1.49
#help-49
grand pondBOT
What a wonderful world !
twilit field
and here delta is the foward difference for which term?
This is wher I'm currently at
what do I do now
nvm, I made mistakes
<@&286206848099549185>
clarficiation, first want to use the regular newton polynomial method
.close
midnight plankBOT
midnight plankBOT
Available help channel!
last slate
factor x³+y²+1
midnight plankBOT
factor x³+y²+1
last slate
$x^3+y^2+1$
grand pondBOT
rivenrivers
grim vector
Is it what you're asked to do or its part of a bigger problem?
last slate
Is it what you're asked to do or its part of a bigger problem?
ill handle myself on the bigger problem
i just dont know how to factor this one
paper inlet
**rivenrivers**
i doubt this is factorable
grim vector
Yeah me neither
last slate
difference of squares should be possible on 2 variables right
all my factoring methods cant do this specific problem
winged maple
you cannot factor this
last slate
gotta find a way for this
midnight plankBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
last slate
i got myself some new factoring methods but this one, idk anymore
last slate
Please show the original problem, **exactly as it was stated to you**, with the ...
my problem is the integral of 1/(x³+y²+1)
this needs partial fractions procedure
paper inlet
with respect to x?
last slate
i already solved 1/(x⁵+1)
last slate
with respect to x?
it's a double integral, inner int is dx, outer is dy
paper inlet
oh okay
simple field
it's a double integral, inner int is dx, outer is dy
bounds or indefinite ?
last slate
i doubt i can do definite integration on this one though
grand pondBOT
rivenrivers
last slate
there is the problem
ill work on this for days
it's way harder than the integrals i solve than usual
wtf?!
how did this calculator manage to solve it
i think i can try my old factoring methods
but since theres +1
it would be like
(±√u) once again
so
2 variables
simple field
where'd you get the problem from
last slate
where'd you get the problem from
my mind,i keep thinking of hard integrals
simple field
well theres no guarantee there is a nice form for these integrals
just as a warning
even ones like this that dont look super out there
last slate
i know
i looked at the answer of calces
so it has answers and doesnt have any weird symbols
meaning theres a way to factor it
OH
(u)²
wait since the form is x³+y²+1¹
i can just do
wait this is cuberoot i think
i havent tried factoring resulting in cuberoots
nah how tf
calces is cracked
simple field
if you write a^3 = y^2 + 1
then its x^3 + a^3 = (x + a)(x^2 - ax+ a^2)
i dont think its particularly helpful, but you can do that
last slate
if you write a^3 = y^2 + 1
then its x^3 + a^3 = (x + a)(x^2 - ax+ a^2)
no thats not too helpful
finding x's solution
i think
it will be
³√(-y²-1)
this integral is cracked
how tf do i factor
there might be a brilliant idea here
ill take 2x+1 roots
(x±√1x+1)
OHHHHHHHHHHHH
I GET IT
nvm, i dont
how tf
i swear if i finally discover a factoring method for ts im gonna try to publish my factoring methods
i need help
WAIT PERHAPS TRANSFORMING?
paper inlet
transforming?
last slate
if you write a^3 = y^2 + 1
then its x^3 + a^3 = (x + a)(x^2 - ax+ a^2)
so thats if a=√(y²+1)
last slate
if you write a^3 = y^2 + 1
then its x^3 + a^3 = (x + a)(x^2 - ax+ a^2)
i recognize the form, thank you
ill gamble this
seems incorrect
wait im wrong that should be x+
seems wrong
i conclude that this has no factor
ok if this is the case
this has a factor
i cant just prove it somehow
last slate
ill gamble this
maybe i can try this
it should match
i need some serious help
,w
.w
,w integral of 1/(x^3+y^2+1)
grand pondBOT
midnight plankBOT
@last slate Has your question been resolved?
last slate
struggled on an integral
midnight plankBOT
@last slate Has your question been resolved?
fallow scarab
ill do this shit
so you don't need help anymore?
last slate
so you don't need help anymore?
i still do
fallow scarab
but you were already told
fallow scarab
wolfram used cubic formula and partial fractions
read that and factor your denominator while treating y as a constant
fallow scarab
where's the partial fraction step
,w expand (x-(-y^2-1)^(1/3)) * (x^2 + (-y^2-1)^(1/3) * x + (-y^2-1)^(1/3))
grand pondBOT
fallow scarab
check that it equals x^3 + y^2 + 1
don't think you used the right formula
try using this one
last slate
,w factor x^3+y²+1
last slate
try using this one
how about the +1
fallow scarab
can you ask a complete question
last slate
there are no actual factors? ☠️
last slate
can you ask a complete question
how do i factor x^3+y^2+1 for partial fraction
fallow scarab
try using this one
there are if you write x = a and b^3 = y^2 + 1
last slate
$\int\int\frac{1}{x^3+y^2+1}dxdy$
grand pondBOT
rivenrivers
last slate
this is my problem
last slate
there are if you write x = a and b^3 = y^2 + 1
really? b³ as y²+1
fallow scarab
that's what i said yes
if you're confused you can ask a question about what you're confused by
fallow scarab
substitution yes
fallow scarab
can you ask a complete question
last slate
do i use cube roots for this one
this
fallow scarab
use cube roots for what?
last slate
x=a
b³=y²+1
(x)(x²)
last slate
**rivenrivers**
it's this
to find the factor for the denominator to start partial fractions
fallow scarab
i mean what are you trying to solve for with cube root
last slate
i mean what are you trying to solve for with cube root
just in case theres a need to cancel
fallow scarab
?
last slate
like the factor i managed to make with 2x+1
fallow scarab
that doesn't answer my question
last slate
(x+√1x+1)(x-√1x+1)
last slate
that doesn't answer my question
it does
with foil method
there are some that can be left
fallow scarab
(x+√1x+1)(x-√1x+1)
what is this supposed to be?
can you start writing equations rather than random expressions
last slate
what is this supposed to be?
