nothing
#help-19
glossy smelt
Aight thx
glossy smelt
Nah but how do I find the curriculum
pallid trellis
on google
vivid wyvern
.close
pallid trellis
.close
odd edgeBOT
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).
odd edgeBOT
Available help channel!
charred oasis
i need help with this question
odd edgeBOT
i need help with this question
late sinew
late sinew
x-6 is not equal to x(-2)(3)
charred oasis
but i know it's not right because the next question is "why isn't it equivalant" 😭
charred oasis
x(-2)(3) is -6x
oh
late sinew
Well?
charred oasis
late sinew
Ok sure you can do that
But the numerator and denominator cannot be simplified no matter what you do
$x-2 \neq 3(x-6)$
clever fjordBOT
late sinew
what does that mean
wdym
charred oasis
why
late sinew
oh oops i meant 1/3
late sinew
Better now
charred oasis
where did this come from?
charred oasis
whats rhs and lhs ;;
late sinew
right hand side
and left hand side
ok lets start over
@charred oasis
what u need to show
is that (x-2)/(x-6) is not equal to 1/3
that is, $\frac{x-2}{x-6} \neq \frac 13$
clever fjordBOT
late sinew
now, to prove this, let's see the cases where they are equal
can you solve the equation $\frac{x-2}{x-6} = \frac 13$ for x
clever fjordBOT
late sinew
are you sure about that
strange aspen
late sinew
charred oasis
i cant think of any 😓
charred oasis
ok
glass vault
i need help with this question
could you do proof by contradiction?
strange aspen
<@&268886789983436800>
charred oasis
charred oasis
glass vault
yeah its a bad idea to make a fraction thats set to zero
charred oasis
tho it wouldve been better to cross multiply
how would i do that
late sinew
that's unecessarily long and not really what you wanted either
glass vault
how would i do that
you multiply both sides by the denominators
late sinew
how would i do that
$\frac ab = \frac cd \implies ad= bc$
clever fjordBOT
charred oasis
charred oasis
3x-6 = x-6
late sinew
yes
charred oasis
late sinew
why u dividing by 3
once u get 3x=x
u take the x on rhs to lhs
or, subtract x from both sides
clever fjordBOT
ImOakley
glass vault
so this would not simplify to 1/3
charred oasis
im a bit confused so 3x is the only way 1/3= (x-2)/(x-6)?
charred oasis
i dont think i do
late sinew
do you agree that we can subtract 1x from both sides of the equation 3x=x
ancient pier
man Ya'll are awsome TvT
charred oasis
strange aspen
yep
so the expression (x-2)/(x-6) ONLY simplifies to 1/3 when x=0 and other than that it won't
late sinew
man Ya'll are awsome TvT
Welcome to mathcord! 
charred oasis
so the expression (x-2)/(x-6) ONLY simplifies to 1/3 when x=0 and other than tha...
and that proves that it can't be simplified
if the only condition is x=0?
strange aspen
if the only condition is x=0?
how did you come up with that ?
charred oasis
how did you come up with that ?
MEANT x=0
i mean how does that prove it as being unequivalant and (x-6)/(x-2) not simplify to 1/3
strange aspen
it simply won't, test some values and find a counterexample and that would easily disprove it
odd edgeBOT
@charred oasis Has your question been resolved?
sturdy cape
Bit of logical reasoning - if that fraction does simplify to 1/3, then it shouldn't matter what value x is equal to
However, that fraction can only be 1/3 if x = 0; you can try plugging in any other value for x (e.g. x = 1) and you can see that the fraction doesn't equal 1/3
ancient pier
Welcome to mathcord! <a:Wave:1025121767573958746>
Thxssssss
mystic saffron
odd edgeBOT
mystic saffron
tried angle chasing but doesnt really work
i was trying to prove that angle AED and AFD are equal if and only if T lies on AD
brittle plinth
One idea is using Apollonius circle
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
One idea is using Apollonius circle
could you please explain?
brittle plinth
wait a second
mystic saffron
@brittle plinth do you have any breaktrhoughs?
brittle plinth
so the problem I'm having now is
brittle plinth
i was trying to prove that angle AED and AFD are equal if and only if T lies on...
if T lies AD and if we suppose that the bisector of angle E goes through it, there are actually 2 points for F
eager tapir
if T lies AD and if we suppose that the bisector of angle E goes through it, the...
I don''t think so
brittle plinth
apollonius circle
mystic saffron
ok
brittle plinth
so suppose we know ET is the bisector of DEA
We need to find F so that DAF = DAE and FT is the bisector of DFA
mystic saffron
yup
brittle plinth
hmm
ancient pier
yall big brains T-T I dread going to school next month-
brittle plinth
If F lies on that isoceles point then we're done
if F lies on the "C" point...
