^2 <= 0 and so a = 0
humble siren
yes
pure stone
when does the equality in AM-GM happen
humble siren
when the two terms are equal
pure stone
when the terms are equal right?
so use it to prove that the equality only happens when x = 2
devout snowBOT
devout snowBOT
Available help channel!
lunar locust
shouldnt this function have a jump discontinuity at x = pi/2
devout snowBOT
shouldnt this function have a jump discontinuity at x = pi/2
lunar locust
floor of sin(90)=1 is 1 right?
pseudo basin
yes, it's just a removable jump discont and desmos cant really show these well
lunar locust
yes, it's just a removable jump discont and desmos cant really show these well
if i am asked to plot it on paper i will show the discontinuity right
pseudo basin
yes
lunar locust
.close
devout snowBOT
devout snowBOT
Available help channel!
jade owl
devout snowBOT
jade owl
Pls help me I'm stuck here i wanted someone to explain me
pseudo basin
Pls help me I'm stuck here i wanted someone to explain me
can you express 2.25 as a fraction first & foremost?
jade owl
Yea it would be 225/100 i.e. umm 9/4
jade owl
Ohh i seee , I see something like loga-logb
pseudo basin
that's half of one law
jade owl
We have log2 and log3 , 9/4 is square of 3 and 2 right
jade owl
Sorry my bad
jade owl
9/4 = **3^2 / 2^2**, sure.
Yes
pseudo basin
ok, do you have paper on you
jade owl
ok, do you have paper on you
Thank you tho you ignited my brain cells 😭
I'm thankful
I gotta have the approach developed
coarse flume
Did I do correctly?
Its 2 lg(3) not 3lg(3), also im pretry sure you mixed up the values for lg(2) and lg(3)
jade owl
Its 2 lg(3) not 3lg(3), also im pretry sure you mixed up the values for lg(2) an...
Ah yeah , marks deducted like this in exam 😭
Ty for correction @coarse flume
.close
devout snowBOT
devout snowBOT
Available help channel!
lunar locust
if LHL and RHL limits both are +infinity then can I say that the limit exists at that point
devout snowBOT
if LHL and RHL limits both are +infinity then can I say that the limit exists at...
lunar locust
and the limit is +infinity
carmine veldt
if LHL and RHL limits both are +infinity then can I say that the limit exists at...
strictly speaking, no
cold haven
<@&268886789983436800> troll.
pseudo basin
if LHL and RHL limits both are +infinity then can I say that the limit exists at...
whether +∞ counts as "existing" is kinda author-dependent
copper harbor
Limits taking infinite values are a lot trickier than limits taking finite values
lunar locust
whether +∞ counts as "existing" is kinda author-dependent
who is my author
is this dude even alive
carmine veldt
is this dude even alive
didn't he die in like 05
copper harbor
What Ann means is that you can define a notion of limit existing if f goes to infinity, it depends on if the text you're reading uses that
lunar locust
What Ann means is that you can define a notion of limit existing if f goes to in...
im js solving this problem
(at -3)
copper harbor
Personally I'd say that's infinite but it depends on your curriculum
lunar locust
do i say limit of -3 infinit
lunar locust
Personally I'd say that's infinite but it depends on your curriculum
so infinity ehh
copper harbor
this thing doesn't have a universal answer
lunar locust
not undefined
copper harbor
it depends on what curriculum you're following, go read your textbook to find out
this will be explained somewhere
lunar locust
i thought math was supposed to be objective
copper harbor
it is objective in the sense that once you fix your definitions everything has exactly one answer
but fixing those definitions is subjective
mystic scarab
I think that in this case the answer is +∞
lunar locust
it is objective in the sense that once you fix your definitions everything has e...
suppose im doing a continuity question and i get both side limits equal to +infinity
then what should i conclude abt the limit
does it exist or not
mystic scarab
I think that in this case the answer is +∞
Because both left-hand and right-hand limits exist and are +∞
copper harbor
reading is an important life skill 
lunar locust
read your textbook and see what it says
what would YOU do
carmine veldt
read his textbook 💀
lusty sapphire
what would YOU do
We would all read the textbook
copper harbor
I would check which one will not make me lose marks by reading my textbook
lunar locust
We would all read the textbook
waaat
lunar locust
I would check which one will not make me lose marks by reading my textbook
okay let me open the pdf
ok here
damn chartbit is here
copper harbor
ok here
you didn't need to go straight to the answers, usually your textbook will explain the content to you in the pages before the problems, you should read those pages when you're stuck
lunar locust
you didn't need to go straight to the answers, usually your textbook will explai...
