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#help-13
cursive cedar
What's the strategy for this?
Completing the square with 3 variables?
cedar kilnBOT
What's the strategy for this?
Completing the square with 3 variables?
@cursive cedar Has your question been resolved?
tranquil oracle
What's the strategy for this?
Completing the square with 3 variables?
Maybe complete a square first using some of the terms
cursive cedar
I'm doing d right now
tranquil oracle
d doesnt seem to be a positive combination of squares
Plug in 1 1 1
hmm looks like negative squares are allowed?
tranquil oracle
Theres a strategy involving eigenvalue decomposition but that might be overkill
tranquil oracle
Write quadratic form as v^T A v for some symmetric matrix A
cursive cedar
The symmetric matrix
tranquil oracle
Yeah
cursive cedar
And then we look at the columns of Q?
cedar kilnBOT
cedar kilnBOT
Available help channel!
rancid phoenix
I need help with both of these graphing problems, for both of these we need to find the domain, range, x-value intervals on which f(x) is decreasing, x-value intervals on which f(x) is increasing, x-value intervals on which f(x) is constant, and x value relative maximum and minimum
high bridge
um, which of those do you actually need help with?
high bridge
I need help with both of these graphing problems, for both of these we need to f...
which of those things lkisted
all of those? like domain, range stuff?
rancid phoenix
Ye
high bridge
ok sure yeah
rancid phoenix
Alr
high bridge
can you tell me what a domain of a funtion is?
high bridge
not accurate enough
the domain of a function is all the x values that is allowed by the function
for example: if you have f(x)=x
then the domain is x is an element of the reals
another example: if you have f(x)=1/x
then the domain is x does not equal to 0 and x is an element of the reals
x does not equal to 0 because f(0)=1/0 is not allowed
knowing this, can you tell me what is the domain of funtion 1?
rancid phoenix
f(x) = -6
rancid phoenix
Because theres a arching point where its above the x value -6
high bridge
the domain of a function is all the x values that is allowed by the function
so you did not read my text
winged tinsel
hello
high bridge
if you want help to to a different open channel
rancid phoenix
f(x) = -6,-4,1 and 3
high bridge
again the domain is ALLLLLLLLLLLL the values x CAN be
x is not ONLY -6 -4 1 and 3 in the first function
rancid phoenix
So its everything?
high bridge
define everything
rancid phoenix
Is it all x values like infinite and negative inf
high bridge
ok so you did not look at my examples at all
the correct term is x is an element of the reals
rancid phoenix
What is reals?
high bridge
you know real numbers>?
high bridge
basically saying that x is an element of the reals, you are saying x can be any real numbers
rancid phoenix
I see
high bridge
written down on paper it looks like this:
x ∈ R
the central symbol means "is an element of"
and the capital R means all Real numbers
alright range
like how domain means ALL X values allowed
range means ALL Y values
can you tell me what the range is for the first function?
rancid phoenix
y ∈ R
high bridge
um
now is that true?
where on the graph do you see y can be... let's say 4?
is there anywhere on the graph where y is 4?
rancid phoenix
No
high bridge
so y is not just an element of the reals
a critical question to ask yourself when finding the range:
can you see a highest point/ lowest point on the function?
winged tinsel
please solve this question.
high bridge
Suryansh please open another channel instead of posting another problem here
another open channel
rancid phoenix
can you see a highest point/ lowest point on the function?
There is only one high point and two low points
high bridge
There is only one high point and two low points
what gave you that idea?
there can be a max of 1 high point and 1 low point, however, there could be none of those accordingly
rancid phoenix
I think theres atleast one high and one low
rancid phoenix
Oh
high bridge
can you tell me, where do you think is the highest point on the function?
rancid phoenix
3
rancid phoenix
No?
tropic oxide
please solve this question.
!occupied
cedar kilnBOT
please solve this question.
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).
high bridge
No?
that is correct
so now you have figured out that the highest point of y-value is 3 and there is no lowest point
you can conclude that all y-values must be (put an inequality sign here) 3
rancid phoenix
Alr
rancid phoenix
y ≠ 3
high bridge
also I need to leave after 19 minutes, better make it quick
um
why is y not equal to 3?
rancid phoenix
i cant make inequality sign
rancid phoenix
Greater sign underlined
high bridge
that is called greater or equal sign
so you are saying y>=3?
well 4 is >= 3
is 4 a part of the range?
rancid phoenix
No
rancid phoenix
It would be <=
high bridge
exactly
≤
less or equal sign
there you have it
the range of function 1 is y≤3
next: where is f(x) decreasing
well that is simple, where is f(x) going down
rancid phoenix
-5
high bridge
now now
it is not going to be a point
it is going to be a range of values
where is f(x) going down you go left to right
high bridge
oops sorry I need to go
winged tinsel
anyone please clear my doubt.
random dirge
Someone else is already using this help channel. If you need help with a questio...
@winged tinsel u need to start a new channel
winged tinsel
i am unable to start a new channel, i am new on discord. please help me
random dirge
#❓how-to-get-help click into this
gilded frigate
how can i set up the integral to find its volume?
cedar kilnBOT
how can i set up the integral to find its volume?
open grove
how can i set up the integral to find its volume?
$$\int_a^b f(x) \dd{x}$$
wraith daggerBOT
@open grove
gilded frigate
<@751533372890677398>
uh this is the definition of the integral i understand
open grove
how can i set up the integral to find its volume?