... a factor for 2x+1
fallow scarab
2x + 1 can't be factored any further
last slate
yeah try foil then
fallow scarab
unless you count 2(x + 1/2)
last slate
it cancels out
x² - √1x² + x
√1x² - x² + √1x
x - √1x + 1
wait did i do it right
yeah i did
2x + 1
cancel like terms
last slate
2x + 1 can't be factored any further
i just did
fallow scarab
you factored it in terms of square roots?
factoring usually means factoring in terms of linear factors
last slate
yes
fallow scarab
saying x can be factored as sqrt(x) * sqrt(x) is not common language
last slate
my factoring method is pretty confusing
fallow scarab
because then you can say sqrt(x) = x^(1/4) * x^(1/4) and you can factor sqrt(x) even further
please don't make up your own definitions for words that already have an established definition
last slate
because then you can say sqrt(x) = x^(1/4) * x^(1/4) and you can factor sqrt(x) ...
i dont think this is what i meant
i only put squares to cancel out terms to receive the final input
fallow scarab
did you factor x^3 + y^2 + 1 yet?
fallow scarab
try using this one
set x = a and b^3 = y^2 + 1. then the right side becomes (x + ...) (x^2 - ...) and it's factored as a product of a linear term times a quadratic term.
then you can further factor the quadratic term with quadratic formula
you fill in the ... with the equation i gave
fallow scarab
no that's not the right order
fallow scarab
you fill in the ... with the equation i gave
this is what you do first
$x^3 + y^2 + 1 = a^3 + b^3$
grand pondBOT
riemann
fallow scarab
solve for b
fallow scarab
try using this one
and plug b into the right side
last slate
(x+a)(x²-ax+a²)
x³-a³+y²+1=b³
transpose?
im guessing
cuberoot(x³-a³+y²+1)
if b is that value
then uhh
fallow scarab
set x = a and b^3 = y^2 + 1. then the right side becomes (x + ...) (x^2 - ...) a...
read this again.
x = a
last slate
oh wait x = a
so i dont need to solve for a
skrry
is there a way to get cuberoot in keyboard
∛
fallow scarab
cbrt is fine
last slate
b=∛(x³-a³+y²+1)
last slate
(x+a)(x²-ax+a²)
going back, do i have to perform an operation?
i dont know whats next
factor?
fallow scarab
read this again.
.
last slate
b=∛(x³-a³+y²+1)
this?
last slate
b=∛(x³-a³+y²+1)
,w simplify cbrt(x³-a³+y²+1)
last slate
do you or do you not understand this?
i really do not
fallow scarab
if x = a then x^3 - a^3 = ?
last slate
my brain isnt braining at all for the first time
fallow scarab
**riemann**
the left side of this is what you're starting with. the right side is what the form factoring sum of cubes gets you
fallow scarab
yes substitute 0 into your expression for b
fallow scarab
,w simplify cbrt(x³-a³+y²+1)
.
last slate
so i dont substitute it?
fallow scarab
yes substitute 0 into your expression for b
expression for b means
b=∛(x³-a³+y²+1)
x^3 - a^3= 0
use that in the right side of b
fallow scarab
get in the habit of writing complete equations
you're confusing everyone by writing random expressions without context
fallow scarab
b=cbrt(y²+1)
this is correct
last slate
am i even doing it right
fallow scarab
try using this one
plug your a and b into the right side
fallow scarab
what does split mean
last slate
(x+cbrt(y²+1))(x²-cbrt(y²+1)x+cbrt(y²+1)²)
last slate
what does split mean
like splitting the factors, i dont know the actual term
OHHHH SHIT
THATS REALLY IT
THANKS
cuz i tried calculating it in my mind via foil method
then i got
x³+y²+1=0
ok this is the hardest factoring method ive learned so far, thanks!
fallow scarab
,w expand (x+cbrt(y²+1))(x²-cbrt(y²+1)x+cbrt(y²+1)²)
grand pondBOT
fallow scarab
nice
midnight plankBOT
last slate
how do i give this man an upvote
midnight plankBOT
Available help channel!
graceful ferry
https://www.instagram.com/reel/DILpKWUS6yp/?igsh=MW5rOTl5M3JnN3g0Mw==
Can someone explain/translate what he did please
Instagram
midnight plankBOT
https://www.instagram.com/reel/DILpKWUS6yp/?igsh=MW5rOTl5M3JnN3g0Mw==
Can someon...
fallow scarab
!ss
midnight plankBOT
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.
livid python
https://www.instagram.com/reel/DILpKWUS6yp/?igsh=MW5rOTl5M3JnN3g0Mw==
Can someon...
lol i know this account
graceful ferry
lol i know this account
Lmao
livid python
multiplied and completed the square i think
fallow scarab
,tex .cts
grand pondBOT
riemann
graceful ferry
-x^2+x-(1/2)+1/2=x^2-x+(1/2)-(1/2)=x^2-x+(1/4)+1/4-1/2=(x-1/2)²-1/4=(1/4-(x-1/2))²)
?
