@zenith compass Has your question been resolved?
#help-0
lone heartBOT
neon berry
ay
neon berry
Ima wait until someone asks me what I want
trim wagon
okay
neon berry
What I currently need is double checking my answers to algebraic questions
I'm gonna just download lightshot to show them here
The first three need to be simplified, 4th must have the root evaluated.
wanton tusk
okie where’s ur work
neon berry
1 sec
ornate condor
okie where’s ur work
ello
trim wagon
how do you take so crisp quality img
neon berry
how do you take so crisp quality img
I used my pc camera
wanton tusk
quality is super crisp
trim wagon
lmfaooooo
trim wagon
i’m literally die hahahahha
wanton tusk
is ur ans to 2 $(256)^{\frac{1}{8}}$
ocean sealBOT
swaggofishballs
neon berry
**swaggofishballs**
it's 256 powered to 1/8
wanton tusk
simplify
wanton tusk
oh
fluid basin
256 is a power of 2
wanton tusk
ya u can still simplify
neon berry
Write
fluid basin
swedish?
neon berry
understand that
its Swedish
wanton tusk
oooo
neon berry
yes I can answer it with 2
neon berry
256 = 2^k for some k
I can also do that, one moment
done
Now let me show my 4th answer and solution, caught in 4k
neon berry
what is the qn asking btw
finding the x
wanton tusk
okie
neon berry
I like being precise when it comes to solving
neon berry
I need to get an undergrad-level problem solving skills in order to attend undergrad courses next year
neon berry
as long as ur able to do it fast+precisely
It didn't take me long to do it
neon berry
btw why do u have equal signs at the end
Because I'm simplifying the equations
wanton tusk
presentation error
why is my name green
but ya ure dealing with equations
don’t need to have that = sign
when ure simplifying expressions
then ya
neon berry
If you look at the point where I eliminate the 3's, I don't put the equal signs because it would be incorrect to do that
wanton tusk
but ya ure dealing with equations
^^
an example
im just saying this to be safe HAHAH bec I’ve been penalised for it before 😭
neon berry
In these cases, I'd definitely not write with equals signs
wanton tusk
yepp! that’s gd
neon berry
though, if I'm simplifying only one side of the equation, it should be correct when it comes to the first steps that I did
Tomorrow I have my first math exam, I don't know what I can do further to improve
wanton tusk
ya the steps u did are fine (:
just the = sign
u seem to have the knowledge so ya
all the best ya
neon berry
thanks
ornate condor
@wanton tusk GREEN
wanton tusk
GREEN
lone heartBOT
Available help channel!
quartz cave
lone heartBOT
quartz cave
I know that with the power rule, the derivative of this function should be df/dx = -1x^-2
But how do we get there algebraically?
karmic rapids
limit definition
lucid bridge
first principals? f'(x) = lim h -> 0, [f(x + h) - f(x)]/h
karmic rapids
first principals? f'(x) = lim h -> 0, [f(x + h) - f(x)]/h
use tex
quartz cave
Alright but then you are left with 1/x - 1/x
mortal trellis
No
karmic rapids
If you let the h run to 0 immediately
wut?
quartz cave
first principals? f'(x) = lim h -> 0, [f(x + h) - f(x)]/h
He says it over here
karmic rapids
if you directly substitute h as 0 you get something divided by 0
mortal trellis
Well you can't let it run to 0 immediately. You would divide by 0
lucid bridge
you have to "remove" the denominator before applying your limit
karmic rapids
so you have to do other work first
lucid bridge
simplify
quartz cave
Alright well if I try to then I end up with (x/x(x+dx) - x+dx/x(x+dx))/dx
Is this the moment to let dx -> 0?
Then it would be x/x^2 - x/x^2
Still not possible I suppose
mortal trellis
You would still divide by 0
quartz cave
Right so multiply the numerator by dx first?
But then still I would run into the same problem
mortal trellis
Oh wait you can just combine the fractions
quartz cave
so -dx / x(x + dx)?
quartz cave
How do I cancel the dxs?
tawny condor
You forgot a dx at the bottom
mortal trellis
Well you have a dx in the numerator and in the denominator. Those cancel
quartz cave
also I thought you could only leave out dx^2 because those are negligible not dx
quartz cave
Well you have a dx in the numerator and in the denominator. Those cancel
right but in which numerator and denominator exactly? because I got 2 of both xD
tawny condor
I have the full process written in latex
do you want me to send it or you want to continue yourself?