Cross section length is just the y-value, then you can use A = bh/2 to find the area of the triangle
And then use that as your f(x)
Find a and b by finding the zeroes of y = 2x^2 - 2
open grove
how can we find b and h to get the area though
The cross section (AKA the base) spans from the curve y = 2x^2 - 2 to the x-axis.
open grove
The cross section (AKA the base) spans from the curve `y = 2x^2 - 2` to the `x`-...
It’s basically the y-value
gilded frigate
but how can i find base and height of the cross section so that i can find the area of the triangle
open grove
Then use this to find the height
gilded frigate
so the lenght is basically the y value?
OH
the parabola is bounded by the x axis
and its base runs from a to b
if i find a to b and its distance
i get its base
and then using its base i get its height
then compute for the area of the triangle
then integrate from a to b
and thats it?
@open grove
gilded frigate
if i find a to b and its distance
hmm how is this incorrect
gilded frigate
These are the cross sections
yeah im stuck on how to find the base of the cross section
open grove
yeah im stuck on how to find the base of the cross section
The base is cross-section.
gilded frigate
so its dx???
oh no
UH
is the base length
2x^2 - 2
@open grove
ohh
then i just multiply by 2
and find area
open grove
and find area
No, this is for the height.
open grove
i think i got it
!done
cedar kilnBOT
i think i got it
If you are done with this channel, please mark your problem as solved by typing .close
cedar kilnBOT
cedar kilnBOT
Available help channel!
queen stirrup
Let f : R → R be a twice differentiable function such that f ′′ ≥ 0. Prove that f is
bounded below.
queen stirrup
I tried to do a proof by contradiction, by looking at a monotone sequence x_n such that f(x_n)<-n
i got kinda far but no results
untold marten
Are you sure it's ≥ and not >
queen stirrup
its >=
queen stirrup
Then that is a false statement, counterexample being f(x) = -x
nice counterexample
i wonder if anything would change if f'' > 0
how to prove it ?
there might be a counterexample
ancient cliff
i don't think there is
queen stirrup
hm
untold marten
Yea I think the statement is untrue even for f" > 0
Because f' can be a function that goes from like -2 to -1, and be continuously increasing
In which case f">0
But f will tumble down to negative infinity
untold marten
Let f : R → R be a twice differentiable function such that f ′′ ≥ 0. Prove that ...
Where did you get this from? Any book?
queen stirrup
Because f' can be a function that goes from like -2 to -1, and be continuously i...
f''(x)>0, f'(x)<0 but f'(x) is increasing and say it converges to some cosntant at infinity
this is what i was thinking about too
queen stirrup
Where did you get this from? Any book?
my teacher gave me this
untold marten
f''(x)>0, f'(x)<0 but f'(x) is increasing and say it converges to some cosntant ...
Yeah, this is a counterexample
queen stirrup
Where did you get this from? Any book?
i looked at -ln x but ln x isnt defined over all the reals
then i checked -ln(|x|) but its not differentiable at 0
untold marten
Send it here
untold marten
this is what i was thinking about too
You thought of it yourself
queen stirrup
i only thought of ln x
like how do you think of the appropriate functions
arctan x would never come to me
untold marten
lnx isn't bounded above
We wanted a function that is bounded within two constants
Arctan(x) is usually the best go to
queen stirrup
right
queen stirrup
We wanted a function that is bounded within two constants
yeah thats why ln x is wierd at 0
untold marten
Then move it up or down
Based on if u want it fully negative or fully positive or intersecting x axis
untold marten
You're welcome
cedar kilnBOT
cedar kilnBOT
Available help channel!
dense bane
cedar kilnBOT
dense bane
guys ion even know how to begin this 😭
opal hinge
sub $3^x=u$
wraith daggerBOT
Alexis_Fx
twilit escarp
And in case you wonder for $3^{2x}$ its the same as $(3^x)^2$
wraith daggerBOT
msg db "YakuBros", 0
twilit escarp
Yep and then you make the sub that Alexis suggested
dense bane
3^x
wraith daggerBOT
joseph
dense bane
oh wait it's not finished
sullen hedge
yeah, since we did a substitution, we need to revert
dense bane
yes
sullen hedge
but we also said $u = 3^x$
wraith daggerBOT
joseph
sullen hedge
and the original question is to find x
dense bane
3^x = 3
sullen hedge
yep
dense bane
and x=1?
sullen hedge
yes
dense bane
ohhh I see
sullen hedge
nice
dense bane
thank you!!
sullen hedge
lol, so its not really possible is it
3 raised to any real number can not be a negative
so x = 1 is your only solution
sullen hedge
np
dense bane
.close
lime ether
we need to prove that the func is bounded in the intreval (0,pi/2) now i understand that the func is countious on all of R excpect where sinx /= 0 so at zero so we need to check the right hand limit of the func as x approches
lime ether
that is what the teacher wrote in the sol why did he wrote that the func value of zero its equal to 1
slender ginkgo
F(x) is continuous at 0
lime ether
but if we plug 0 the func isnt defined
slender ginkgo
that is what the teacher wrote in the sol why did he wrote that the func value o...
this one is
tropic oxide
F(0) [capital F] is defined, explicitly.
however $\lim_{x \to 0} \frac{2x^2+x}{\sin(x)}$ can be calculated!
wraith daggerBOT
Ann
slender ginkgo
approximation 😎
lime ether
yeah i know its equal to 1
that isnt the problem we need to prove that f(x) is countious on the interval so we can use the extreme val therom
slender ginkgo
F(x) is continuous on [0, pi/2]
slender ginkgo
so u can use evt on F(x)
slender ginkgo
f(x) has a hole on [0, pi/2] so it is not continuous at x = 0
tropic oxide
f(x) is the restriction of F(x) to (0, pi/2)
the restriction of a bounded function is bounded
royal finch
The point is that if you can show that F(x) is bounded, then deleting two points to get f(x), it is still going to be bounded.