@mystic saffron ayy I managed to get a complete proof
So there are 2 cases for F
If F lies on F1 then you can easily finish the problem
if F lies on F2 then we're going to prove that D, E and F2 are collinear
mystic saffron
If F lies on F1 then you can easily finish the problem
i think considering this will be enough
tbh
mystic saffron
ohh alr
brittle plinth
if F lies on F2 then we're going to prove that D, E and F2 are collinear
We know that C is the intersection of AF and DE so if we proved this then C and F2 must be congruent, from that you can quickly prove that something weird has to happen
brittle plinth
We know that C is the intersection of AF and DE so if we proved this then C and ...
So from this E be congruent to B and so D lies on BC
charred oasis
what does this mean
odd edgeBOT
what does this mean
charred oasis
wouldn't it be a yes? if two expressions are simplified to the same expression
it would be equivalant
i feel like its quite obvious but im overthinking
graceful viper
yeah you are right
rotund steeple
Well consider the difference between $\frac{15}{3x + 9}$ and $\frac{5(x + 1)}{(x + 3)(x + 1)}$
clever fjordBOT
Elite
rotund steeple
One of them has a hole at x = -1, the other doesn't
graceful viper
oh right
eager tapir
what does this mean
What would "equivalent" generally mean in your definition?
charred oasis
What would "equivalent" generally mean in your definition?
if you were to simplify a function
like if you have 2 expanded forms and you factor them down and theyr the same i think
eager tapir
like if you have 2 expanded forms and you factor them down and theyr the same i ...
Not quitte
quasi kindle
Not quitte
really?
eager tapir
Equivalent means two or more expressions which is equal in value
"Equal-value" = Equivalent
quasi kindle
if they factor down into the same wouuldnt they have the same value>
eager tapir
So let's say you have a function f(x) = y, and g(x) = y
quasi kindle
?
eager tapir
Then would f(x) = g(x)?
quasi kindle
if they both =y
eager tapir
if they factor down into the same wouuldnt they have the same value>
Yes but not necessarily
quasi kindle
then they represent the same
quasi kindle
yes
eager tapir
if they factor down into the same wouuldnt they have the same value>
Hmm
Scrap that, that is true
My fault
graceful viper
let us first establish this:
does 0/0 make sense to you, cat?
eager tapir
Like for example 4/8 = 1/2 is equivalency, yeah
quasi kindle
let us first establish this:
does 0/0 make sense to you, cat?
0/0 is undefined
graceful viper
indeed!
graceful viper
**Elite**
now let us look at this example
both of them "simplify" to 5/(x+3)
do you agree?
graceful viper
the second one, however, has a hole (undefined) at x=-1
quasi kindle
restrictions right?
graceful viper
yes
quasi kindle
different restrictions
quasi kindle
x/x = 1, yes?
yes
quasi kindle
mhm
graceful viper
similarly, for $\frac{5(x + 1)}{(x + 3)(x + 1)}$
clever fjordBOT
dj
graceful viper
if x=-1 then we'd have 0/0
we can cancel x+1 and simplify the expression given x≠-1
however, 15/(3x+9) does not have that restriction
it is defined for all x≠-3
quasi kindle
so would it not be equivilant because of the different restrictions?
graceful viper
yeah
odd edgeBOT
@charred oasis Has your question been resolved?
quasi kindle
yes but!
i do believe this solution is correct for simplifying
but the question is
graceful viper
your simplification looks good
graceful viper
here, they forgot to scale the numerators
(x+3)/4 ≠ (x+3)/12
(x-3)/6 ≠ (x-3)/12
quasi kindle
here, they forgot to scale the numerators
what does scaling the numerators mean
graceful viper
a/4 = 4a/16
you multiply 4 on both the numerator and denominator
$\frac{x+3}{4}-\frac{x-3}{6}=\frac{(x+3)-(x-3)}{12}=\frac{6}{12}$
clever fjordBOT
dj
quasi kindle
where did the 12 come from ;; i understand how the 12 is there for the actual simplified denominator but why would it be half if only the numerators r multiplied
wouldnt it be 24
graceful viper
where did the 12 come from ;; i understand how the 12 is there for the actual si...
what should have happened was
$\frac{x+3}{4}=\frac{3(x+3)}{12},\quad
\frac{x-3}{6}=\frac{2(x-3)}{12}$
clever fjordBOT
dj
graceful viper
but the student didnt multiply by 3 or 2
also we take 12 as our denominator because it is the lcm of 4 and 6
quasi kindle
ohh
OHH Wait
i forgot i could do that instead of
just multiplying by the other denominator
odd edgeBOT
odd edgeBOT
Available help channel!