@quartz cave
$$\frac{\frac{1}{x + h} - \frac{1}{x}}{h} = \frac{x}{xh(x + h)} - \frac{x + h}{xh(x + h)} = \frac{-h}{xh(x + h)} = \frac{-1}{x(x + h)}$$
$$\lim_{h \to 0} \frac{\frac{1}{x + h} - \frac{1}{x}}{h} = \lim_{h \to 0} \frac{-1}{x(x + h)} = \frac{-1}{x(x + 0)} = \frac{-1}{x^2}$$
quartz cave
Hmm let me see
ocean sealBOT
RedstonePlayz09
quartz cave
do you want me to send it or you want to continue yourself?
Alright
So how does -h turn into -1?
Oh I see
tawny condor
it cancels out
quartz cave
So this was not correct
It should be
(x/xdx(x+dx) - x+dx/xdx(x+dx))/dx instead of (x/x(x+dx) - x+dx/x(x+dx))/dx correct?
Oh no I see
In my step I leave the over dx
But you add it to the denominator in one go do you not?
tawny condor
In the first step, I take the h in the denominator and distribute it to the denominators of both fractions, while also making a common denominator.
quartz cave
In the first step, I take the `h` in the denominator and distribute it to the de...
Right exactly so you do 2 steps at once correct?
Multiplying by the LCD and distributing the h
Because then I follow allong what is happening
tawny condor
$$\frac{\frac{1}{x + h} - \frac{1}{x}}{h} = \frac{1}{h(x + h)} - \frac{1}{xh} = \frac{x}{xh(x + h)} - \frac{x + h}{xh(x + h)}$$
ocean sealBOT
RedstonePlayz09
lone heartBOT
@quartz cave Has your question been resolved?
quartz cave
$$\frac{\frac{1}{x + h} - \frac{1}{x}}{h} = \frac{1}{h(x + h)} - \frac{1}{xh} = ...
Right, perfect thank you
Now I am onto the derivative of sqrt(x)
tawny condor
Good luck!
alpine sable
hi, so i wanted to ask that what works interms of solving quadratic equations, for middle term do you use the lcm or another method that is other than taking lcm
alpine sable
im currently learning the lcm one and ive entirely forgotten about another one that was without taking the lcm one
and i find taking lcm a little harder
for solving quadratic equations specificalli
thanks
lcm u mean prime factorization?
if u find factoring tedious
just use quadratic formula
or just complete the square
thats if u dont like the guessing part
manic wind
methods of factorizing a quadratic?
alpine sable
it just depends person to person
sometimes its kinda hard to find two numbers which add up to something
alpine sable
sometimes its kinda hard to find two numbers which add up to something
oh
so if u cannot do it in case
u can always use quadratic formula
alpine sable
thats the last thing u wanna use
alpine sable
there's no LCM method for factorizing a quadratic
i think he means middle term split
alpine sable
i think he means middle term split
she haha
alpine sable
help :')) ive been trying to solve this but i keep erasing my answers because they might be wrong
lone heartBOT
help :')) ive been trying to solve this but i keep erasing my answers because th...
@alpine sable Has your question been resolved?
alpine sable
help :')) ive been trying to solve this but i keep erasing my answers because th...
show everything you have tried
i deleted them- but im rlly only struggling with finding the ratio
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
.close
wispy urchin
How do you solve these kind of problems?
lone heartBOT
How do you solve these kind of problems?
tawny condor
Divide by numerator and denominator by 4^x (for the first limit)
Then you should be able to apply limit arithmetic.
lone heartBOT
@wispy urchin Has your question been resolved?
lone heartBOT
tawny condor
No problem!
lone heartBOT
Available help channel!
lilac silo
Hey, I need to prove that 1-1/2+1/3-1/4+.... = ln(2) but I'm not sure where I am wrong in this
uncut torrent
vague coral
yea its true
but if you want to switch sum and integral, you need to prove why its possible
Unless you are an engineer or physicist
alpine sable
lol
lone heartBOT
@lilac silo Has your question been resolved?
lilac silo
<@&286206848099549185>
keen plinth
i mean
your integral looks like its wrong
g(0) = 1
and now you're missing both the constant term and the x term
broken beacon
how can I tell how many roots this equastion has?
lone heartBOT
how can I tell how many roots this equastion has?
trim wagon
uhh 
well 8x^2 is dominating term so for very large values it will just shoot off to infinity, at least thats what i believe
have you checked on desmos?