The extreme value theorem is a bit stronger than what you actually need since it also guarantees that the mina and maxima are achieved, but you only care about boundedness.
This is why you can start on a closed and bounded set, and shrink it down to an open set and still get the result you care about from the EVT
tropic oxide
u mean that F(x) = f(x) on the interval (0,pi/2)
yes
tacit aurora
does anyone know a good video that explains pulleys and newtons laws?
tacit aurora
i already tried googling this lol
its just that most of what i saw until now only touched some laws or more laws or used friction
dire geode
does anyone know a good video that explains pulleys and newtons laws?
so what are you actually looking for
tacit aurora
a video about pulleys with only the 3 motion laws without slants and slopes
slender ginkgo
https://duckduckgo.com/?q=pulleys+and+newtons+laws&t=chromentp&ia=videos&iax=vid...
duckduckgo 😭
dire geode
duckduckgo 😭
🦆 🦆 🥭 ➖ 👨
tacit aurora
less of a video with example practice more about explaining generally
dire geode
explaining what generally ?
dire geode
a video about pulleys with only the 3 motion laws without slants and slopes
what does "only the 3 motion laws" mean?
tacit aurora
f = ma
for each movement one that counteracts it
and if sigma f is 0 speed is const
tacit aurora
explaining what generally ?
what happens when one mass hangs in the air and when the other doesnt, what is the "t" of the rope, how to calculate the acceleration of the whole thing,
flint cape
and if sigma f is 0 speed is const
You mean "Newton's (3) laws of motion"
tacit aurora
yeah those
flint cape
(which aren't in the right order)
flint cape
(the order you've listed is 2nd, 3rd, 1st)
tacit aurora
i need to get a hang of this in a few hours
but with the practices we got i just dont understand enough to even start
charred oriole
Hey guys, idk if I'm being stupid but I don't know how this is wrong
charred oriole
It says a discount, so I did 400 - 35 = 365, then I took 20% of 365 and added that onto the total because it says discount of 35 and 20% more
But apparently the answer is 515? I don't understand
obtuse ice
So 20% more of the original cost would be $400 multiplied by 1.20 which is 120%. Then add $35 to that you get the price it was listed as before the $35 discount if I’m correct
Yeah cuz 400 times 1.2 is 480+35=515
obtuse ice
Because it says after giving a discount of 35 the price is now 20 percent higher than originally
charred oriole
Now I'm even more confused. My understanding is that if you take a discount, you're subtracting by however much that amount is
Not adding it
That's marking it up
obtuse ice
It could also be written as x-$35=$400x1.2
wraith daggerBOT
Zoey
obtuse ice
Now I'm even more confused. My understanding is that if you take a discount, you...
I suck at explaining sorry
charred oriole
I suck at explaining sorry
It's most likely not you. it's fucking ATI and their shitty wording
So don't feel bad, it's just how they like to write their stupid word problems
obtuse ice
Yeah verbal exercises can be so confusing
charred oriole
Yeah next time im just writing it as an equation
obtuse ice
Yep it usually helps
cedar kilnBOT
cedar kilnBOT
Available help channel!
young shard
Am i wrong to think that this process is mistaken? my proffesor seems to have taken -i * i to be equal -1 for simplification, but isn't it actually 1? what am i missing?
young shard
i fail to see where the (-1) comes from at all in -3 (-1)
split ice
, because 2-i is actually (2) + (-1)i. so (3)i * (-1)*i = (3)(-1)(i^2) = 3 as msg said
jagged flicker
Am i wrong to think that this process is mistaken? my proffesor seems to have ta...
he just wanted to make everyone understand that i^2 equals -1, but ye, in that case it'd be easier just to know that -i*i = 1
young shard
right it results in 3, but how do you arrive at that 13 at the end? 10 - 3 = 7 so you get 7 on the real side of the complex number
am i missing a sign somewhere?
mental trail
right it results in 3, but how do you arrive at that 13 at the end? 10 - 3 = 7 s...
No, -3*(-1) = +3
jagged flicker
right it results in 3, but how do you arrive at that 13 at the end? 10 - 3 = 7 s...
-3*(-1) = 3
mental trail
10+3 = 13
jagged flicker
then 10 + 3 = 13
young shard
arent you supposed to substract the number you get? according to (a.c) - (b.d) for the real part in complex multiplication
mental trail
It's already done!!!
jagged flicker
arent you supposed to substract the number you get? according to (a.c) - (b.d) f...