tough jungle
iooo
tough jungle
hello so uh
I have this problem where the denominator is always zero
and I'm just trying to make a problem for me to solve because that's what they tasked us to do
the denominator would always be equal to zero somehow
it's always false
wooden python
uhhh
tough jungle
what changes can I make in the denominator for the equation to be definable?
wooden python
are you sure you mean "always zero"...
wooden python
you're trying to solve the equation x^6 + 3x^2 + 5 = 0
and you're getting that it has no solutions?
is that what you tried to say
tough jungle
I'm never good at math, I'm looking at apps that says it's equal to 0
wooden python
what grade are you in?
tough jungle
and you're getting that it has _no solutions_?
yes, which makes the original equation undefinable
wooden python
that's the exact opposite of "denominator is always zero"! you get no solutions to x^6+3x^2+5=0,
which means the denominator is NEVER zero!
which means your fraction is defined for all real x!
tough jungle
tell me more
please
because when I try to do it, the equation which where both can't be factored anymore
wooden python
sadly i don't really know what you mean by "do it" here
but the fact that you couldn't factor the denominator is in fact a direct consequence of it being never zero
...do you know in general how to work with quadratic equations?
tough jungle
sort of
wooden python
in 11th grade this should be well known to you unless maybe you're in america and/or in a dogshit school
tough jungle
I'm just working with dividing this quadratic function
wooden python
hold on, forget about division
im trying to get you to recall something earlier
do you know the relationship between factorization and roots?
tough jungle
like I said, I'm never good with math😓 so my answer should be no😭
wooden python
ok maybe it's a language barrier thing? what's your native language
tough jungle
actually my original equation was
fx=4x^2+6x+3, gx=19x^2-8x-5
but ive done modifications for the denominator (g)
and yet undefined still
wooden python
... hold on.
tough jungle
ok maybe it's a language barrier thing? what's your native language
even in my native language, I wouldn't understand much because I specialize in humanities
😭😭
so sorry
wooden python
please do not call me "dude"!
wooden python
edit that word out, please.
anyway... now i'm confused WTF you're trying to do.
so let me ask you a clarifying question: where did you get this whole problem from?
tough jungle
we were tasked to create 5 examples of functions and I went with 2 linear, 1 quadratic, and 2 rational. Then from those 5 examples we have to pick 2 and operate functions on it from addition to division
I'm done with linear, my problem is the quadratic function in division operation
wooden python
okay? and what else? maybe you could send us the full problem statement and written instructions for what EXACTLY they want you to do?
tough jungle
wooden python
that's it?
tough jungle
yes
wooden python
well...
then you can just... write down the fraction?
they don't ask you to find its domain
tough jungle
hmm
wooden python
so you simply don't really care about when your denominators are and aren't 0
tough jungle
so you simply don't really _care_ about when your denominators are and aren't 0
well I really wanted my answer to be in its final form, but whenever I try, the equation is the answer
wooden python
wdym by "final form"
wooden python
can you show your f(x) and your g(x)?
btw i saw you write fx when you meant f(x) earlier. don't do that! you have to put the brackets every time.
tough jungle
can you show your f(x) and your g(x)?
the modified one or the previous?
wooden python
god fuck. whichever.
tough jungle
btw i saw you write `fx` when you meant `f(x)` earlier. don't do that! you have ...
noted!
tough jungle
god fuck. _whichever_.
f(x)=4x²+6x+3
g(x)=19x²-8x-5
wooden python
ok
f(x)/g(x) doesn't really simplify in any meaningful way
for these
you won't need to do any manipulation after just writing down f(x)/g(x) = (4x^2 + 6x + 3)/(19x^2 - 8x - 5)
the bottom has two roots but they're ugly radicals and i wouldn't expect you to factor it
brittle plinth
god I hate when the problem asks to make an example of linear functions and quadratic functions
tough jungle
the bottom has two roots but they're ugly radicals and i wouldn't expect you to ...
which...?
which means the equation should also be the answer?
wooden python
which means that that fraction is the simplest form and yes it is the answer
sometimes it be like that.
tough jungle
thank you
wooden python
i hope i won't have to rephrase it several more times before you understand it
cause maybe i have been cryptic and unclear this whole time without even knowing it
tough jungle
i hope i won't have to rephrase it several more times before you understand it
I'm sorry, I've never been an expert with mathematics😭🙏
I'm like a kid learning how to walk
but anyways
thank you
.close
odd edgeBOT
odd edgeBOT
Available help channel!
ember wing
Can anyone help me😭my brains not functioning rn😓
odd edgeBOT
Can anyone help me😭my brains not functioning rn😓
vernal yacht
Can anyone help me😭my brains not functioning rn😓
u wat question?