I should've added and subtracted 1/4 right ??
graceful ferry
-x^2+x-(1/2)+1/2=x^2-x+(1/2)-(1/2)=x^2-x+(1/4)+1/4-1/2=(x-1/2)²-1/4=(1/4-(x-1/2)...
I technically did it but with more steps I think
What did he do here ?
How is it arcsin
dusty portal
Because $\dv{x}\arcsin(x)=\frac{1}{\sqrt{1-x^2}}$.
grand pondBOT
;(
graceful ferry
But denominator has 1/4
Isntead of 1
Isn't it $\dv{x}\arcsin(f(x))=\frac{1}{\sqrt{1-f(x)^2}}$.
grand pondBOT
prograce
fallow scarab
**prograce**
this is incorrect
fallow scarab
**;(**
do some factoring and u sub to get it into the form where you can use the arcsin formula here
dusty portal
Isn't it $\dv{x}\arcsin(f(x))=\frac{1}{\sqrt{1-f(x)^2}}$.
Yes, with the modification you have.
You’re meant to take ||u=x-1/2||.
And also $\int\frac{1}{\sqrt{a^2-x^2}}dx=\arcsin(\frac{x}{a})$.
grand pondBOT
;(
midnight plankBOT
midnight plankBOT
Available help channel!
wicked mauve
midnight plankBOT
lyric charm
!nogpt
midnight plankBOT
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).
sharp coral
can you show the original question? I can't really tell which forces are which from the diagram alone
wicked mauve
yeah im aware
wise moon
what is F' here?
wicked mauve
you cant demonize ai
lyric charm
F_CB and F' look orthogonal to one another; are they?
wicked mauve
F_CB and F' look orthogonal to one another; are they?
no clue
sharp coral
ok but can you show the diagram that came with the question?
wise moon
what is F' here?
?
wicked mauve
hang on
wicked mauve
send it anyway
i cant send it all in one ss is what im saying
cedar mason
im gonna die
wicked mauve
they made it astronomically spaced out
lyric charm
ok then paste it into Paint or something and scale it down
cedar mason
make it ten screenshots in one message
lyric charm
or that
lyric charm
it's very hard to comprehend when we don't have the question in front of us and cannot scroll back and forth through the parts
bold mango
<:bleakkekw:913344117981999125>
most real reaction
fathom jetty
this is the explanation but lowk idk
Do you understand this
fathom jetty
Do you know how to write the forces
sharp coral
at which part do you stop following?
wicked mauve
yeah
i just dont understand where they get 3F/2
i understand how they got sqrt2 f
bold mango
i just dont understand where they get 3F/2
pythagoras right?
fathom jetty
What even is the question
sharp coral
they are at right angles, so the pythagorean theorem applies
fathom jetty
this is the explanation but lowk idk
One side is f/2 the other is root2f
wicked mauve
but then dont you get sqrt(2)/2
sharp coral
,tikz[thick, -Latex, scale=2]
\draw (0,0) coordinate(O) -- node[below left]{$\sqrt 2 F$} (-45:{sqrt(2)}) coordinate(A);
\draw (A) -- node[below right]{$F/2$} ++ (45:0.5) coordinate(B);
\draw (O) -- node[above right]{$3 F/2$} (B);
\draw pic[draw, -, thin]{right angle=O--A--B};
grand pondBOT
cloud
fathom jetty
Can you solve it on paper and send a pic
@wicked mauve
wicked mauve
oh type shit
i got it
i forgot about the 1 in 1/4
which makes it 9/4 under the radical
lol
thanks folks
.close
midnight plankBOT
midnight plankBOT
Available help channel!
subtle peak
Hi! I was wondering if anyone has good website recommendations for checking problems like these
midnight plankBOT
Hi! I was wondering if anyone has good website recommendations for checking prob...
subtle peak
I suspect my answer is wrong
paper inlet
Hi! I was wondering if anyone has good website recommendations for checking prob...
why dont you just use wolfram?
is that a cursive s
paper inlet
oh alright im not sure of any that do but good luck
blissful zinc
I need help with my calc 2 homework. I am learning about taylor polynomials and im confused about what im doing wrong here. The screenshot on the right is the one the video from my homework shows how to do. The squared paper on the left is my attempt. I am confused as to why im not getting the same answer.
midnight plankBOT
I need help with my calc 2 homework. I am learning about taylor polynomials and ...
grim vector
Where are these pi/2 comings from?
@blissful zinc
f^n (pi/2) aren't involving pi/2 anymore
Its the numbers that you calculated
grim vector
I need help with my calc 2 homework. I am learning about taylor polynomials and ...
Its supposed to be just -1 here
Same for the other pi/2 that is lasting
blissful zinc
Where are these pi/2 comings from?
Oh I thought I was supposed multiply pi/2 times the derivatives shown in the formula here
blissful zinc
ohhhhhh I see
blissful zinc
that makes more sense, thanks!
grim vector
Yw
You're ending with their result normally if you erase these pi/2
Oh and btw pi/2 * pi/2 is pi/4 not pi
grim vector
Fact
dusty portal
grim vector
pi²/4
twin ridge
I am trying to decipher how this problem works.
midnight plankBOT
I am trying to decipher how this problem works.
twin ridge
From what I understand, this means that the derivative and the parent function have the same value the entire time, but I'm not really sure how that works.