-(-3) = +3
young shard
oh i see i think, i´ll go over it for a bit but i see where i was going wrong
.close
cedar kilnBOT
young shard
.reopen
cedar kilnBOT
✅
young shard
sorry to the person typing i need to figure out something else
i passed it through wolfram alpha and it gave me the result i got?
this should have given me 13 instead with the 3 adding instead of subtracting, did i type it wrong?
split ice
,w (5+3i)(2-i)
wraith daggerBOT
split ice
as a sanity check
young shard
i saw that too
split ice
doing partial FOIL, you should get 5*2 + (3i)(-i)
slender ginkgo
(without having yet combined liked terms)
split ice
the formula takes i * i out of this, and so the rule is 5*2 - 3*(-1)
slender ginkgo
doing partial FOIL, you should get 5*2 + (3i)(-i)
- friends
split ice
considering the real part here*
slender ginkgo
oh right
split ice
what you seem to be doing is using the formula, but adding an extra i*i in; the formula takes care of this by doing subtraction
young shard
the formula takes i * i out of this, and so the rule is 5*2 - 3\*(-1)
see i feel like there's a - missing there, i*i = -1, no? but then you have the - leftover from the (-i), so where does that - go? wouldn't it make it a 1?
if it was 3i * i then it would be -3 but since you have -i instead then that has to affect something right?
split ice
i think it's easier to explain if you forget about the formula for a sec, and just try FOIL on (5+3i)(2-i)
young shard
i'm not familiarized with FOIL, i assume you mean the distributive property? i think it's something like that from what i've seen
could you walk me through it?
split ice
yes sorry, i do mean distributive property
treating i as a variable for a second, how would you multiply the binomials?
young shard
10 - 5i + 6i - 3i^2
flat mica
first-outer-inner-last it's a mnemonic
split ice
, just another way to multiply binomials
flat mica
personally I like doing "FIOL" better
young shard
no wait that yields a different result though?
split ice
now, let's rearrange this as (10 - 3i^2) + (6i - 5i)
young shard
oh yes
split ice
this would actually give us 13 + i so it works out :) can you see why?
young shard
yes, but i still don´t see what was leading me astray in the first method, this way is much clearer so i might stick to it but i wouldn´t want to not know how to do it the usual way
thanks for explaining so far by the way
split ice
it's a little confusing because there's a subtle difference between the formula and the binomial expansion
firstly, to clarify, im gonna write it as (10 + (-3)i^2) + (6i - 5i). i.e. we are adding the terms
if you do the binomial expansion on two arbitrary numbers, say $(a+bi)(c+di),$ you will always end up with $$\big(ac + (bd)i^2\big) + \big((bc)i + (ad)i\big)$$. hopefully you agree?
wraith daggerBOT
haseeb
young shard
i see how that is yes
split ice
ok perf. the formula then does two things to simplify this:
- changes i^2 to -1
- factors out i from the second bracket
so we end up with $(ac - bd) + (bc + ad)i$, aka the general formula
wraith daggerBOT
haseeb
split ice
this is the subtle difference between the formula and the expansion. and to complicate things more, we had $d = -1$, so we should actually get $$(ac + b) + (bc - a)i$$ in that case!
wraith daggerBOT
haseeb
split ice
i think what you were doing is going along with the formula for your binomial expansion
which led to an extra pair of i*i
does that make sense?
cedar kilnBOT
split ice
gl ^^
cedar kilnBOT
Available help channel!
pseudo ingot
why is math so weird at patterns. im learning how to factor quadratic equations and i feel like every exception to the base concept of difference squares. just throws it out the window.
For example (x^2 - 15 = 0)
square root both and then do a positive and negative version of the equation to get both of the valid answers. Oh suddenly theres a number behind x^2?
(8x^2 - 15 = 0)
Throw out the square root step and find what 8 times -15 equals and then find the factor pairs to -120 to do this other stuff
what throws me off is the fact that theres no reason as to why i suddenly changed the whole way im solving the problem without there being a smooth connection or reason as to why other then (its basically a whole different problem so use a different method)
slender ginkgo
what does 'number behind x^2' mean
lone dune
i think hes talking about the coefficient
pseudo ingot
yeah
wraith daggerBOT
satvik
lone dune
$x^2 = \frac{15}{8}$
wraith daggerBOT
satvik
lone dune
and root both sides
pseudo ingot
huh whyd u do 8x^2 = 15? im factoring 8x^2 - 15 = 0
lone dune
you cant really factor that nicely
if you're solving a quadratic and you have only one term containing x which turns out to be the x^2 term, you can just isolate it and root both sides like I did here
pseudo ingot
the tutor video im watching had me multiply 8 and -15 and then find hte factor pairs and then square root 8x^2 into 4x and then write it like 8x + 12x - 10x -15 = 0
into then 4x(2x+3) -5(2x+3)=0
and then write (2x+3) (4x-5) = 0
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
paper bluff
If ( p(x) ) is a polynomial that satisfies
[
2p(x) + 2x^2 = p(x^2 - 2x + 4) + 8x + 5,
]
determine the units digit of ( p(2^{2022}) ).
wraith daggerBOT
isuckatmath
paper bluff
How can i prove that $deg(p(x)) = 2$
wraith daggerBOT
isuckatmath
paper bluff
k
paper bluff
divide into 2 cases
if deg(P(x)) = 1 and if deg(P(x)) > 2
if deg(P(x)) = 1, take P(x) = ax + b
then 2(ax + b) + 2x^2 etc
tropic oxide
How can i prove that $deg(p(x)) = 2$
wait, can you?
oh err
wait
if deg(p) = 2 doesn't the RHS become a quartic in x?
paper bluff
wait, can you?