its easier to read the answers
lunar locust
but then you don't learn
i just learnt
lunar locust
and you do badly on your exams
ok on it
1 sec
it says does not exist
but why did it write +inf in the answers then
just write dne
acoustic leaf
we write +infinity for these limits because it is more informative than just saying "DNE"
even if "DNE" is technically true it's less helpful
lunar locust
even if "DNE" is technically true it's less helpful
which one is more helpful in solving continuity questions
acoustic leaf
well you should just get into the habit of writing 'infinity' where it applies and then just remember that also implies it DNE
lusty sapphire
Which is basically what the book said. It's just a convenience to convey the f grows without bound
lunar locust
are undef & dne the same
stiff karma
Why is x^-1 = 1/x^1
devout snowBOT
Why is x^-1 = 1/x^1
polar chasm
x^3 = x * x * x
x^2 = x * x (we divided by x)
x^1 = x (we divided by x)
x^0 = 1 (we divided by x)
x^-1 = 1/x (we divided by x)
it's defined this way because it preserves many nice properties and patterns
thin inlet
that exponent property being...
$x^{a+b}=x^{a}x^{b}$
woven radishBOT
🫎 Moosey 🫎
thin inlet
and it works nicely with the other exponent properties as well
$x^{(ab)}=\left(x^{{(a)\right)}^{b}}$
stiff karma
also why is x^0 = 1?
woven radishBOT
🫎 Moosey 🫎
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
thin inlet
also why is x^0 = 1?
well, again, it works nicely with your exponent properties
you know x^(a+b)=x^a x^b
if you have x^2 * x^3 then that's equal to x^5
2^2 * 2^3=2^5
2^0*2^1=2^1, it only makes sense for 2^0 to be 1 in this circumstance
stiff karma
but we don't have to add 1^1 to 1^0...
thin inlet
well yeah because 1^x is just going to be 1
its the same reason why we define square root as x^(1/2) as well
an nth root as x^(1/n), because when we take the n-th power, we get back to x (atleast for odd powers)
(x^n)^1/n=x (for even n its |x|, because even root functions don't account for negative signs)
mystic scarab
also why is x^0 = 1?
#help-27 message you could read this conversation here
stiff karma
,calc (4a)^2
woven radishBOT
The following error occured while calculating:
Error: Undefined symbol a
stiff karma
,w (4a)^2
woven radishBOT
devout snowBOT
@stiff karma Has your question been resolved?
devout snowBOT
@stiff karma Has your question been resolved?
supple knot
,w (4a)^2
what further questions are you working on that helpers didn't already answer
devout snowBOT
@stiff karma Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
devout snowBOT
loud lynx
gray geyser
I have to test this equation for x-axis, y-axis, and origin symmetry. x = 2y^4 - 9y^2
devout snowBOT
I have to test this equation for x-axis, y-axis, and origin symmetry. x = 2y^4 -...
gray geyser
First I was doing y-axis
I know that you gotta substitute x for -x
But now I am confused
Would I make the negative x back to positive?
.close
devout snowBOT
devout snowBOT
Available help channel!
royal laurel
devout snowBOT
hollow ice
its pretty easy to see if you try to achieve the LHS by expanding the RHS in this
devout snowBOT
@royal laurel Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
mellow willow
Am I crazy or does this not have a gcf
devout snowBOT
Am I crazy or does this not have a gcf
cyan surge
I think what you need to do is to find lowest power of variables and coefficients that appear in all terms
i.e. 2x^2 + 4x= (2 * x * x) + (2 * 2 * x).