The only function I know that has this behavior is e^x.
brisk iris
From what I understand, this means that the derivative and the parent function h...
That’s a différential equation
twin ridge
But if they want the instantaneous rate of change and the value itself to be the same, is this not the only way to do that? I guess I'm not really understanding the question.
twin ridge
Is that different from what I said? In my head it's the same thing.
brisk iris
It is !
Now you can solve it, and use initial conditions to get rid of the intégration constant
twin ridge
Wait what am I solving
twin ridge
Is that not already an equation
It's been nearly a decade since I've taken calculus, so I don't really comprehend much of what I'm reading.
brisk iris
It's been nearly a decade since I've taken calculus, so I don't really comprehen...
Ok let’s take it slow
brisk iris
dP/dt = P
This does not give you the value of P
You need to have an expression for P(t)
In order to do that, you are given a differential équation that you can solve
twin ridge
I am not understanding what you mean by "solve" at all.
You gotta know I've been extremely out of the calculus game.
What am I solving?
brisk iris
Wait
when you are given f’(x) + a f(x) = 0
That’s called a différential equation
You can solve it to find an expression for f(x)
twin ridge
Dang teach really got me doing differential equations in an Algebra 2 class.
brisk iris
It’s a simple one
What kind of function does not change when you take its derivative ?
twin ridge
So $f(x)=-\frac{1}{a}f'(x)$?
grand pondBOT
MJames
brisk iris
**MJames**
Ok, but that does not solve it, cause you don’t know f’(x)
twin ridge
I don't know any of these terms
twin ridge
That's a whole lot of stuff I don't know lol
brisk iris
twin ridge
e^x is the same
brisk iris
e^x is the same
Good but it’s not the only possibility !
twin ridge
I got nothing then.
brisk iris
Any function of the form : A.exp(t) could work
twin ridge
I'll be frank with you, I'm super sick right now, but teach wants this assignment today, so I'm just trying to struggle through it as best as I can.
brisk iris
How come you haven’t done calculus in 10 years ?
twin ridge
I appreciate the help, I'm just not understanding any of it.
twin ridge
How come you haven’t done calculus in 10 years ?
Haven't had to for my major.
I'm surprised I have to now for an algebra class.
brisk iris
I'm surprised I have to now for an algebra class.
Ok I can give you the full solution but you have to catch up on this or it’ll only get harder
Give me 5 min
twin ridge
Well this is the last assignment of the entire class then I'll never have to use it again. But I understand what you mean.
brisk iris
twin ridge
Oh that's what you meant by solve. I thought you meant integrate.
I forgot there were points and stuff. My brain just skipped over them.
brisk iris
Oh that's what you meant by solve. I thought you meant integrate.
It IS a form or intégration but Let’s not get into that
twin ridge
What is exp?
brisk iris
Exponential
brisk iris
e^x is the same
This is exp
grand pondBOT
MJames
twin ridge
Where A is the initial conditions?
twin ridge
So $A=\frac{3000}{e^{2015}}$?
grand pondBOT
MJames
twin ridge
Close but not quite
I plugged in y=3000e^(x-2015) into a graphing calculator and it didn't behave how I expected.
brisk iris
How so ?
meager ore
Let $G$, $G'$ be abelian groups, and let $\varphi \colon G \to G'$ be an isomorphism of groups. Prove that:
[
G_t \cong G'_t.
]
midnight plankBOT
Let $G$, $G'$ be abelian groups, and let $\varphi \colon G \to G'$ be an isomorp...
grand pondBOT
Halex
meager ore
I'm suspecting the same function works
but would have to restrict both domain and codomain
and show it is still well defined
can anyone confirm?
brisk iris
What's Gt ?
meager ore
What's Gt ?
Oh, sorry, should have defined that first
Gt is a group in which every element has finite order.
It is called, Torsion group
brisk iris
Oh ok, I'm sorry I can't help
Actually Can’t you prove that phi(Gt) = Gt’ ?
You know that phi(Gt) is a subgroup cause phi is an isomorphism.
You can prove that any element of phi(Gt) is of finite order using phi^-1, so that gives you phi(Gt) included Gt’.
midnight plankBOT
@meager ore Has your question been resolved?
meager ore
Actually Can’t you prove that phi(Gt) = Gt’ ?
I was afraid I had to prove that phi(Gt) is a subset of Gt’, and phi^{-1} (Gt') is a subset of Gt
brisk iris
I was afraid I had to prove that phi(Gt) is a subset of Gt’, and phi^{-1} (Gt')...
Don’t phi(Gt) and Gt’ have the same cardinal ? (as Gt)
meager ore
Don’t phi(Gt) and Gt’ have the same cardinal ? (as Gt)
would it prove phi is well defined?
meager ore
Don’t phi(Gt) and Gt’ have the same cardinal ? (as Gt)
since phi is surj and Gt is a subset of G, phi(Gt) = Gt
meager ore
Actually Can’t you prove that phi(Gt) = Gt’ ?
brisk iris
Soo you're done ?