i think there is a contradiction somewhere if deg(P) > 2
reef glade
deg ( p(x^2 -2x + 4) - 2p(x)) is 2
tropic oxide
p(x^2 - 2x + 4) is p evaluated at a quadratic
the degree of p(x^2-2x+4) is 2*deg(p)
reef glade
the degree of p(x^2-2x+4) is 2*deg(p)
why
tropic oxide
$p(x) = a_n x^n + \text{(lower order terms)}$
wraith daggerBOT
Ann
tropic oxide
$p(x^2-2x+4) = a_n (x^2 - 2x + 4)^n + {}$ lower order terms of degree at most $2n-2$
wraith daggerBOT
Ann
reef glade
huh
paper bluff
sorry guys i suck a polynomials
tropic oxide
i mean maybe change your name to something that is not so self-deprecating while you're at it 💀
but also, again,
i'm not sure a polynomial even exists that satisfies this?
paper bluff
i mean maybe change your name to something that is not so self-deprecating while...
nah i like it this way lol
tropic oxide
self-hate is not good for the soul
flat mica
i'm not sure a polynomial even _exists_ that satisfies this?
why's that?
the contradiction is only if n>=2
flat mica
How can i prove that $deg(p(x)) = 2$
this is false
paper bluff
oops
paper bluff
the contradiction is only if n>=2
can u explain why
flat mica
so let's take a look at lhs and rhs seperately
what's the degree of the LHS?
suppose p(x) has degree n
what's the degree of p(x)+2x^2?
let's go through cases
if deg(p)=2, what's the degree of p(x)+2x^2?
paper bluff
oh yea
flat mica
let's just rule out p=0 because zero polynomial doesn't have a degree
it would give 2x^2=8x+5, which is false
p(x)-2x^2 has degree 2 or lower if deg(p)=2
agree?
paper bluff
yes
flat mica
great, let's go on the right hand side
paper bluff
and RHS has degree 4
paper bluff
since like 8x + 5 can cancel out the x^4
flat mica
cannot you meann
paper bluff
so that's impossible
because the coefficients of x^n has to be equal for them to be equal?
paper bluff
for n>= 2 it follows that LHS < RHS aswell
paper bluff
two polynomials are equal if and only if all coefficients are equal
i see
flat mica
correct
let's try n=0, 1
in other words, p(x)=Ax+B, where A and B might be 0
but not both zero we already tested
paper bluff
if n = 0 we can take P(x) = c for any constant c
if n = 1 we can take P(x) = ax + b for any a and b
paper bluff
and just bash, then we can get P(x) = bla bla bla, and we can get P(2^2022)
paper bluff
ah it must be n = 1 then
paper bluff
also degree 2
flat mica
so that's the only possibility
write p(x)=Ax+B, with A!=0
LHS = 2Ax+2B+2x^2
RHS = ?
flat mica
Almost but not quite
flat mica
right
try again
A(x^2-2x+4)+B
so i'll just fix it for yiou, you were close
Ax^2-2Ax+4A+B+8x+5
is the RHS
2Ax+2B+2x^2
is the LHS
now you equate coefficients
A=2 like you said
wait
no not quite
wait yes
what am i saying
A=2
flat mica
yup
paper bluff
alr tysm
flat mica
np
paper bluff
.close
cedar kilnBOT
flat mica
i didnt solve the question on the paper though
cedar kilnBOT
Available help channel!
digital spoke
how do i do 9 the gpt isnt explaining it clearly
cedar kilnBOT
how do i do 9 the gpt isnt explaining it clearly
tropic oxide
how do i do 9 the gpt isnt explaining it clearly
!nogpt
cedar kilnBOT
how do i do 9 the gpt isnt explaining it clearly
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
tropic oxide
anyway try to think about it visually: imagine rotating a line while keeping the point (-3,4) fixed, so that it kinda pivots around that point. and imagine rotating it clockwise until it starts going through Q4
what will its slope be then
digital spoke
huh
that makes no sense to me
i figured out this one
wait nvm its not gonna be on the test
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
violet galleon
can anyone one help me in this question that came in my test? A is not the right option
people did it by value putting and stuff but how can we like get the answer by using standard location of roots or any other concept required for this?
wicked mantle
,rotate
wraith daggerBOT
cedar kilnBOT
@violet galleon Has your question been resolved?
exotic sundial
Would my sols be worthy of 3 marks
cedar kilnBOT
Would my sols be worthy of 3 marks
exotic sundial
These are the sols btw
cedar kilnBOT
@exotic sundial Has your question been resolved?
exotic sundial
<@&286206848099549185>
jagged tide
These are the sols btw
I mean your solution is correct so you're getting full marks no matter whatever points are assigned
exotic sundial
Would my sols be worthy of 3 marks
these ones are correct?
exotic sundial
I mean your solution is correct so you're getting full marks no matter whatever ...
^
jagged tide
^
Idk I don't have the energy to check thoroughly but if you've arrived at your answer without any weird assumptions then it's more probable to be correct
exotic sundial
ight thanks
jagged tide
Np
exotic sundial
.close (FYI part of my 'proof is wrong - the top part)
cedar kilnBOT
cedar kilnBOT
Available help channel!
zealous haven
I need help with the basics of algebra
cedar kilnBOT
I need help with the basics of algebra
zealous haven
I'm struggling with my genmath because I lack the knowledge of the basics;-;
coral jewel
do you have a specific question in mind?
wraith daggerBOT
Bread
zealous haven
Breh
violet flume
$$1/x-1 - 2/x+3 = 3/(x-1)(X+3$$
solve for x?
violet flume
But honestly Idk how
start a list off to the side
we want to collect all the unique denominators
zealous haven
we want to collect all the unique denominators
And that (X-1) (x+3)?
violet flume
on the right hand side, yea, theres those two
are there any other unique ones?
or just more (x-1) and (x-3)
zealous haven
1?
violet flume
we want to just check every term, and if its divided by something, we make sure its in the list
zealous haven
how do you meaan?