You could see that only 2x is common in both the terms
mellow willow
I have no idea how to do that
flat ibex
Am I crazy or does this not have a gcf
it does have a gcf
fossil locust
there's no constant term
fossil locust
so it's not about the numbers 3, 8, 5, 44 (their gcd = 1, of course)
but it's about...
fossil locust
What did I do wrong
why are you showing us a completely different part of the question
cyan surge
Am I crazy or does this not have a gcf
You could write:
3x^4 = (3x^3) * x
8x^3 = (8x^2) * x
5x^2 = (5x^1) * x
44x = (44) * x
What is common in all the terms?
fossil locust
What did I do wrong
,rotate
woven radishBOT
mellow willow
why are you showing us a completely different part of the question
I gave up on the other one
fossil locust
You could write:
3x^4 = (3x^3) * x
8x^3 = (8x^2) * x
5x^2 = (5x^1) * x
44x = (44...
did you have a look at this?
mellow willow
So I’m trhing the other one but the answer doesn’t seem rigjt
mellow willow
did you have a look at this?
Yea but I’ve never done anything like that before so I don’t understand it at all
fossil locust
Yea but I’ve never done anything like that before so I don’t understand it at al...
can you factorise $x^2 + x$ for example?
woven radishBOT
south
mellow willow
Yes
I understand that part but I don’t know what to do with the • X outside the ()
mellow willow
But you need to solve the equation
flat ibex
it implies one of the roots is 0
fossil locust
But you need to solve the equation
yes, so that implies $x (3x^3 - 8x^2 - 5x - 44)$
woven radishBOT
south
flat ibex
and you can factor inside the parenthsis
mellow willow
But there’s four of them so now you just have to x^4
But then your just where you started?
fossil locust
But there’s four of them so now you just have to x^4
wdym?
mellow willow
Do you have to factor out the gcf or can you just solve it by doing long devisition twice
fossil locust
Do you have to factor out the gcf or can you just solve it by doing long devisit...
you need to factor the gcf
mellow willow
You could write:
3x^4 = (3x^3) * x
8x^3 = (8x^2) * x
5x^2 = (5x^1) * x
44x = (44...
There’s four •X
fossil locust
the gcf is x
cyan surge
You could write:
3x^4 = (3x^3) * x
8x^3 = (8x^2) * x
5x^2 = (5x^1) * x
44x = (44...
You just gotta find what you took outside(which is common in both the terms), that is your gcf.
As stated here, only x can be taken out
mellow willow
I don’t know how to do long deviation with an extra x on the outside …
fossil locust
I don’t know how to do long deviation with an extra x on the outside …
you just leave it there
can you long divide (3x^3 - 8x^2 - 5x - 44) by (x - 4)?
mellow willow
Yes
fossil locust
to make a simpler example, imagine I have $x(x^2 - 3x + 2) = 0$
I factor $x^2 - 3x + 2 = (x - 1)(x - 2)$
subbing that back into the equation, $x (x - 1)(x - 2) = 0$
woven radishBOT
south
mellow willow
I kinda understanding factoring out X but I don’t know how to do long devision with just the value X on the outside
fossil locust
can you long divide (3x^3 - 8x^2 - 5x - 44) by (x - 4)?
after you long divide
you get $x(x - 4)(\text{some quadratic}) = 0$
woven radishBOT
south
mellow willow
But why don’t we divide the X?
fossil locust
But why don’t we divide the X?
cause x can be 0
so dividing by 0 would be undefined
mellow willow
No I understand us getting (X-4)( quadrant ) if we where just using 3x^3-8x^2-5x-44
fossil locust
do you understand this?
I'm asking if you understand this or not
I know you know how (polynomial) long division works
mellow willow
I mean techinally only polynomial long division I can’t do normal
mellow willow
How is it equal to zero and how the X value is there and was not in the long deviation
fossil locust
How is it equal to zero and how the X value is there and was not in the long dev...
to find the roots of a polynomial, you set it equal to 0
do you agree?