I'm sorry I haven't done abstract algebra in years, so perhaps there is some fancy theorem out there
But this looks like it works !
meager ore
But this looks like it works !
wouldn't this mean that Gt = Gt'?
meager ore
Isn't f(Gt) = Gt as well? since f is surj
brisk iris
Isn't f(Gt) = Gt as well? since f is surj
No !
meager ore
am I confusing things
brisk iris
cause the image of f is not in G, it's in G'
No no you just proved that f(Gt) = Gt'
and since f is an isomorphism, you're done
grand pondBOT
Andy
tough shale
!occupied
midnight plankBOT
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).
@meager ore Has your question been resolved?
midnight plankBOT
midnight plankBOT
Available help channel!
odd lagoon
hi again
odd lagoon
so im trying to find the inverse of a 3x3 matrix
and im doing the row operations
but i dont know how to continue from where im at
i will take a photo of where im at and send it
i want to turn this 2 into a 0
but i dont see how i can do that without turning that 0 to something non-zero
oh nvm
i multiply the second row by -2 and add it
whoops
.close
midnight plankBOT
prime patio
The referential sets in Russell’s paradox has a contradiction Like for example R = set of x Such that x is not an element of its self
We can use first order set logic
I dont know how to prove that
midnight plankBOT
Available help channel!
tough shale
When it is mentioned as "an isosceles triangle PQR" without mentioning which side is the base or which angle is opposite to it, what am I supposed to consider?
midnight plankBOT
When it is mentioned as "an isosceles triangle PQR" without mentioning which sid...
tough shale
That Q is the angle opposite to the base?
slender walrus
is there nothing else at all?
midnight plankBOT
midnight plankBOT
Available help channel!
chilly cobalt
'A frog starts on the line at x = 0 and chooses either to go to the right 2 units, to the right 1 unit or to the left 1 unit with an equal probability of them happening. What is the probability that, in 6 turns the frog is at x = 6?'
midnight plankBOT
'A frog starts on the line at x = 0 and chooses either to go to the right 2 uni...
chilly cobalt
im lowkey trash at probability and idk what to do..
lyric charm
here is how you can rephrase this problem:
every turn, the frog slides 2 to the left unconditionally, then with a 50% probability chooses to leap 3 to the right
after 6 turns:
- how far would the leftward drift have taken the frog?
- how many leaps of size 3 would place it at x=+6?
chilly cobalt
after 6 turns:
- how far would the leftward drift have taken the frog?
- how man...
uhhh it would have to go to the right 3 times? then do nothing for 3 other turns
and then these events can happen in different orders? i think
lyric charm
uhhh it would have to go to the right 3 times? then do nothing for 3 other turns
... no
leaping right 3 times would put it at -12 + 3*3 = -3 and not 6
in fact you should have gotten that the frog has to leap EVERY turn
chilly cobalt
oh wait i think i read what you wrote wrong sorryy
chilly cobalt
in fact you should have gotten that the frog has to leap EVERY turn
oh yeah i see
chilly cobalt
in fact you should have gotten that the frog has to leap EVERY turn
so.. then what do i do? the probability of this happening should be 1/64
lyric charm
congratulations you just got the answer
chilly cobalt
'A frog starts on the line at x = 0 and chooses either to go to the right 2 uni...
'A frog starts on the line at x = 0 and chooses either to go to the right 2 units, to the right 1 unit or to the left 1 unit with an equal probability of them happening. What is the probability that, in 6 turns the frog is at x = 6?'
lyric charm
'A frog starts on the line at x = 0 and chooses either to go to the right 2 uni...
oh so the frog has 3 choices.
that complicates things a bit...
viral dagger
'A frog starts on the line at x = 0 and chooses either to go to the right 2 uni...
think of it as there being a constant 1 push to the left, so find the number of ways of it not going anything, its either the frog do nothing fully, the frog go left once and right twice, or the frog goes left twice and the right 4 times
for the first way, ill let you do it
for the second way, choose 2, then choose 1 from the remainding
for the third way you can choose 2
chilly cobalt
wait how do you guys think of these..
viral dagger
what did i even write in the first time 😭
viral dagger
wait how do you guys think of these..
magic
chilly cobalt
magic
i am scared of people that can do combi
anyways thanks! ill go think about it
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viral dagger
i am scared of people that can do combi
i suck at combi so dont fear me :p
last slate
Can someone check 12)b)
Is the final answer correct?
lyric charm
!msgdel
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earnest forge
How does a graph of this function look?
midnight plankBOT
How does a graph of this function look?
rose pilot
dense set of points on y=0 and dense set of points on y=1
earnest forge
1 for almost all values, and infinite number of jump discontinuities for all the irrational numbers?
rose pilot
1 for almost all values, and infinite number of jump discontinuities for all the...
kinda but its not just infinite number but dense at any point.
on each segment of x there are rationals and irrationals. So there is no segments its dense set of points
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fossil wagon
How to do qn b
midnight plankBOT
How to do qn b
exotic stratus
How to do qn b
What is the objective and what have you tried so far?
fossil wagon
I've tried doing the cross method but it doesnt seem to work for me
exotic stratus
I've tried doing the cross method but it doesnt seem to work for me
What is the objective?
fossil wagon
factorise it
rose pilot
I've tried doing the cross method but it doesnt seem to work for me
how many options of cross method did you checked?
fossil wagon
how many options of cross method did you checked?
wym
exotic stratus
Do you know the AC method of factorization?