That was just a guess😭
violet flume
And that (X-1) (x+3)?
you were right here 
i just wanna make sure you believe you have the whole list
zealous haven
do you need help solving this or wha
I need help on how to solve and how it works;-;
zealous haven
Yep
zealous haven
But how do you identify LCD's?
violet flume
But how do you identify LCD's?
lcd is just the list
glass sphinx
I need help on how to solve and how it works;-;
am I tripping or is this just algebra
well make sure each side has same denominators then you can cancel them out
violet flume
lowest common denominator is lowest common multiple of the bottoms
violet flume
But how do you identify LCD's?
so, you just did it
zealous haven
so, you just did it
Yeah but this whole LCD is confusing, I just realized that LCD are located on the denomanator sides..
violet flume
Yeah but this whole LCD is confusing, I just realized that LCD are located on th...
lcd is just a special word for lowest common multiple
you know lcm?
zealous haven
NAH
glass sphinx
$$\frac{1}{x-1} - \frac{2}{x-3} = \frac{3}{(x-1)\cdot(x-3)}$$
violet flume
also, lowest is really just a convenience
wraith daggerBOT
Ren🍓
violet flume
for our purposes, any common multiple will work
can you find a common multiple of 6 and 4?
zealous haven
can you find a common multiple of 6 and 4?
5?
violet flume
$$\frac{1}{x-1} - \frac{2}{x-3} = \frac{3}{(x-1)\cdot(x-3)}$$
do you want to take over or what 
glass sphinx
$$\frac{(x-3)\cdot1 -2\cdot(x-1)}{(x-1)\cdot(x-3)}= \frac{3}{(x-1)\cdot(x-3)}$$
wraith daggerBOT
Ren🍓
glass sphinx
$$(x-3)\cdot1 -2\cdot(x-1) = 3$$
wraith daggerBOT
Ren🍓
glass sphinx
Now this is making me dizzy
can you understand what I have done here
basically I have simplified the fractions
violet flume
not leaving bc youre doing bad bread lol
this guy just barged in and i dont wanna cross talk
glass sphinx
this guy just barged in and i dont wanna cross talk
I'm on a mission to close as many channels as possible
kinda bored so
I will leave if you wanna help
violet flume
make as many enemies as possible speedrun
violet flume
I will leave if you wanna help
i was in the middle of explaining
zealous haven
can you understand what I have done here
You connected them and add the lcd to each side
crimson sedge
violet flume
You connected them and add the lcd to each side
we multiply every term by lcd
thats the first step
zealous haven
we multiply every term by lcd
By both of the 2 lcd?
zealous haven
Soo that is just 1 lcd right?
zealous haven
Soo we add the lcd besides the upper numbers?
violet flume
Soo we add the lcd besides the upper numbers?
that person skipped a few steps
we start with $\frac{1}{x-1} - \frac{2}{x-3} = \frac{3}{(x-1)(x-3)}$
wraith daggerBOT
jan Niku
violet flume
then, you multiply every term by the LCD
$\frac{ 1 \cdot (x-1)(x-3) }{ (x-1) } - \frac{2 \cdot (x-1)(x-3) }{ (x-3) } = \frac{3 \cdot (x-1)(x-3) }{ (x-1)(x-3) }$
wraith daggerBOT
jan Niku
$\frac{ 1 \cdot (x-1)(x-3) }{ (x-1) } - \frac{2 \cdot (x-1)(x-3) }{ (x-3) } = \frac{3 \cdot (x-1)(x-3) }{ (x-1)(x-3) }$
violet flume
**jan Niku**
it maybe looks like a lot, but we didnt really do anything, just compare the tops from here
violet flume
**jan Niku**
```latex
$\frac{ 1 \cdot (x-1)(x-3) }{ (x-1) } - \frac{2 \cdot (x-1...
. to here
does that step make sense?
zealous haven
Yeh after we find the LCD we add them side by side
violet flume
yea but not add, we multiply every term by it
maybe you mean, we uhh, introduce it to each side
violet flume
Yeh after we find the LCD we add them side by side
were allowed to multiply everything by a number, because it means its still equals
idk anyways
violet flume
**jan Niku**
```latex
$\frac{ 1 \cdot (x-1)(x-3) }{ (x-1) } - \frac{2 \cdot (x-1...
do you see what happens now?
zealous haven
maybe you mean, we uhh, introduce it to each side
Yepp
violet flume
like, do you see the cancels?
wraith daggerBOT
jan Niku
violet flume
well, like in the first term, you have x-1 in the bottom, and in the top
so we can cancel
zealous haven
Can you illustrate?
violet flume
$1 \cdot (x-3) - \frac{2 \cdot (x-1)(x-3) }{ (x-3) } = \frac{3 \cdot (x-1)(x-3) }{ (x-1)(x-3) }$
wraith daggerBOT
jan Niku
violet flume
the x-1 goes away in the top and the bottom
this is just like if we had $\frac{2x}{2}$, it would become just $x$, because the 2's would cancel
wraith daggerBOT
jan Niku
zealous haven
Soo first we cancel out the bottom then next is the 2nd?
violet flume
you mean the next term
?
by design each term will have something that cancels out
violet flume
yea, each term will have something that cancels
zealous haven
Man I wished there were arrows to point out the steps
zealous haven
Man I wished there were arrows to point out the steps
Because it gives clarity;-;
violet flume
- find the lcd
- multiply by the lcd
- do the cancellations
- solve the new problem
zealous haven
Can you use a website sketchboard?