tawny condor
Well, f(0) = -1
and this function is continuous
so you have a positive root
and since this is an even function
you also have a negative root
I'm not sure how to prove these are all of the roots though
ocean sealBOT
tawny condor
Any inequality or equation with this will be very hard
Well, if there are anymore roots, there must be at least 4.
trim wagon
if we can show its derivative is positive for x> 0 and even function is then ig we should be good no?
tawny condor
Yeah
carmine reef
you mean odd function?
tawny condor
Proving that f''(x) is positive will also work
trim wagon
,w plot 8x^2 -ln(1+x^2) -cos(2x)
ocean sealBOT
trim wagon
i mean f(x)
carmine reef
ah
f(x) is even right
for some reason i saw the ln and was like nah that's not even
trim wagon
well even is easy to show
trim wagon
this >0 for x>0 maybe hard
carmine reef
i think second derivative would be useful here
ocean sealBOT
tawny condor
If we can show that f''(x) > 0 it would go like this:
Assume that there are more than 2 real roots, meaning there are at least 4 (since f is even).
Between the 2 positive roots and the 2 negative roots, we have a point where f'(x) = 0.
So in between those 2 points, there is a point where f''(x) = 0.
But f''(x) > 0, contradiction.
trim wagon
hmm
carmine reef
$\frac{2(8x^4+17x^2+7)}{(1+x^2)^2}+4cos(2x)$
ocean sealBOT
monikanicity
tawny condor
We need to show that this left fraction is bigger than 4.
Then this whole thing will be positive.
lone heartBOT
@broken beacon Has your question been resolved?
trim wagon
the guy better not go afk
tawny condor
I think he already did
broken beacon
yeh I'm here guys
keen plinth
use rouche's theorem 
8x^2 dominates -ln(1+x^2) - cos(2x) on the boundary of the unit disc
so they have the same number of zeroes counting multiplicity
broken beacon
use rouche's theorem <:kekw:752021756650455061>
It's way too complicated for the test this question from HAHA
Maybe you are right about solving this problem with the theorem but it was not thought in the course this question from
ocean sealBOT
monikanicity
carmine reef
Isn't this obviously >4
tawny condor
8x^2 dominates -ln(1+x^2) - cos(2x) on the boundary of the unit disc
ok what the heck
my next stop after linear algebra is complex analysis
or maybe I'll finish calculus first
lone heartBOT
@broken beacon Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
meager lotus
lone heartBOT
shell widget
use sin and cos formulas
meager lotus
ok thanks ✅
floral river
What to do here??
meager lotus
idk but my teachers explaining it now
floral river
x=y
meager lotus
idk what to do after i find out my cos and sin
upper grail
Need help with line integrals. tried different yt vids. not one gives proper explanation about parameterisation or etc etc
lone heartBOT
Need help with line integrals. tried different yt vids. not one gives proper exp...
@upper grail Has your question been resolved?
hollow lantern
lone heartBOT
@upper grail Has your question been resolved?
lone heartBOT
@upper grail Has your question been resolved?
lone heartBOT
@upper grail Has your question been resolved?
real gazelle
Need help with line integrals. tried different yt vids. not one gives proper exp...
which ones have you tried so far?
limpid nymph
I need help with my tenth grade homework on Linear equations
lone heartBOT
@upper grail Has your question been resolved?
upper grail
which ones have you tried so far?
Mostly uni questions and some examples found on internet. Still stuck on how to do parameterization
lone heartBOT
@upper grail Has your question been resolved?
mortal trellis
What exactly do you mean with "how to do parametrization" ?
It's not always obvious how to parametrize a given curve if that's what you are asking
(Depends on how you are given that curve of course)
upper grail
What exactly do you mean with "how to do parametrization" ?
how would u parameterise a curve?
ornate condor
what type of curve
if its just a straight line u can just use
given it starts at x1 and ends at x2
x1(1-t)+x2t
for t in 0,1
upper grail
if its just a straight line u can just use
no its not a straight line, also am not understanding what u did there
mortal trellis
Well it depends on the curve
ornate condor
...
mortal trellis
You can parametrize a line by x1+t(x2-x1), where x1 is your startpoint, x2 is the endpoint and as t runs from 0 to 1 you run between them. What they wrote is just this but rearranged
upper grail
You can parametrize a line by x1+t(x2-x1), where x1 is your startpoint, x2 is th...