ember wing
My brain not functioning rn help:/
vernal yacht
what?
mighty siren
are you in class right now ?
static totem
that's impossible
vernal yacht
Is that everything?
mighty siren
(There are probably informations about the kind of sequence this is)
static totem
cuz sequence doesn't mean arithmetic sequence
they may mean arithmetic sequence though
in that case it's easy, in the artithmetic sequence the middle would just be the arithmetic mean
vernal yacht
In case it's an geometric sequence
a1 = 46, a2, a3, a4, a5 = 23/648
a1 / a5 = 2^4 * 3^4
static totem
like grui says, the context is close by, previous slides would tell you what we'er talking about
vernal yacht
I'll leave this hint on the board.
ember wing
no,just studying bc it's our test tomm I'm prob COOKEDI still don't understand geometric sequence but arithmetic sequence and arithmetic means its too easy also series
lavish jackal
why did u leave this at last moment
outer meteor
yeah i also have a doubt in this can anyone explain this
lean yew
show working please
i asked the OP to show his working in another channel and he merely thanked me, so i wanna see exactly what's going on
odd edgeBOT
@ember wing Has your question been resolved?
odd edgeBOT
@ember wing Has your question been resolved?
ember wing
Almost
late sinew
i asked the OP to show his working in another channel and he merely thanked me, ...
!noclopen
odd edgeBOT
i asked the OP to show his working in another channel and he merely thanked me, ...
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
ember wing
it's solve now:)
ember wing
How do I close it,OMG my brain cells fr not functioning rn
faint knot
.close or .solved
ember wing
.solved
shrewd trellis
odd edgeBOT
nimble blaze
you lost the -h in the numerator, got semi covered up from crossing out the +2
shrewd trellis
you lost the -h in the numerator, got semi covered up from crossing out the +2
Semi covered?
nimble blaze
partially covered
narrow crypt
u crossed it out unintentionally
nimble blaze
obscured it, likely making you miss it / not see it
shrewd trellis
hold on I’ll redo the q
nimble blaze
ignored that -h again
odd edgeBOT
shrewd trellis
.reopen
odd edgeBOT
✅
nimble blaze
yes
though its weird not seeing you express that x^-4 in d) as a fraction with positive powers like you did in the other parts
shrewd trellis
oh yes i forgot about that
are these correct too?
or do i need to show further prove
/not enough
nimble blaze
didn't you ask this already a couple of weeks ago
nimble blaze
yes
nimble blaze
factorise the (2x+6) further
you actually did that last time iirc
but made a mistake elsewhere
shrewd trellis
yes i assume this is my weak area
why do we need to factoor 2x+6 out
ik u need to cancel but
isnt it already simplified
narrow crypt
2(x+3)
nimble blaze
the idea is to explictly get a common factor in the numerator and denominator
shrewd trellis
oh makes sense
narrow crypt
the thing cancels and remove the thing that makes it indeterminate
nimble blaze
you could cancel / divide directly if you can see it
shrewd trellis
I just find it hard to recognise it
nimble blaze
in questions like these, its usually a good idea to factor as much as possible
also in the original expression,
its clear that 2 is a common factor of the terms in the denominator
so factoring that out first will make factoring the quadratic less tedious
shrewd trellis
i just feel like something is incorrect
or is it correct?
wait
yes i messed up
nimble blaze
you have a notation issue
ensure you have parentheses around the -3
$$\red{(\black{-3})}^2$$
clever fjordBOT
ℝαμOmeganato5
nimble blaze
if thats what you're squareing
clever fjordBOT
k
narrow crypt
,w lim_{x to -3}((x^4 - 81)/(2x^2 - 4x - 30))
clever fjordBOT
shrewd trellis
odd edgeBOT
shrewd trellis
is my answer correct?
vivid wyvern
3x²+2 has a derivative too
wooden python
you fumbled in several places
first you swallowed the ^2 in (3x**^2**+2)^4 on the denominator
then you swallowed that denominator wholesale
are you hungry? cause mathematical notation isn't very nutritious.
shrewd trellis
so two fumbles?
shrewd trellis
then you swallowed that denominator wholesale
wdym
shrewd trellis
oh true
wooden python
second line, you messed up factoring out (3x^2+2)
the stuff inside [these] should have been 5(3x^2+2)^2 - 12x(x^3+2x)
shrewd trellis
besides that
everything i scorrect?