silk gust
Man I wished there were arrows to point out the steps
do you mean something like $\implies$?
wraith daggerBOT
Frances
zealous haven
But this works
zealous haven
Ok contunue
violet flume
yea
not to drop anything too crazy on you, we accidentally messed up a sign because of that ren guy
you did everything right but it should be
$1 \cdot (x+3) - 2(x-1) = 3$
wraith daggerBOT
jan Niku
violet flume
how do you feel baout solving the problem from here?
zealous haven
Umm what do I do next exactly?
violet flume
solve for x
zealous haven
Yep cuz 1 is basically x at thi point, right?
remote nacelle
same property as saying 2(1+3)= 2x1 + 2x3
remote nacelle
**jan Niku**
put together the x and the numbers on the left hand side of this
violet flume
Yep cuz 1 is basically x at thi point, right?
yea. see if you can distribute the other terms
fast osprey
**jan Niku**
I have problem with that too
zealous haven
yea. see if you can distribute the other terms
Ok now I'm lost with the 2nd
violet flume
Ok now I'm lost with the 2nd
for 2(x-1)?
zealous haven
Yes
glass sphinx
omg are you still helping
zealous haven
I do it like this?
violet flume
yea, exactly
zealous haven
-2x
wraith daggerBOT
jan Niku
zealous haven
Where did the positive 2 came from?
fervent badger
Where did the positive 2 came from?
$(-)*(-) = +$
wraith daggerBOT
Ivan_Holy
zealous haven
Dang the signs also counts?
fervent badger
Yeah
zealous haven
Soo that becomes -4x?
violet flume
Soo that becomes -4x?
not quite
inside the ( ) you have an x, and a number
so we get a term with an x
and then a term thats just a number
$-2(x-1) = -2x+2$
wraith daggerBOT
Bread
remote nacelle
-2x+2 no?
wraith daggerBOT
jan Niku
violet flume
sorry im packing 
running around a hotel room
soon i will have to power down my computer 
but @zealous haven youre very close
it seems like we have $x-3-2x+2=3$
wraith daggerBOT
jan Niku
violet flume
final stretch 
zealous haven
**jan Niku**
Isn't this suppod to be $$x-3-2x+1=3?$$
zealous haven
soon i will have to power down my computer <:bearlain:762653539092529182>
Soo you gonna be back?
wraith daggerBOT
Bread
violet flume
Soo you gonna be back?
i have to drive to an airport
zealous haven
Or am I wrong;-;
fervent badger
Isn't this suppod to be $$x-3-2x+1=3?$$
No because, $-2(x-1)=-2x+2$
wraith daggerBOT
Ivan_Holy
violet flume
@fervent badger can you take over
zealous haven
i have to drive to an airport <:bearlain:762653539092529182>
OOF
fervent badger
<@709393938275893278> can you take over <:blobsweat:584506239661113371>
I am a little busy, so, barely.
remote nacelle
i can do it
zealous haven
i can do it
Now lezz continuee
remote nacelle
that’s what we have until now from the beginning
the next step is to combine the x’s and the numbers together in the left hand side of the last equation
remote nacelle
Now lezz continuee
so x-2x = ? and 3+2=5?
zealous haven
Ain't x-2x=-2x?
remote nacelle
remote nacelle
Ain't x-2x=-2x?
no wait up x-2x=-x
zealous haven
Dang never seen =-x before;-;
remote nacelle
it’s -1 times x
fervent badger
Yeah, but normally in math, you dont write that 1, you just write -x.
remote nacelle
Ain't x-2x=-2x?
so you had 1 x -2 x = -1 x the same way you would do 1-2 or 1x2-2x2=-1x2
fervent badger
soo pretty much its just 1-2=1 which is X
Yup
remote nacelle
x is a number, we just don’t know what it is yet, so it obeys the same rules as the other numbers
remote nacelle
so can you see what goes here in the ?
zealous haven
Yep
zealous haven
Soo in total we have 5x?
remote nacelle
no it’s -x+5
fervent badger
Soo in total we have 5x?
No, you only do that when doing multiplication.
When its plus, you just "glue" that -x to five.
zealous haven
soo 5 ib total?
remote nacelle
zealous haven
How-
remote nacelle
the simplify part we did earlier with x-2x= -1x = -x
then since x+3-2x+2=-x+5, i could substitute it as the left hand side
remote nacelle
How-
at this point i will permit myself to recommend this https://www.youtube.com/watch?v=vhm8ri0XNBM&list=PL0o_zxa4K1BVoTlaXWFcFZ7fU3RvmFMMG
you have to be able to simplify expressions with x’s in them before to solve them
it’s in pre-algebra
zealous haven
Wait the value of x is 2 right?
remote nacelle
then in algebra you will use this to simplify equations like i did here
yeah once you have -x+5=3
you can see it or subtract 5 from both side
to get -x=-2
then multiply -1 both sides to get
x=2
i think i will also give you this table summarizing some things you can do with numbers including x to simplify expressions
zealous haven
yeah once you have -x+5=3
ohhh so -2+5=3?
fervent badger
ohhh so -2+5=3?
Yes
zealous haven
Ahh I seemed to forget that a variable's value is always 2
fervent badger
Ahh I seemed to forget that a variable's value is always 2
Huh?
remote nacelle
fervent badger
Like X value is default to 2
Well, you just solve the equation above and get the answer.