Ahh got it now
Thanks alot both of u @ornate condor @mortal trellis
ornate condor
hm
i still find my way of writing more intuitive
np harri
imma just close dis too
.close
lone heartBOT
mortal trellis
Yeah it's interesting what people see as more intuitive. I personally like my way a lot more
Don't just close a channel lol
lone heartBOT
✅
ornate condor
wot oki
trim wagon
hello, this is preoccupied channel, you can read on how to make ur own channel in #❓how-to-get-help
pulsar breach
hello, this is preoccupied channel, you can read on how to make ur own channel i...
So I need to Ask to this people? is it? I thought Help-0 need to start
trim wagon
So I need to Ask to this people? is it? I thought Help-0 need to start
currently help-0 is occupied, you can choose one from available help section
the ones you’ve circled
pulsar breach
ok, Thanks👍
trim wagon
lilac nest
.close
lone heartBOT
coarse socket
lilac nest
Initially I thought the question hadn't been answered since the last message wasn't sent by op, then I read above and closed it
lone heartBOT
Available help channel!
trail delta
.open
compact coral
This is what im trying to solve, i knew how to solve it a year ago but now i have forgotten everything. I know that there's a short way. I don't want to just calculate the values of everything.
echo socket
Factor out powers of 3
minor needle
factor 3^2
compact coral
like cross them out?
echo socket
No, put them out of brackets
echo socket
echo socket
3^2 (3^3 + 1) on top and 3^2 (3^2 + 1) on bottom
compact coral
and then i cross out 3² right?
echo socket
Yes
compact coral
and then i just calculate the rest?
echo socket
Yeah
lone heartBOT
lone heartBOT
Available help channel!
hard remnant
lone heartBOT
hard remnant
in a chessboard of nXn, we define that p(i,j) is the placement of a square in that chessboard where i = 1,2,3,4 ... n and j=1,2,3,4 ... n
why in the second picture it says that two squares given that the first square is in p(i,j) and second square is in p(i',j') are diagonal, i+i' = j+j'
hard remnant
any value of p(i,j) all it diagonals can be found by adding the same number to i and j
it should be like this p(i+n, j+n) where n is an integer
hard remnant
where did u get it from>
I get it from logic and proofs book
specifically the application of satisfiability
when we add them we find that
2i+n = 2j+n
meaning for this to be equal i and j must have the same value
and that's not the case for different values of i and j
Could someone explain please
lone heartBOT
@hard remnant Has your question been resolved?
tepid drum
Hi everyone
lone heartBOT
Hi everyone
ornate condor
hi
tepid drum
I'll send the question just gimme a sec
First of all let A be a subset of N
If A is finite then a part of the theorem is already proved
Now if A is infinite then I have to prove |A|=|N|
Now first of all if I consider the function g:A→N where g(x)=x+1
Assume that g(a)=g(b) for some a,b included in A
Then a+1=b+1 which means a=b
So this function is injective
vale wigeon
why +1? you can just consider the inclusion map from A into N w/o that complication
vale wigeon
well it's not fatal
just a bit odd
||i assume now you will want an injection the other way around to apply csb, which is where the least-element principle comes in||
tepid drum
Now let x=y-1 where x belongs to A and y belongs to N then g(y-1)=y-1+1=y then this function is also surjective
Then it is bijective and thus |A|=|N|
vale wigeon
wait can you state more clearly your function N -> A
your g is not surjective unless A happens to be all of N !
tepid drum
That's what someone told me but the theorem states that for every infinite set A in N |A|=|N|
How should I do this
earnest topaz
Hey guys am I doing this right?
vale wigeon
try to think about the least element principle
tepid drum
||i assume now you will want an injection the other way around to apply csb, whi...
Excuse me but I didn't understand what you mean here
vale wigeon
@earnest topaz channel busy please move
keen plinth
g is not surjective even if A = N because of the +1 
vale wigeon
don't worry about it for now.
tepid drum
try to think about the least element principle
What's the least element principle
It says that for every non empty set there is a least element that set right
But what does that have to do with this
worn fox
Whenever yall are done
earnest topaz
<#488120190538743810>
Hey yea, just saw the format of this sever has changed, been away for a while
Thanks mate imma catch on
keen plinth
least element principle will help you create the function from N -> A
tepid drum
Let me think about it for a moment
Is the function f:N→A where f(x)=x+c such that x for x in N and a constant c such that c starts from 0 and for c=0, f(x) is the least element in A a surjection ?
vale wigeon
no you're kind of overdoing it...
let A be your subset of N.
it has a least element, call it a_1.