I'm giving you a new question which is to find the roots of $x(x^2 - 3x + 2)$
woven radishBOT
south
mellow willow
Are the roots the zeros?
fossil locust
Are the roots the zeros?
yes
mellow willow
I don’t do that then I use the box or quadratic formula
fossil locust
yes, I know you don't need polynomial long division here
fossil locust
I don’t do that then I use the box or quadratic formula
do you understand how $x(x^2 - 3x + 2) = 0$ becomes $x(x - 1)(x - 2) = 0$ then?
woven radishBOT
south
mellow willow
But it says to use long divisiton
tall linden
,rcw
fossil locust
But it says to use long divisiton
your problem is why there's an x on the outside, right?
woven radishBOT
mellow willow
This is easy
My teacher sped through directions
fossil locust
I can help
read through all the previous conversation then
mellow willow
your problem is why there's an x on the outside, right?
Yea usually I would just divide it was by a factor of (X+4
fossil locust
Yea usually I would just divide it was by a factor of (X+4
okay
lost tide
@mellow willow what are u stuck at
woven radishBOT
south
mellow willow
Wdym on both sides
fossil locust
you've lost a solution: you've lost x = 0
mellow willow
Wait
mellow willow
(X-0)?
mellow willow
I’m saying is that a zero?
fossil locust
I’m saying is that a zero?
0 is a zero, correct
lost tide
@fossil locust
mellow willow
So could I just do long devision twice one time with (X+4) and then with (X-0)
lost tide
💔
fossil locust
So could I just do long devision twice one time with (X+4) and then with (X-0)
to divide by x, you don't need long division haha
you just divide every single term by x
mellow willow
I just don’t know that way
fossil locust
but then yes, you then divide that cubic with (x + 4)
fossil locust
I just don’t know that way
okay, let's start with something simple
lost tide
@mellow willow write the work that u are stuck at
fossil locust
$\frac{x^2 + 2x}{x} = \frac{x^2}{x} + \frac{2x}{x} = \cdots$?
woven radishBOT
south
fossil locust
<@695456015805710337> write the work that u are stuck at
you're being disruptive
mellow willow
<@695456015805710337> write the work that u are stuck at
fossil locust
you're being disruptive
I've chatted with them for half an hour and figured out what they don't understand
flat ibex
im with obama on this one
fossil locust
I don’t really understand
it's like $\frac{30 + 50}{10} = \frac{30}{10} + \frac{50}{10}$
woven radishBOT
south
fossil locust
Wouldent it be just the same thing
yes, they're equal
when we split the fraction, those two things are equal
mellow willow
I just don’t get how this relates
fossil locust
I just don’t get how this relates
we're talking about how you can divide an entire polynomial by x without needing long division
mellow willow
I don’t really understand how to decide by just X tho
devout grotto
I don’t really understand how to decide by just X tho
$\frac{2x}{x}$ is just dividing 2x by x
woven radishBOT
Mirror
fossil locust
I don’t really understand how to decide by just X tho
surely you know what 2x / x is
fossil locust
I dont understand how that can be X but 2/1 is 2
yes, 2/1 is 2
$\frac{2 \cancel{x}}{\cancel{x}}$
woven radishBOT
south
fossil locust
oh yeah and when you cancel, that becomes (2 * 1) / (1)
devout grotto
(South, if I'm not being helpful feel free to tell me to stop!)
mellow willow
I never take the gcf out in general which is why it’s even more confusing
Like I cant remember me doing that ever
devout grotto
Can I back us up a step?
lost tide
@mellow willow are u in grade 9?
lost tide
Isn’t quadratic equation for grade 9
mellow willow
See I’m not good at math bht some how get A’s
devout grotto
Isn’t quadratic equation for grade 9
dude you are not helping
mellow willow
Isn’t quadratic equation for grade 9
I likely forget it or learned it in middle school which basically means I did not learn it because of Covid
lost tide
Ahh
devout grotto
Allie, backing us up a step: $f(x) = x({3x}^{3}-{8x}^{2}-5x-44)$ is what we're starting with
woven radishBOT
Mirror
devout grotto
so if f(x) = 0 what does that mean?
pure stone
<@695456015805710337> are u in grade 9?
please don't take any conversations unrelated to the helpee's problem into help channels
devout grotto
yes, that's related. if i were to tell you that $a \cross b = 0$ can you deduce anything about a and/or b?
woven radishBOT
Mirror
devout grotto
Right! That's the idea here.