is*
ik the answer will be wrong
but im talking about the working out after that
wooden python
line 3 can be salvaged but after that it's a no-go
you will need to fix the [] stuff
shrewd trellis
the stuff inside [these] should have been 5(3x^2+2)**^2** - 12x(x^3+2x)
wdym i did factorise it out properl
y
if i did ^2, that would make it
^3
wooden python
look at the first line
the 1st big product of brackets is 5(x^3+2x)^4 * (3x^2+2)^3
shrewd trellis
oh ur right
its like terms
but i thought that woudnt happen because there is subtration
@wooden python
wooden python
it's not like terms... this is just within the first term
fuck
ok let me just abstract this all away
let's call x^3 + 2x =: A and 3x^2 + 2 =: B
shrewd trellis
wooden python
your denominator from line 1 is $5A^4 \cdot B \cdot B^2 - 12x BA^5$
clever fjordBOT
Ann
wooden python
agree/disagree/disappear?
shrewd trellis
I dont understand this
nvm
i do
agree
btw be quick because i gotta leave in few mins
or we can discuss this once i come home
wooden python
there's no possible way i can be quick about this, sorry.
odd edgeBOT
@shrewd trellis Has your question been resolved?
wheat prairie
i tried this and yeah like Ann said, [] contains 5(3x^2+2)^2 and not 5(3x^2+2), this is i think the only problem with your attempt - after you fix that and simplify the [] expression, you should be good to go - but I will say, double check if anything could be factorised at the end
shrewd trellis
alr I’m home now
odd edgeBOT
alr I’m home now
shrewd trellis
i tried this and yeah like Ann said, [] contains 5(3x^2+2)^2 and not 5(3x^2+2), ...
Simplify the [] expression?
shrewd trellis
agree/disagree/disappear?
I agree btw
wooden python
Simplify the [] expression?
yes, simplify the stuff inside the []
it keeps surprising me that you ask for clarification on the most transparent (from my pov) phrasings
shrewd trellis
So u want me to expand the bracket and multiply it and simplify
wooden python
i can't say it with full confidence but yes.
shrewd trellis
i can't say it with full confidence but yes.
inc this?
desert jolt
One thing you can do is take the denominator to LHS and then use product rule
wooden python
what part of "simplify the stuff INSIDE the square brackets" was unclear?
sorry, but it's getting a bit frustrating having to go through this song and dance for the N'th time in a row!
desert jolt
wooden python
when i said inside, i meant inside, not inside plus a little bit outside!
like FUCK
desert jolt
One thing you can do is take the denominator to LHS and then use product rule
I believe this would be much quicker
wooden python
gah
wooden python
if you want quickness then op should have done it with logdiff
but i am not going to get into that
desert jolt
if you want _quickness_ then op should have done it with logdiff
Wasn't he complaining about using quotient rule on such a big expression
wooden python
he also doesn't know logdiff iirc.
shrewd trellis
Im not understanding
wooden python
im still frustrated at the fact that, even though i do my best to phrase things clearly,
shrewd trellis
can we restart?
wooden python
things are getting misunderstood
and i get asked to clarify things that are already as clear as i could possibly make them, short of drawing a thing in paint telling you exactly which sub-expression i want simplified
shrewd trellis
its okay then, ill get someone else to help me @wooden python
desert jolt
its okay then, ill get someone else to help me <@183668144404037632>
Did you read what I said
shrewd trellis
"One thing you can do is take the denominator to LHS and then use product rule"
desert jolt
Yes
desert jolt
Take (3x^2 + 2)^2 to LHS
desert jolt
So that it becomes f(x) * (3x^2 + 2)^2 = (x^3 + 2x)^5
desert jolt
So that it becomes f(x) * (3x^2 + 2)^2 = (x^3 + 2x)^5
You understand this?
desert jolt
or use texit
I dont know how to texit
shrewd trellis
then write it down
shrewd trellis
underneath the (3x^2+2)^2
desert jolt
That's V
desert jolt
Nothing
Im not gonna solve the question for you
Youre gonna do that
Im only going to help you
shrewd trellis
thats what im asking, for help?
odd edgeBOT
desert jolt
very unclear
If 3 people tryna help you and you are the one getting confused maybe its your fault
shrewd trellis
If 3 people tryna help you and you are the one getting confused maybe its your f...
Ill get someone else to help
odd edgeBOT
Available help channel!
gloomy flower
.reopen
odd edgeBOT
manic sleet
<@&268886789983436800>
twin vigil
Find the value of m for which the coefficient of X in the expansion of (x^m + 1/x²)^22 is 1540
twin vigil
Then after that what I would do
steep mantle
wait
steep mantle
figure out what k would be so the coefficient matches with 1540
graceful viper
- what should the exponent be for the x term?