fossil wagon
Do you know the AC method of factorization?
there's three formulas right?
fossil wagon
Do you know the AC method of factorization?
a^2-b^2
a^2+2ab+b^2
a^2-2ab+b^2
fossil wagon
4 have few variants of factorization
isnt there 3?
exotic stratus
a^2-b^2
a^2+2ab+b^2
a^2-2ab+b^2
These are three identities
rose pilot
isnt there 3?
im talking about cross method
fossil wagon
there's also completing the square and quadratic formula I suppose
fossil wagon
im talking about cross method
oh Im not really sure on that
exotic stratus
I mean luckily enough for you, since you know these identities, it does fit one of these
fossil wagon
I mean luckily enough for you, since you know these identities, it does fit one ...
what would you have done tho
grand pondBOT
HitenTandon
fossil wagon
**HitenTandon**
uh I dont really understand this
exotic stratus
Which part?
fossil wagon
what's the point of multiplying 1 with the constant 4
twilit field
How to do qn b
Have you considered the quadratic formula or, writing it as a perfect square
fossil wagon
Have you considered the quadratic formula or, writing it as a perfect square
no but I dont think that formula applies here tho
twilit field
no but I dont think that formula applies here tho
it does
exotic stratus
what's the point of multiplying 1 with the constant 4
The proof is a bit complicated but I can go over that if you want to
fossil wagon
The proof is a bit complicated but I can go over that if you want to
sure
exotic stratus
sure
Ok, if we factorize this expression completely can you see that the answer would be of form $(ax + by)(cx + dy)$?
grand pondBOT
HitenTandon
fossil wagon
Solve for x in terms of y
but there's another term as xy
fossil wagon
**HitenTandon**
is this like the (a+b)(a-b)
exotic stratus
is this like the (a+b)(a-b)
In what sense?
rose pilot
@fossil wagon do you know that in cross method you sometimes need to check different factorizations?
fossil wagon
In what sense?
probably the way ita written
fossil wagon
<@1017151697967124480> do you know that in cross method you sometimes need to ch...
what are the 4?
exotic stratus
probably the way ita written
It is product of two binomials but the similarity ends there
rose pilot
ill just drop example
fossil wagon
It is product of two binomials but the similarity ends there
ok so how do I go about doing it then
fossil wagon
ill just drop example
yeah I've tried that but you said that there are 3 other types
twilit field
but there's another term as xy
Can you expand (x+y)^2 for me
rose pilot
yeah I've tried that but you said that there are 3 other types
show it because you made mistake somewhere
grand pondBOT
HitenTandon
fossil wagon
Can you expand (x+y)^2 for me
x^2+2xy+y^2
twilit field
x^2+2xy+y^2
good, now try something similar here
fossil wagon
**HitenTandon**
true
fossil wagon
good, now try something similar here
you mean the qn I'm stuck in is similar?
grand pondBOT
HitenTandon
twilit field
yes
grand pondBOT
HitenTandon
exotic stratus
How does what happen?
fossil wagon
how would you get acbd by multiplying x^2 and y^2
grand pondBOT
HitenTandon
fossil wagon
oh ok yeah I get it now
exotic stratus
Ok cool
exotic stratus
So yea that's what we were doing
slow thorn
a^2-b^2
a^2+2ab+b^2
a^2-2ab+b^2
yeah so
$x^2 + 4xy + (2y)^2$
grand pondBOT
slow thorn
can you write the middle term into something like +2ab in the original identity?
exotic stratus
Oh hey @slow thorn nice meeting you again
slow thorn
hi
fossil wagon
Something like this?
fossil wagon
oh yeah because the b value is 2y right?
slow thorn
yes
exotic stratus
oh yeah because the b value is 2y right?
Yep
Alr if your question has been solved, use .close to close the thread
fossil wagon
Alr if your question has been solved, use .close to close the thread
wait that's it?
grand pondBOT
HitenTandon
exotic stratus
Sure
fossil wagon
I changed it after you guys taught me
exotic stratus
I changed it after you guys taught me
That's one step before the answer
fossil wagon
then how does part b not have a second step then
slow thorn
I changed it after you guys taught me
correct
slow thorn
then how does part b not have a second step then
it does
stark tartan
You ve almost found it man, true
slow thorn
you didnt finish it
exotic stratus
then how does part b not have a second step then
It does, we want you to do it
slow thorn
compress it to (a+b)^2
stark tartan
All you have to do is find what a and b are
fossil wagon
for a its (x-3)^2?
exotic stratus
Yes
stark tartan
Nice
fossil wagon
for b its (x+2y)^2?
exotic stratus
YES
stark tartan
Now do the same for b)
exotic stratus
🎊
exotic stratus
You're welcome
stark tartan
High five
fossil wagon
can I add yall
fossil wagon
High five
high five
how do I close this again its been quite a while since I used this server
exotic stratus
Use .close
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autumn folio
Hi, need some help with this
midnight plankBOT
Hi, need some help with this
tough shale
How about we start by assuming $x = 0.5^{\frac{t}{40}}$?
grand pondBOT
Suika
tough shale
It will make the equation easier to write
autumn folio
👍
autumn folio
And then the other one will be sqrt x
tough shale
No, assume $x = 0.5^{\frac{t}{20}}$
grand pondBOT
Suika
autumn folio
tough shale
How about we start by assuming $x = 0.5^{\frac{t}{40}}$?