$x({3x}^{3}-{8x}^{2}-5x-44) = 0$ means that $x = 0$ or ${3x}^{3}-{8x}^{2}-5x-44 = 0$, are you with me so far?
woven radishBOT
Mirror
mellow willow
Uh
devout grotto
it looks long and complicated but it's just our a x b example from before
mellow willow
No I think it’s just not showing up for me
devout grotto
(Think x = a and The Big Scary Function = b, does that help?)
bc it doesn't matter what we multiply by once we multiply by zero
mellow willow
But I just don’t know how to do long divisiton witu x(the quadratic )
devout grotto
We don't have to! Let's break it up.
We know that if x = 0 the function equals zero, so let's set that off to the side and remember it later.
Now our big function is ${3x}^{3}-{8x}^{2}-5x-44$ and we're looking for when that function is zero.
woven radishBOT
Mirror
devout grotto
We also know that x=4 is an intercept, so what does that mean?
mellow willow
Wait so do we just divide the quadratic and not the x
devout grotto
thanks for helping Mirror
ofc! you're doing fantastic too, btw! sometimes just needs another way to word
devout grotto
Wait so do we just divide the quadratic and not the x
Possibly. Can you be more specific?
(What are we dividing by what?)
mellow willow
devout grotto
There we go! Can you tell me why you're dividing by $x-4$?
woven radishBOT
Mirror
mellow willow
There we go! Can you tell me *why* you're dividing by $x-4$?
Cus it’s a zero
devout grotto
(It's the right move here, by the way: just want to make sure you understand why!)
devout grotto
Cus it’s a zero
Perfect.
Next step here is the long division, which (as far as I understand) you can do?
So do that and report back if you encounter some more trouble!
(Broader picture, by the way:
${3x}^{4}-{8x}^{3}-{5x}^{2}-44x) = 0$ if $x = 0$ OR $({3x}^{3}-{8x}^{2}-5x-44) = 0$ \newline
$({3x}^{3}-{8x}^{2}-5x-44) = 0$ IF ($ x-4 = 0$ OR <some other function> = 0)
woven radishBOT
Mirror
mellow willow
I’m not sure how to continue because I need to write smth witu i but I don’t know how since it’s not a perfect square
unreal edge
this is pre-cal?
devout grotto
Let me double-check that long division
mellow willow
this is pre-cal?
Yea
devout grotto
Long division is correct 
fossil locust
,w (3x^3-8x^2-5x-44)/(x-4) quotient and remainder
woven radishBOT
mellow willow
I haven’t done get before
devout grotto
the Wolfram i mean
mellow willow
For c would I leave it as is
mellow willow
the Wolfram i mean
Ohh
devout grotto
I'm inclined to agree that we leave it as is since there are no real solutions to $3x^2 + 4x + 11 = 0$
woven radishBOT
Mirror
devout grotto
,w sqrt(-116)
woven radishBOT
devout grotto
Do you have any other questions, Allie?
mellow willow
I know I have to do the quadratic formula since it’s a step and it’s a little similar to a class problem but it’s not a perfect square
fossil locust
I'm inclined to agree that we leave it as is since there are no real solutions t...
yes, in fact you can check the discriminant of the quadratic
,calc (4)^2 - 4(3)(11)
woven radishBOT
Result:
-116
< 0, so no real roots
devout grotto
yes, in fact you can check the discriminant of the quadratic
They did this above!
mellow willow
Yea but I need to write it with i some how
fossil locust
ah, of course cause your class wants the complex zeroes
then yes you need the quadratic formula
mellow willow
I’m not sure how to continue because I need to write smth witu i but I don’t kno...