- what should 22 choose k be?
twin vigil
- 5040
That would be very long exapsio
why my mind do not work
Ill work out
. Close
.close
odd edgeBOT
odd edgeBOT
Available help channel!
ivory grove
!msgdel
odd edgeBOT
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inner field
hi
jaunty cliff
hi
vernal yacht
hiiii
crimson beacon
!status
odd edgeBOT
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
let me explain
i made something called the superdence burst theory
i need a minute let me pull it up
The Burst-Core Hypothesis proposes a theoretical mechanism for faster-than-light (FTL) travel through the uncontrolled release of energy from a highly compressed core. Encased in a multi-layered shell capable of withstanding neutron star-level heat and pressure, the burst core could, in theory, release an energy pulse strong enough to push an object beyond the speed of light. This process is theorized to be one-way and unsteerable, posing extreme risk but offering radical implications for superluminal exploration.
In Einstein's theory of relativity, no object with mass can reach or exceed the speed of light due to the infinite energy requirement. However, the Burst-Core Hypothesis circumvents this by not relying on continuous propulsion, but on an uncontrollable energy burst strong enough to create a one-time superluminal event. The idea rests on the possibility that unknown phenomena may occur when extreme energy is released under dense containment conditions.
And if you could get it to hit you You should be launched far by the beam as it is not just light but electromagnetic radiation. First to make the pod you would need reflective plasma armor layer, Hyperdense Compression Lattice layer, Magnetic Containment Field layer, and a Quantum Phase Layer
proposed by an 11 year old
crimson beacon
The Burst-Core Hypothesis proposes a theoretical mechanism for faster-than-light...
well a single energy pulse,even of extreme magnitude ; does not inherently allow superluminal travel. High-speed particles (like cosmic rays) never exceed light speed despite enormous energies. They approach c but never cross it. There is no known mechanism by which momentum transfer alone can break this limit.
and furthermore a burst of EM radiation (light or other) can push objects (like solar sails), but only with finite momentum transfer. No arrangement of mirrors, plasma armor, or fields can amplify this effect to infinite velocity. Photons themselves always travel at c and they cannot push something faster than c.how do you explain that with this?
inner field
im not sure let me continue my research
crimson beacon
yeah .close
quasi sparrow
mystic owl
Can we prove this inequality never holds true for integer value of p and positive integer value of q. Like either the upper bound is false or the lower bound is false. I tried taking cases like
- q is even and p is negative
- q is even and p is positive
- q is odd and p is positive
- q is odd and p is negative
mystic owl
Case 1 is trivial but the rest of the cases are a hassle
Also for case 2 and 3 I have tried taking sub case of the big bracket expression being 1) greater and 2) lesser than equal to 0.
digital kestrel
whats E_1(1)?
mystic owl
whats E_1(1)?
You can think of it as a constant
mystic owl
It’s basically defined like this
E_1(1) is approximately 0.2193
<@&286206848099549185>
digital kestrel
exponential integral at 1, ok
odd edgeBOT
@mystic owl Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
brave kelp
how do i solve this by using quadradic functions? pre calc 11 btw
brave kelp
yes sorry
shut nymph
do you know the formula?
shut nymph
ok so what does that give you here?
brave kelp
y = a(x - p) + q
shut nymph
quadratic formula is with b^2 - 4ac
brave kelp
i forgot the square
shut nymph
yes (x-p)^2
shut nymph
in the first two terms
brave kelp
so its -5(x^2 - 7) + 8
shut nymph
you need to find something that resembles (a+b) ^2
shut nymph
so its -5(x^2 - 7) + 8
thats not the final form no
shut nymph
yes
shut nymph
you need to find something that resembles (a+b) ^2
next you need to do this
$(a+b)^2 = a^2 + 2ab + b^2$
clever fjordBOT
TheVibe
brave kelp
AHH sorry i need to go
shut nymph
no worries
willow furnace
odd edgeBOT
@brave kelp Has your question been resolved?
odd edgeBOT
@brave kelp Has your question been resolved?
signal oar
how do i solve this by using quadradic functions? pre calc 11 btw
Are you still going about this?
shut nymph
He said he would come back, he had to go for 1h
uneven burrow
can someone teach me races and gamesw
odd edgeBOT
can someone teach me races and gamesw
digital kestrel
teach you what?
digital kestrel
"this too" lmao
nimble trail
matrix algebra??