A \ {a_1} is also a subset of N, and also has a least element. call it a_2.
there is a way to describe in words the relationship of a_2 to the original set A.
if you want to think on your own from here that's fine, but do still answer my question here.
vale wigeon
But what does that have to do with this
the least element principle has everything to do with this, by the way.
tepid drum
if you want to think on your own from here that's fine, but do still answer my q...
So your question here is to find a relation between the element a_2 and the original set A ?
vale wigeon
of course it belongs to A, but that isn't what i'm looking for
tepid drum
I don't think it's the description you want bc it's obvious that it belongs to A
vale wigeon
in the set {4, 20, 69, 533, 895475, ...}
4 is the smallest element
20 is the ______
tepid drum
2nd smallest one
tepid drum
I thought of that but I didn't think that this Is what you want
vale wigeon
you can similarly construct the third smallest, and the fourth smallest, and so on.
tepid drum
Yea I can do this continuously since A is infinite
vale wigeon
in fact this alone already gives you a bijection between A and N, since every element of A will be numbered in this way eventually!
and injectivity is obvious as each n'th smallest element is obviously different from any below it, by construction.
tepid drum
And each element in N won't have more than 1 a that gives it as an output since each a is greater than the one before it
So it is also surjective
Then it's bijective and thus |A|=|N|
vale wigeon
yes
tepid drum
But I just still have to write the expression of the function
vale wigeon
nyeh
tepid drum
Which is f(a)=a_n
vale wigeon
i think writing f: N -> A, f(n) = n'th smallest element of A
will be just fine
and for the inverse you could send a in A to the number of elements in A that are less than or equal to a, if you so desired
tepid drum
Which is f(a)=a_n
But with the condition that n= c+1 for some c in N is this correct
tepid drum
i think writing f: N -> A, f(n) = n'th smallest element of A
Ok but how to write nth smallest element in A symbolically (instead of verbally )
vale wigeon
are you penalized for non symbolic expressions or just allergic to them personally?
tepid drum
No I don't have problems with them but its good to know how to use the symbols
vale wigeon
i don't think it's worthwhile to worry about a symbolic expression for f, honestly.
icy wedge
Hello i dont know how to start on answering this question
Show that a^4 + a^2 + 1 = (a^2 - a + 1) (a^2 + a + 1)
echo socket
Expand the RHS
swift sky
II think you can turn (a^2 - a + 1) = (a+1)^2
echo socket
First figure out the prime factors of 111
echo socket
II think you can turn (a^2 - a + 1) = (a+1)^2
No
echo socket
Still wrong
vale wigeon
still no
swift sky
that is wrong never mind
icy wedge
First figure out the prime factors of 111
Alright thank you i think i got this now :)
.close
versed island
Hi can anyone give a hint for my problem?
we have a sequence of $n>=6$ numbers, first 3 numbers arbitrary, others follow $a_{i+3}=2a_{i+2}-a_{i+1}+a_{i}$, we know $a_2=-2, a_3=6, a_{n-2}=2022,a_n=6226$, find the sum of the sequence
ocean sealBOT
AlterNet
lone heartBOT
@versed island Has your question been resolved?
alpine sable
$a_{i+3}+a_{i+4}=2a_{i+3}+a_{i+2}+a_i$, so {$\sum_{i=1}^m a_i=-a_{m-2}-2a_2-a_1+2\sum_{i=1}^{m-1}a_i$}
ocean sealBOT
Toby
alpine sable
(that should be correct now)
proud igloo
Okay here's a problem I've been trying to solve:
A cucumber weighs 500g. It's 96% water. It dries. Now it's 92% water. How much weighs the cucumber?
mellow tusk
tries?
mellow tusk
Okay here's a problem I've been trying to solve:
A cucumber weighs 500g. It's 9...
oh it must be dries*
long axle
Maybe “dries”
proud igloo
because of the lack of information of what it's 92% off I assume it just lacks water after drying
yes.
mellow tusk
let the dried amount be x
initial water=480, final water=480-x, final weight=500-x, final water is also=0.92(500-x)=480-x
on solving- 0.92(500-x)=480-x
u will get ur ans
mellow tusk
Okay here's a problem I've been trying to solve:
A cucumber weighs 500g. It's 9...