And thats the x.
remote nacelle
Like X value is default to 2
idk if i would word it like that, it’s more we found out that that the only x value you can plug that satisfy the complicated equation you started with is x=2
for any other x you will plug in, you have that 1/(x-1) - 2/(x+3) won’t equal 3
and we did that by applying rules that simplify the equation you started with while preserving the x where it’s true
to the point where we ended up with -x+5=3 and you were able to just see that only x=2 works
zealous haven
Soo the final answe is -2?
remote nacelle
no it’s 2
fervent badger
Soo the final answe is -2?
Multiply that by (-1) and you get 2.
$-2*(-1) = 2, because (-)*(-) = +$
zealous haven
I don't see -1 here;-;
wraith daggerBOT
Ivan_Holy
fervent badger
I don't see -1 here;-;
But you must get rid of that minus, and the way to do that is to multiply by (-1).
remote nacelle
remember -x = -1 times x
zealous haven
Soo -x here is a given?
remote nacelle
it’s simply a notation for -1 time x which is the same for numbers like you write -6 or -32
zealous haven
remember -x = -1 times x
Soo after the result of -2 we bring it down to -x-2=2?
remote nacelle
no you have to MULTIPLY both sides by -1
fervent badger
Soo after the result of -2 we bring it down to -x-2=2?
No.
fervent badger
But you must get rid of that minus, and the way to do that is to multiply by (-1...
.
remote nacelle
or you can look at the equation and see that the only solution is x=2
zealous haven
But you must get rid of that minus, and the way to do that is to multiply by (-1...
Which is -x?
fervent badger
Which is -x?
Well you got the -x which is -2, but once you get rid of minus you get the real x which is 2.
zealous haven
Soo just keep stacking up till you get the final answer? (From what I understand)
remote nacelle
fervent badger
Soo just keep stacking up till you get the final answer? (From what I understand...
Just simplify the equation as far as you can get, and in final you will get the result.
remote nacelle
annotated
zealous haven
Ok I understand a bit
zealous haven
But where did 0 came from?
remote nacelle
from the 5-5
fervent badger
Did you learn how to solve basic equations?
remote nacelle
i was more explicit showing you the move of subtracting 5 from both sides
rapid mauve
(it's called equation balancing, by the way)
remote nacelle
Did you learn how to solve basic equations?
i will even go further and say that a subskill that will help you a lot with algebra is to be able to simplify expressions containing x before doing moves on equations with <=>
things like 1 (x+3) -2(x-1) from before
being simplified to -x+5
zealous haven
Did you learn how to solve basic equations?
I do but my mind is pretty much foggy when attaining knowledge and answering
fervent badger
I do but my mind is pretty much foggy when attaining knowledge and answering
That's when exercise comes in.
zealous haven
That's when exercise comes in.
Fr, I mean I know how to answer but most of the time my mind is foggy to the point I make mistakes with the steps
fervent badger
Fr, I mean I know how to answer but most of the time my mind is foggy to the poi...
Everybody makes mistakes, its good to have mistakes rather than doing nothing.
zealous haven
Everybody makes mistakes, its good to have mistakes rather than doing nothing.
That's why I always take notes just incase;-;
fervent badger
The more you exercise, the more you will understand.
The key point is not just to solve this, but to understand how you did it.
zealous haven
The key point is not just to solve this, but to understand how you did it.
Yep, but I swear I managed to understand precal because of its pattern;-;
Cuz every equation is the same steps.
Which is the same with algebra from what I have observed y'all teaching me
frail citrus
**Ivan\_Holy**
...
remote nacelle
imo instead of memorizing steps and patterns to solve each kind of question, it’s more efficient to understand how the game works, what are the move you can make whatever the equation may be
zealous haven
imo instead of memorizing steps and patterns to solve each kind of question, it’...
Which is the case in algebra, thinks change depending on the equation;-;
fervent badger
When you are ready, you can close this channel.
zealous haven
Ok!
remote nacelle
that might be intimidating but if you are very explicit
here are the main moves that were played for this problem
zealous haven
Thanks man, y'all the goat🙏
cedar kilnBOT
Available help channel!
supple wigeon
here is a problem i'm thinking of, but unsure the field. topology? geometry?
question: how to know from the output string that the resulting shape is real, truchet, and which parts are concave and convex?
supple wigeon
here is the newer version not transparent
it is a valid shape if the shape is closed, and the path doesn't intersect itself.
whether it is truchet is another problem. detecting convexity is another...
cedar kilnBOT
@supple wigeon Has your question been resolved?
tropic oxide
what's a truchet shape
dire geode
tilings are interesting, but not well discussed in help channels. i would guess #discrete-math or #alg-top-geo-top are better places to ask
cedar kilnBOT
@supple wigeon Has your question been resolved?
random swift
I think "truchet" is talking about the tiles themselves, not the tiling?
What do you mean by "real" also?
supple wigeon
What do you mean by "real" also?
a more detailed explanation of what i am trying to do
i think the term 'grid based rounded shapes' rather than truchet might be more accurate
cedar kilnBOT
@supple wigeon Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
craggy haven
cedar kilnBOT
craggy haven
im slumped
silk gust
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
im not really sure i see what the chart is for
i have another way but i want to hear your thought process first
silk gust
ok uh
craggy haven
heh
silk gust
dyk why there are specific values of 5 and 3 on the rightmost column?
craggy haven
no that’s what i got after mathing