^
devout grotto
you can substitute $\sqrt{-116}$ into $i\sqrt{116}$ and keep crunching!
mellow willow
Ohh ok
woven radishBOT
Mirror
mellow willow
devout grotto
that is technically correct but i think you can clean it up a lil more
mellow willow
My teacher did say in clas it’s fine to not simplify but how would I?
devout grotto
since you're at a stage where the answer is complete i will just tell you!
since $4 \cross 29 = 116$, $\sqrt{116} = 2\sqrt{29}$
woven radishBOT
Mirror
mellow willow
Ohhh kk
One more question for another problem I’m trying to do the box but I don’t know if 7 would be positive or negative
devout grotto
It'll be negative in both. A great way to approach is to work from the innermost set of parentheses outward
so before you even start distributing turn $(x-[7+3i])$ into $(x-3i-7)$
woven radishBOT
Mirror
mellow willow
This doesn’t seem right
upper schooner
,rccw
woven radishBOT
upper schooner
(one thing I will say is that for this, I would personally be tempted to write what we're expanding as ((x - 7) - 3i)((x - 7) + 3i), from which it becomes a tiny bit easier as you can difference of two squares to begin with)
mellow willow
You forgot a term!
Really which one?
I’m not supposed to have I left I’m very confused
Ohhh I see
devout snowBOT
@mellow willow Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
lost laurel
Are there any nice propeties for fin-dim vector spaces that neatly carry into the inf -dim case
devout snowBOT
Are there any nice propeties for fin-dim vector spaces that neatly carry into th...
flat ember
Here for example, is it x y^-2?
devout snowBOT
Here for example, is it x y^-2?
flat ember
…
hollow ice
well, what more do you want?
devout snowBOT
devout snowBOT
Available help channel!
compact hawk
devout snowBOT
compact hawk
Hi can someone just tell me what the question means by sum of the perimeters of region a,b,c and d
soft umbra
,rccw
woven radishBOT
compact hawk
Like does it means the entire square (basically combine a,b,c and d and the perimeter of that is 152) or is it that like if we took it apart individually perimeter a + b + c + d = 152
restive river
perimeter of A + perimeter of B ... = 152
id assume its double counting edges due to how its phrased
compact hawk
Oh alright ty
hollow jolt
If it meant perimeter of the whole thing then it would probably just state that
Rather than give of each region
compact hawk
If it meant perimeter of the whole thing then it would probably just state that
Yea i got kidda confused cus if it was like one by one
Double edges would be counted
😭
Anyways ty
.close
sand girder
\begin{gather*}
2 a^2 + \sqrt{b} = 8 \
a^3 + ab - b = -34
\end{gather*}
woven radishBOT
Thomas
fossil locust
\begin{gather*}
2 a^2 + \sqrt{b} = 8 \\
a^3 + ab - b = -34
\end{gather*}
you want to solve for a, b right?
sand girder
yeah
fossil locust
what have you tried so far?
vital edge
Are we given anything else
sand girder
not rlly
vital edge
For example are they integers or smth
fossil locust
,w a^3 + a(8-2a^2)^2 - (8-2a^2)^2 = -34
woven radishBOT
sand girder
ok so there's one good solution
fossil locust
the other roots are all very ugly, yes
vital edge
It's still a quintic though
sand girder
so...now what?
fossil locust
so...now what?
where did you get this problem from?
sand girder
where did you get this problem from?
from a friend's book from their extracurricular class
fossil locust
this is a terrible problem cause you can only solve it through guessing
sand girder
so...now what?
.
sand girder
i think it's a, b are real numbers
fossil locust
I mean, like what chapter this question comes from
and if there's a worked solution
fossil locust
what grade is this?
sand girder
Advanced grade 9
fossil locust
if you know that a must be a rational number, then the rational theorem gives the possible values of a as:
plusminus (factors of 30)/(factors of 4)
that's still too many possibilities to check
fossil locust
Advanced grade 9
I think this is a terrible question and you should skip it
sand girder
okay
sand girder
.close
devout snowBOT
devout snowBOT
Available help channel!
empty star
I'm just learning this now sort of, as I understand it, D) would be DNE, but what do I put for C??? the coords for the darker point? both?
devout snowBOT
I'm just learning this now sort of, as I understand it, D) would be DNE, but wha...
empty star
When I first saw c i assumed it was asking what d is asking
but since it's not idk what it's asking
i don't know what to do about the hole
proud mural
but since it's not idk what it's asking
it's asking what the value is at x = -3
the darker point means its defined at x=-3 right?