wdym how much weighs the cucumber? isnt it already given
proud igloo
How much weighs it after drying I meant
mellow tusk
ok
mellow tusk
let the dried amount be x
initial water=480, final water=480-x, final weight=500...
x=250, so final weight=250
proud igloo
Okay where was my reasoning wrong then
Cause I assumed 0.04 * 500 of non-water was kept
And that the WATER decreased so we get 0.92 * 500
mellow tusk
Now it's 92% water
the word now
mellow tusk
yea cuz some of its weight dried
lone heartBOT
@proud igloo Has your question been resolved?
proud igloo
yea cuz some of its weight dried
Okay, I didn't look at your calculation, but with a slow thought process and your clue you gave me right there I managed to get 250.
Yeah, thank you
bronze pilot
this is continius when x=pi/3 ((tan(x)-tan(((π)/(3))))/(x-((π)/(3)))
bronze pilot
right?
mellow tusk
dude the number of brackets
vague coral
this is continius when x=pi/3 ((tan(x)-tan(((π)/(3))))/(x-((π)/(3)))
that's a lot of brackets...
ocean sealBOT
mellow tusk
this right
mellow tusk
hm
mellow tusk
yea
mellow tusk
np
bronze pilot
.close
lone heartBOT
mellow tusk
shank's is a villan?
bronze pilot
maybe
mellow tusk
potential
bronze pilot
like 80%
mellow tusk
yh
lone heartBOT
Available help channel!
gilded vale
Are you allowed to use the word “greater” when describing distribution?
lone heartBOT
@gilded vale Has your question been resolved?
gilded vale
it's not a distribution
So how can I describe distribution?
Like there is an equal/unequal distribution?
untold panther
How do you solve this?
untold panther
.close
compact swallow
lone heartBOT
compact swallow
i dont get which one would be uncalculatable
since each of them are rewrites of each other
btw this is a practice test
.close
lone heartBOT
lone heartBOT
Available help channel!
frail geyser
help
frail geyser
I am confused because I am trying to solve this problem: 3x-4=12
How do I solve it?
.close
vernal lance
I'm not sure where to progress on this
lone heartBOT
I'm not sure where to progress on this
snow furnace
well you can start by moving the -2 to the outside
and remembering that the derivative of cot(x) is -csc^2(x)
and derivative of cscx is -cot(x)*csc(x)
then you should just be able to use the chain rule like normal
lone heartBOT
@vernal lance Has your question been resolved?
vernal lance
thank you
quick laurel
Hello
quick laurel
Currently struggling to solve the separable equation for y
My work is posted above
Thank you in advance.
sudden herald
Im stuck on which one to choose can someone help the answer is 61
quick laurel
@sudden herald Hey, I am currently occupying this channel. Do you mind reposting in a free help channel?
sudden herald
sorry i dont know how to use this
slender marten
Fix this:
quick laurel
Do you mind elaborating for me?
quick laurel
That is actually just a typo.
slender marten
That's what I mean. To fix the typo.
quick laurel
Let me correct.
Will do, but my question still stands on the final isolation of y.
slender marten
A integral calculator returns this for the integral of e^y - y e^(-y).
quick laurel
Right, but that is the Maxima calculation
the "hand" method provides what I have
through integration by parts
slender marten
To be fair, you did never say what you performed integration by parts on.
A lot has been left to the reader to try and understand what you've done on each line.
$\int (e^y - y e^{-y})\dd{y} = 2\int \sin x \dd{x}$
ocean sealBOT
stabulo
slender marten
From using a integration calculator, it would seem you should end up with:
$e^y + (y + 1)e^{-y} = -2\cos x + c$.
ocean sealBOT
stabulo
slender marten
Alternatively, $e^{-y}(e^{2y} + y + 1) = -2\cos x + c$.
ocean sealBOT
stabulo
quick laurel
Hmm, a question similar to this is going to be on my test tomorrow and I don't see how I can derive -2cosx + c from the integral
slender marten
Sine integrates to a negative. That's why it's -2cos(x).
quick laurel
Correct, rather, I don't understand how $2\int \sin x \dd{x} = \int (e^y - y e^{-y})\dd{y}$
ocean sealBOT
Thasis
quick laurel
Okay I'm sorry I understand now
slender marten
I just disagree with your results for the integrations.
ocean sealBOT
Thasis
slender marten
Implicit functions can be harder to solve for y than solving the original equation.