digital kestrel
living up to your name
nimble trail
it's honestly doable even without it
uneven burrow
living up to your name
we being related 🔥
nimble trail
that "Use matrix algebra" is the thing that i don't quite understand
uneven burrow
it's honestly doable even without it
no like ion understand how to make it i did it once but now i cant do it for some reason
uneven burrow
that "Use matrix algebra" is the thing that i don't quite understand
its just given to confuse
basically u have to make 2 matrixes and multiply em
AB
thats it but
i cant make the matrix
nimble trail
Or I am stupid and didn't understand the question
digital kestrel
yea matrix algebra is weird there. it's just adding things up
uneven burrow
matrix algebra meaning = make ur own matrix
digital kestrel
i don't know why you would set up a matrix
nimble trail
||don't tell anybody, but use chatgpt atp||
uneven burrow
😭
atomic marlin
I am not sure what it means for using matrix algebra
But if it’s yo give a table with matrix it’s like this
For first row it’s calorie and second row is protein
First column is male second is female and third is coach
If this isn’t the method or this is, I don’t see the purpose of it though
uneven burrow
yooo its like this only
digital kestrel
the 1 x 3 matrices should be 3 x 1 matrices since you can't multiply a 2 x 3 matrix and a 1 x 3 matrix
but yea maybe that's what it's looking for
atomic marlin
the 1 x 3 matrices should be 3 x 1 matrices since you can't multiply a 2 x 3 mat...
Yes
uneven burrow
it should be like this
atomic marlin
Take the transpose for the latter matrix
digital kestrel
yea you can also use that one instead
uneven burrow
take the common as X
digital kestrel
what emma did will be the same thing
digital kestrel
just be careful with the dimensions
if you use that one, the person amount matrices (A and B) should be 1 x 3
uneven burrow
someone find adj() for some reason im getting some values wrong according to chatgpt???
odd edgeBOT
Available help channel!
solid crescent
i need help, i am in a quantum box
odd edgeBOT
i need help, i am in a quantum box
odd edgeBOT
zinc glacier
at least the troll was funny this time
brittle plinth
aww was about to make a joke
brittle plinth
Can I bust out the hammer?
zinc glacier
dont worry, it wont become a problem soon enough
brittle plinth
would you give me some food
sure will give you some radium
solid crescent
whatever you want it is fine
i am alone
no one is watching me, i am feeling weird, like, another me... idk how to explain it
it ´s just... please, open the box
lavish jackal
!redir
odd edgeBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
lavish jackal
only if u have a math problem sure
odd edgeBOT
Available help channel!
languid hull
Hey there, I'm finding the derivative for g(t) = (t^2+t)^2 * (2t-t^3)^-2, and I've gotten to the point of:
(2(t^2+t)(2t+1))/(2t-t^3)^2 - (2(t^2+t)^2(2-3t^2))/(2t-t^3)^3
(See the pdf for a better representation)
I'm having trouble simplifying this down, as my professor wants it to be as simplified as possible, and honestly I'm just kinda stuck lol
odd edgeBOT
Hey there, I'm finding the derivative for g(t) = (t^2+t)^2 * (2t-t^3)^-2, and I'...
@languid hull Has your question been resolved?
languid hull
<@&286206848099549185>
ivory grove
Hey there, I'm finding the derivative for g(t) = (t^2+t)^2 * (2t-t^3)^-2, and I'...
!filetype
odd edgeBOT
Hey there, I'm finding the derivative for g(t) = (t^2+t)^2 * (2t-t^3)^-2, and I'...
Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.
languid hull
Ah my bad, I can change it
languid hull
Hey there, I'm finding the derivative for g(t) = (t^2+t)^2 * (2t-t^3)^-2, and I'...
Sorry if it's a bit hard to read
I pretty much just need help simplifying it or if I have any errors
tidal matrix
,w d/dx (x^2 + x)^2*(2x-x^3)^(-2)
clever fjordBOT
tidal matrix
looks all good to me! that would be the fully simplified form, if you were to expand the numerator all the way out and simplify it
and its probably "simpler" to have it under one fraction, but id be happy with that response as a teacher - ig it depends how much yours wants simplification
languid hull
Ahh ok so my final answer as of now would be fine?
tidal matrix
yeah it should be (again, depending on teacher a little bit). if you wanna go the extra mile, you can common factor the numerator a bit, and you should end up here
jade trout
Hellooo, i need help evaluating composition of functions(⊙_◎)
jade trout
narrow crypt
!status
odd edgeBOT
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
Please help, im abt to have a nosebleed🙏
narrow crypt
Which step are u stuck
jade trout
Uh i dont know where to begin
narrow crypt
Ok
Do u know what composite function is
And how they work?
[ f\circ g(x) = f(g(x))]
clever fjordBOT
k
narrow crypt
For example let ${f(x) = x^2}$ and ${g(x) = x+1}$,
[ f\circ g(1) = f(g(1)) = f(1+1) = f(2) = (2)^2 = 4]
Meanwhile,
[ g\circ f(1) = g(f(1)) = g(1^2) = g(1) = 1+1 = 2]
clever fjordBOT
k
jade trout
Can you like give me a full step by step example on how to solve it please(・–・;)ゞ
Or like another example
PLEASE
jade trout
I jus need an example so i can like use it as a guide on how to solve
strong sentinel
I can help
gritty spire
you can help
jade trout
PLEASE HELP ME
strong sentinel
Can you like give me a full step by step example on how to solve it please(・–...
so if we define
f(x) = x²
g(x) = 3x
I just picked some random functions but do you understand what I mean by define
we got two different functions
f(x) and g(x)
u with me?