hoary egret
isnt that just a removable discontinuity
therefore we have that it is discontinuous but still retains a limti
empty star
not at -3
that's a jump isn't it
but i guess i have the same question about m
or k i mean
since it has 2 holes at g(4)
empty star
my ass is not getting above 80 in this class 💀
empty star
hoary egret
yes bro it is
proud mural
isnt that point a removable discontuity bro
no?
hoary egret
Why
oh wait
im regarded
sorry i meant to say
that is a jump discontuity
so the limit from both sides approaches diff values
hoary egret
so we have discontinuity and no limit for that point
empty star
did you read my question
proud mural
did you read my question
yes
hoary egret
Bro i just wrote for part D
empty star
i was asking about part c
proud mural
its just gonna be the y value of the dark point
hoary egret
I meant for part C
proud mural
because the function is defined there
hoary egret
its just gonna be the y value of the dark point
isnt it a jump disconuity?
empty star
and what about k
hoary egret
it is discontuityies
proud mural
we dont care about limits or continuity for just evaluating the function at a certain x value
we just care about what the value is
hoary egret
if it is discontinuous how can it have a value?
proud mural
and what about k
same deal
proud mural
if it is discontinuous how can it have a value?
does discontinuous mean not defined?
proud mural
is there no value because there are holes
It looks like there's a value above?
at y=4?
hoary egret
does discontinuous mean not defined?
if it is not defined at the point then how can it have a value?
proud mural
if it is not defined at the point then how can it have a value?
It is defined
that's the point
empty star
okok so if it's not a hole then i put that answer right
on the test it'll be clearer
this is like bad scanning from a textbook lol
proud mural
okok so if it's not a hole then i put that answer right
you just put whatever the value of the function is
whats confusing you?
hoary egret
It is defined
does discontuity mean that it can still have a value at the point?
proud mural
does discontuity mean that it can still have a value at the point?
yes
just means its not continuous
hoary egret
okay thanks
empty star
how do i find the limit at 2 from the graph
unless i "estimate" at 4 but i feel like we haven't estimated anything in a long time
empty star
wait i'm confused
hoary egret
so u cant evaluate the limit
proud mural
how do i find the limit at 2 from the graph
just look at what the y value goes towards as x gets close to 2
empty star
hs you are not helpful
empty star
just look at what the y value goes towards as x gets close to 2
do i estimate 4
hoary egret
empty star
is that the answer for all of these
empty star
okok
thanks so much
i feel like we've been doin a lot of equations and not a lot of pulling from graphs so the graphs are trippin me up
.close
devout snowBOT
devout snowBOT
Available help channel!
stark wigeon
Can someone check my working for biii)? \
let $P(x) = x^3 - 6x^2 + 9x - 15 = 0$; therefore $P(x+1) = x^3 - 3x^2 - 11$ thus $e_3(\alpha - 1, \beta - 1, \gamma - 1) = 11$
devout snowBOT
Can someone check my working for biii)? \\
let $P(x) = x^3 - 6x^2 + 9x - 15 = 0$...
stark wigeon
i cant find the answer sheet anywhere 
woven radishBOT
woomy
wise hamlet
faint hearth
,w expand (x+1)^3 - 6(x+1)^2 + 9(x+1) - 15
woven radishBOT
faint hearth
Can someone check my working for biii)? \\
let $P(x) = x^3 - 6x^2 + 9x - 15 = 0$...
yes
stark wigeon
the logic is fine aswell?
faint hearth
yeah because the roots of P(x+1) will be alpha-1, beta-1, gamma -1
devout snowBOT
devout snowBOT
Available help channel!
compact hawk
A 5 x 7 rectanglebis partitioned into 1x1 squares. Then two opposite 1x1 corners squares are removed resilting in the figure. How many squares with integer lenght sides can be found using the line segments in the resulting figure
devout snowBOT
A 5 x 7 rectanglebis partitioned into 1x1 squares. Then two opposite 1x1 corners...
pseudo basin
Uhhh i js did like 33 + 6+ 2
what's your logic for this
compact hawk
what's your logic for this
33 1 by 1 squares cus (5 x 7) - 2
Then 6 2 by 2 squares
Then 2 3 by 3 squares
plucky marten
i think there might be more than 6 fr
pseudo basin
there are more ways to position a 2×2 square in there.