This one is right
young mortar
can anyone explain the differnce between increasing and stricftly increasing? and also, given then interval [a,b], why are endpoints excluded for increasing wheras included for strictly increasing?
midnight plankBOT
can anyone explain the differnce between increasing and stricftly increasing? an...
fathom atlas
Increasing has that non-strict Inequality defn and strict has the strict Inequality defn.
midnight plankBOT
@young mortar Has your question been resolved?
gaunt plume
Idk about the endpoint thing. If a function~$f$ is strictly increasing, that means that $x<y\Longrightarrow f(x)<f(y)$. But if $f$ is just increasing, that just means that $x<y\Longrightarrow f(x)\le f(y)$
grand pondBOT
depression
young mortar
strict is a<b and f(a)<f(b)
gaunt plume
The function $f(x)=1;\forall x$ is increasing for example
grand pondBOT
depression
gaunt plume
But it's not strictly increasing
young mortar
yes increasing means non-decreasing from waht ive seen
but im unsure about the endpoints
consider y=x, for interval [0,1] its strictly increasing, but in that same restriction, its only increasing from (0,1)
fathom atlas
I feel like if you allow closed intervals for increasing function and the values at the endpoints are equal, it forces the graph to be a trivial horizontal graph. That's probably one of the reason.
sudden yacht
Where have you read this thing about the endpoints though?
sudden yacht
It's quite new (and a little weird) to me
gaunt plume
On literally any domain with an order on it
gaunt plume
Oh sorry
young mortar
im saying y=x is restircted
fathom onyx
You're talking about the function "y = x" on the restricted interval [0,1]
gaunt plume
My point still stands though, f(x) is also always increasing (as well as strictly increasing)
young mortar
yes i agree
gaunt plume
Oh you mean bounded?
young mortar
Oh you mean bounded?
yeah
like a piecewise function
which is what the question was
we werebasically asked for what values was a piecewise function increasing vs strictly increasing
fathom onyx
My guess is that that definition (with the (a,b) mentioned) is to do with discontinuities
sudden yacht
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
fathom onyx
Damn, there's a bot message for this?
gaunt plume
For future, "restricted" means something completely different to "bounded"
fathom onyx
useful
fathom onyx
For future, "restricted" means something completely different to "bounded"
Yh I did think this and was a little confused lol
young mortar
My guess is that that definition (with the (a,b) mentioned) is to do with discon...
do you mean differntiability?
fathom onyx
That is a related theme, yes
young mortar
what i inferred for the reasoning is that, increasing would refer to a interval where the deritive is >=0
fathom onyx
I'm looking on the Wikipedia article on monotone functions and the only bit where they didn't include endpoints in a given domain had to do with continuity, so...
young mortar
but what ive seen online hasnt been that defintion so idrk
fathom onyx
what i inferred for the reasoning is that, increasing would refer to a interval ...
If you're working from that definition (i.e. from the derivative), then (a,b) instead of [a, b] kind of makes sense
Because a derivative has to be defined as a limit from both sides
gaunt plume
I'm looking on the Wikipedia article on monotone functions and the only bit wher...
Not necessarily, y=-x^3 is strictly decreasing but has 0 derivative at 0
fathom onyx
If it's only defined on one side and not the other, it's a lot more messy
gaunt plume
what i inferred for the reasoning is that, increasing would refer to a interval ...
Sorry meant to reply to this message
young mortar
Sorry meant to reply to this message
i said increasing, not strictly increasing (which is also why for strictly increasing, the endpoints would be included)
gaunt plume
Yeah it's not increasing anywhere
young mortar
as it isnt realted to differnetiabillity
and instead relies on the original function
fathom onyx
"If the derivative is non-negative everywhere, then the function is increasing everywhere"
gaunt plume
It's strictly decreasing everywhere. If the derivative is 0 then you can't say anything about if it's increasing
fathom onyx
... is what he meant
fathom atlas
"If the derivative is non-negative everywhere, then the function is increasing e...
*first derivative more precisely, I think.
fathom onyx
That is implied
gaunt plume
That's what derivative means
fathom onyx
I don't think I've ever heard someone talk about a "derivative" to mean any higher-order derivative
gaunt plume
"If the derivative is non-negative everywhere, then the function is increasing e...
But yeah this is correct afaik (assuming the derivative is defined everywhere)
Back to what I think you're actually asking, you can only say that a function is increasing if you also specify what domain you're talking about. To say "which values is this function increasing on" basically means "on which intervals is this function increasing"
But yes it can get quite murky
And that's why they probably did that
A function can be (strictly) increasing on [a,b] and (strictly) decreasing on [b,c]
And it doesn't really mean anything to say that f is increasing/decreasing at b
just on its own that is
But you can get around a lot of those problems by using open intervals (intervals without endpoints)
young mortar
i've looked some more and I think this is a case where the way to define something as inceasing for my class is different to i assume the accepted convention which is why the endpoints are excluded for an interval, rather than included which seems to be the accepted defintion. This i assume is because we utilise a lot of piecewise functions, and for assement purposes wanted to distinguish between students that understood this distinction. anyways thanks for the help everyone
.close
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gaunt plume
Fwiw the normal definition doesn't care if there are endpoints. It makes perfect sense either way
young mortar
Fwiw the normal definition doesn't care if there are endpoints. It makes perfect...
i mean, given the same piecewise function, the endpoints are considered included as they satisfy a<=b f(a)<=f(b)
but our class defines it as f'(x)>=0
hence the discrepency
and since they cannot be differentiated at these points
they aren't included
gaunt plume
Oh sure yeah. I don't want to confuse you more so I won't labor the point. But a function having nonnegative derivative means that the function is increasing, but not the other way around. An increasing function has a different meaning and does not have to be differentiable
But yeah that's fair enough
young mortar
Oh sure yeah. I don't want to confuse you more so I won't labor the point. But a...