@jade trout
jade trout
Yessir
strong sentinel
ok so if we want to find f(g(3))
that's f of g(x) when x = 3
so we are finding out what g(x) equals when x = 3
and then we're plugging that number in f(x)
so tell me what g(3) is equal to
jade trout
HA
strong sentinel
?
jade trout
Im lost.
jade trout
Nope sorry
strong sentinel
so you know how f(x) is a function
you plug in a number for X and you get a value
that's what a function is
so if f(x) = x²
if x = 1 then f(x) = 1²
if x = 2 then f(x) = 2²
if x = 3 then f(x) = 3²
do you understand that ?
@jade trout
oop
they not responding gg
wooden python
so if f(x) = x²
if x = 1 then f(x) = 1²
if x = 2 then f(x) = 2²
if x = 3 the...
better to say f(1) = 1^2, f(2) = 2^2, f(3) = 3^2
jade trout
Mhm a little
tidal matrix
another way of thinking about it that i really like:
Let's say $f(x) = 3x + 2.$ We can mess with the variable, $x$, as much as we want:
\begin{itemize}
\item $f(t) = 3t+2$
\item $f(\tau) = 3\tau + 2$
\item $f(\blacksquare) = 3\blacksquare + 2$
\item and so on\dots
\end{itemize}
So we can also (usually) put in $g(x):$
$f\left(g(x)\right) = 3\left(g(x)\right) + 2$ \
$f\left(g(3)\right) = 3\left(g(3)\right) + 2$
clever fjordBOT
haseeb
jade trout
Can you guys solve one of these, and give me a step by step explanation😭
strong sentinel
you need to understand how functions work
jade trout
Mhm i do
strong sentinel
ok so if g(x) = (2x-1) / 3
what's g(0)
jade trout
3?
strong sentinel
explain how u got that
lean yew
maybe i can share a little bit of my personal notes about functions if it would help
jade trout
Well uh i multiplied the 2 and 0
strong sentinel
ok
jade trout
YES PLEASE
lean yew
here you go
you will still have to do your problems yourself, but i hope this will help you understand what people here are talking about
strong sentinel
oh jesus
jade trout
Wait ok now im confused
clever fjordBOT
r
strong sentinel
can you try and find g(0) again
jade trout
So i replace the x with 0 yeah?
strong sentinel
yea
lean yew
remember, whenever x is replaced by a value, just find all of the x in the function and replace it by the same number
that's all
lean yew
so far so good
strong sentinel
no
lean yew
[2(0) - 1] / 3
jade trout
Ohh 2?
strong sentinel
no
lean yew
the answer is a fraction
jade trout
Huh.
lean yew
show your steps?
strong sentinel
lets evaluate the top part
jade trout
Jesus
strong sentinel
what's (2 times 0) - 1
jade trout
-1
jade trout
MHMM YAY OH MY GOD
strong sentinel
and the bottom part is 3
lean yew
not necessarily
strong sentinel
$$ g(x) = \frac{2x - 1}{3} $$
clever fjordBOT
r
lean yew
this is just an example
jade trout
-1/3
jade trout
SORRY IM STUPID AT MATH
jade trout
9/3???
lean yew
simplify
strong sentinel
which is?
jade trout
3/1? HELP
jade trout
OHHHH OH MY GOD TYSM
lean yew
you got it!
jade trout
Im getting it🙏
lean yew
the same applies for functions too, in case you need clarification
jade trout
lean yew
for example, if wtf is a function, g(wtf) = [2(wtf) - 1] / 3
strong sentinel
@jade trout back to the original question
jade trout
Huhu
strong sentinel
$$ f(x) = 2x^2 + x - 3 $$
jade trout
Im stressin abt the g(wtf)
clever fjordBOT
r
strong sentinel
so if we want to find f(g(0)
we already know what g(0) is right, you found it earlier @jade trout
can you respond
lean yew
Im stressin abt the g(wtf)
if so, ignore my message for now
lean yew
whoa, relax
jade trout
Im sorry :,> i didnt mean it like that
lean yew
i can tell she definitely needs help understanding functions
well i'm on phone so hopefully i can type well
jade trout
Im actually eating lunch rn...
lean yew
ah, another gmt+7-9 guy. well, maybe you can think about this over lunch
jade trout
So do i answer it rn??(´-﹏-`；)
lean yew
ofc