let me reproduce the grid, one moment
these are the possible locations of the southwest corner of a 2×2 square within the grid
pseudo basin
if a 2×2 square fits in the grid, its SW corner has to be one of the green tiles.
this is the same but for 3×3 squares.
and this is for 4×4.
pseudo basin
Oh wait we can js overlap it
indeed. the question did not ask for the max number of non-overlapping 2×2 squares
just how many positions a 2×2 square could go in so that it's contained inside the grid
compact hawk
ok, let's go back: do you understand the diagram with the _green_ color
No 😭
pseudo basin
if a 2×2 square fits in the grid, its SW corner has to be one of the green tiles.
southwest as in bottom left.
compact hawk
Wait lemme try to process what u are saying 💀💀💀💀
plucky marten
i was wondering what u meant but then i realized that u were talking about the bottom left corner or southwest piece of the 2x2,3x3 and 4x4
like the positions they can occupy
pseudo basin
i was wondering what u meant but then i realized that u were talking about the b...
yes thats in fact exactly what im talking about
compact hawk
Okok i understand it now
compact hawk
you understand it after a _man_ repeated it
No 😭😭 i kept trying to think what u mean by bottom left
Then realise oh
compact hawk
When u said i thought like u meant the 2 x 2 squares can only fit onto thr green part
💀💀
Then i got confused on why the unshaded part cant be used
plucky marten
you understand it after a _man_ repeated it
ok there was no need to take that offensively
pseudo basin
i BOLDED the words "southwest corner".
plucky marten
chill
pseudo basin
ok there was no need to take that offensively
ok yeah it's whatever.
compact hawk
😭🙏
plucky marten
some of us are dumb and it takes time to process
devout snowBOT
plucky marten
just a sec
devout snowBOT
✅ Original question: #help-27 message
plucky marten
@pseudo basin can u explain how to use combinitions to do this
compact hawk
<@183668144404037632> can u explain how to use combinitions to do this
How would u even use combinations here
💀
plucky marten
no like if i learnt that then i can do it for even larger ones
like 2025*2029 and 4x4 is removed
from corners
and i just got denied 
compact hawk
and i just got denied <:girlbleak:1195548550378029117>
Lol
Anyways wait how do u use combinations in such questions
Im genuinely curious
plucky marten
i have seen some for like a rectangle
but never with pieces removed
so i wanna know
carmine veldt
i have seen some for like a rectangle
you know how to do it for complete rectangles I take it?
carmine veldt
uh ic
pseudo basin
for a full rectangle the limiting factor is whichever of width and height is smaller
or... ok not quite
i guess you kinda can make a formula for a rectangle of size m by n with m <= n but i honestly do not feel like writing it all out
plucky marten
here
carmine veldt
I'll js explain the steps, simplification if upto you, alr?
plucky marten
ite
carmine veldt
so to find total number of squares in a mxn grid
plucky marten
oh wai
carmine veldt
we take cases finding total number of ixi squares such that 0 < i < min(m,n) + 1
pseudo basin
@plucky marten @carmine veldt get your own channel
carmine veldt
ah alr mb
plucky marten
itw
pseudo basin
this used to be @compact hawk's channel
so yall need to take a new one in one of your names
.closw
.close
snow shore
What am I doing wrong? Everything I read tells me this is how to do it but I keep getting the wrong answer
devout snowBOT
What am I doing wrong? Everything I read tells me this is how to do it but I kee...
snow shore
I feel like I am losing my mind and am over this
I've tried this 8 times
I keep looking for info on what I can be doing right, but all the resources avalible say this is the right way to do it
<@&286206848099549185>
carmine veldt
What am I doing wrong? Everything I read tells me this is how to do it but I kee...
pretty sure that's abt torque balancing
but you can't really do it without knowing the weight of the diver
snow shore
but you can't really do it without knowing the weight of the diver
From what I understand, you get that by subtracting the two values but that might be the part that I don't get
devout snowBOT
@snow shore Has your question been resolved?
snow shore
How should I find the weight
lunar harbor
devout snowBOT
@snow shore Has your question been resolved?
devout snowBOT
@snow shore Has your question been resolved?