Yeah I got that point, its just that for our purposes it doesn't go beyond that consideration. ty tho 👍
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lyric scroll
yo guys
dawn dagger
danke
lyric scroll
danke
OMG
bro
finally
u spawned
A sports aircraft Gamma passes point A (10|10|0.8) at 10:00 AM and two minutes later passes point B (15|7|1). One unit in the coordinate system corresponds to one kilometer. The aircraft flies at a constant speed.
a) Set up the equation of the line g along which the aircraft Gamma is flying. Explain the connection between the line parameter and the corresponding time interval.
grim vector
omg spezi is here
dawn dagger
i will despawn
lyric scroll
i will despawn
today gonna be a long day bro
dawn dagger
lyric scroll
A sports aircraft Gamma passes point A (10|10|0.8) at 10:00 AM and two minutes l...
so basically i dont understand like
explain between the line parameter and the time interval
like
yeah
hello?
fathom onyx
You have a start position vector and a direction-of-travel vector
lyric scroll
You have a start position vector and a direction-of-travel vector
yeah
i can have the direction vector
ik but
what is the connectivity of line prameter and time interval
idk what they mean
fathom onyx
Well what line do you get for g?
e.g. if your direction vector comes straight from B - A, that vector is how far the plane travels in 2 minutes
lyric scroll
e.g. if your direction vector comes straight from B - A, that vector is how far ...
oh
so
every 2 minutes theres a point
fathom onyx
You can use whatever for the scalar
lyric scroll
ok so uhh
fathom onyx
You can use t, that's not a problem
My point is, the question asks for the relationship between that scalar and the time elapsed
lyric scroll
My point is, the question asks for the relationship between that scalar and the ...
yes
so
1 scalar is 2 minutes
:02 on the clock
fathom onyx
yee
lyric scroll
yee
ok thats cool
okay man
my heart is pounding
tomorrow i got my test
30 minute test
im so nervous
i cant even do this shit
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molten bay
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molten bay
So rank of the matrix and rank of augmented Matrix should not be same
So except b option all other options are giving unequal rank
midnight plankBOT
@molten bay Has your question been resolved?
chrome vessel
So except b option all other options are giving unequal rank
can you show your work?
last slate
Thats not proper row echelon form. If you make the k terms 0 then the last row has to be all zeros
last slate
Well you need REF to get rank. The determinant would work too tho yes
last slate
The determinant method doesn't account for all cases
last slate
The determinant method doesn't account for all cases
Why not. You can just set it up as a polynomial and find the roots
It can actually get lengthier than the regular method
Because in A|B you can have two 3X3 matrices, right?
molten bay
last slate
This makes sense
midnight plankBOT
last slate
The rank of A|B will always be greater than or equal to A
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tiny gate
,rotate
grand pondBOT
tiny gate
Is this wrong
vapid adder
how to factorise x⁴+x²+1
vapid adder
how to factorise x⁴+x²+1
i heard it's pretty famous
tribal temple
how to factorise x⁴+x²+1
You'll have to ask in a different channel, you've lost this one 
tribal temple
Is this wrong
And is that $\pdv{f_2}{p_2}$ you're trying to work out? If so, what's $f_2$?
grand pondBOT
@tribal temple
vapid adder
You'll have to ask in a different channel, you've lost this one <:sadCatThumbsUp...
which one
tiny gate
<#903463354654404658> just go here and start typing
Funny username
Lol chartbit to the rescue 😌
tribal temple
I think they’re saying f2 is same as q2
I would guess maybe that $f_2 = y - p_2 q_2$ maybe(?)
grand pondBOT
@tribal temple
tribal temple
In which case, it would work out as they have 
tribal temple
Why is this wrong if f2 = q2
You'd get 0, if q2 doesn't depend on p2
grand pondBOT
tiny gate
Is this possible
tribal temple
You'd have to give me a little while to get back to you 
on the move atm
tiny gate
Thxxx
tribal temple
Yep that's perfectly fine sorryyyy for the wait 
tiny gate
Dw thanks
midnight plankBOT
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rocky copper
What does it even mean to reduce a recursive language to a recursively enumerable one (like the HP)? Given that NPH includes some RE \ R languages, it would mean that any NP language is reducible to some language isn't even decidable, how would that work?
midnight plankBOT
What does it even mean to reduce a recursive language to a recursively enumerabl...
grim vector
CS?
grim vector
No its ok but you might wanna try also there https://discord.com/channels/268882317391429632/1313711459385081876
rocky copper
There's no way to put anything in there
grim vector
Just that here its mostly math thing but i hope you will find someone that can help you
rocky copper
It's closed
grim vector
Now it should be unlocked
prime hornet
rocky copper
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wicked beacon
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wicked beacon
I need help on the 1st and 3rd ones
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