quick laurel
Right, but given the initial condition y(0) = 2; does one not have to find y to then find the value of c in order to get the exact solution to the DE?
slender marten
No. You can just replace y with 2 and x with 0 in the implicit solution to determine c.
quick laurel
Yeah I suppose that makes sense. I don't particularly know why I thought otherwise
slender marten
🙂
quick laurel
Therefore, $y(0)=2 \longrightarrow e^{-2}(e^{4}+3)=2cos(0)+c \Rightarrow e^{2}+3e^{-2}=c$
?
ocean sealBOT
Thasis
quick laurel
.close
keen pewter
Need help with this
lone heartBOT
Need help with this
keen pewter
Its dimensional analysis
I can turn Klygenes into Widgets no problem but idk how to turn Klygenes/Seilas into Widgets/Dueseldorfs
These are just made up units i need to convert
so it'd be like
the answer for klygenes -> widgets divided by seilas -> dueseldorfs?
so for example if kly -> widgets is 10 and seilas -> duese is 5
i can just do 10/5?
im confused on that
okay ill try it out and show you
yea im stumped
what is the name of what you just did?
when i look for dimensional analysis videos i just get the regular one
not the one where its something/something
okay, i'll watch that then try it out and if im still confused ill show you what i got
oh shit
this shit is actually easy
thanks for the resource ill try out the problem now
I got this
so just assuming that the conversions I put there are correct did I do it right?
Ah shit
Thanks a lot
Physics
My teacher didn’t teach us DA
He taught us sigfigs for like 1 day and then 1 day they did an assignment without a lesson on DA but I wasn’t here and then boom had to take a quiz
So I’m tryna learn it rn before I retake it
he could’ve just put normal conversion units but he wants to make his class fail lmao
I already have 3 F’s worth 70% of my grade because I was in a group and they didn’t do work
So imma good it gets better
I hope so
Thanks a lot for the help
crimson isle
lone heartBOT
crimson isle
can someone help with #1?
i got the identity matrix and the row operations,
not sure what to do nex
t
alpine sable
You need to do the same operations to A to find the inverse of A if you're looking for it
crimson isle
after i find the invers
e
do i do those same operations
on the 3x3 identiy matrix
@alpine sable
to get the elementary matrices
or are they obtained another way
alpine sable
Idk, ask helpers after 15m
crimson isle
alright thank you
crimson isle
is it possible for me to get your help on 2.1?
flint tree
Yeah sure thing!
crimson isle
.reopen
lone heartBOT
✅
crimson isle
if we assume A to be noninvertible
that would mean that the column vectors are independent
then the solutions are not all identically 0?
which could contradict
@flint tree whenever you get time please let me know, thank you sm
okay, dont need help
FTIM proves for me
thank you guys
.close
arctic mortar
lone heartBOT
arctic mortar
for 10a I would think that it would just be $$ \frac{1}{7!} = \frac{1}{5040} $$
ocean sealBOT
sytez
snow furnace
you have to remember that there are 52 cards in a deck
arctic mortar
why would that matter tho is my question?
the order of the 7 cards dealt shouldn't be affected by the number of total cards
there's 7! permutations of the cards and only 1 is in ascending order no?
snow furnace
one sec
arctic mortar
alr
snow furnace
it should be 52P7 though
snow furnace
because you are picking 7 cards from 52
ocean sealBOT
arctic mortar
textbook answer
snow furnace
oh I guess that is equal to 1/7! lol
arctic mortar
,wolf 1/7!
ocean sealBOT
arctic mortar
i have no idea what the actual answer is
the textbook doesn't match up with either of what i thought
snow furnace
it wouldnt be 1/52P7
snow furnace
it is 1/7!
arctic mortar
oh i just realized
answer key thru me off because it started with a 4
i see
thanks
.close
lone heartBOT
arctic mortar
.reopen
lone heartBOT
✅
arctic mortar
forgot to ask how to do b
flint tree
Hiii can I say what I need help with now?
ocean sealBOT
sytez
arctic mortar
52^7 being the total number of possiblities
snow furnace
Hiii can I say what I need help with now?
it wouldnt be 52^7, as each time you hand out a card, the total stack decreases by 1
arctic mortar
im thinking it might be 13P7 because there's 13 denominations and they can only be used once
snow furnace
I figured out one way
arctic mortar
how?
snow furnace
dont always have to use ncrs and pcrs, could always just find the probability of each single draw
lunar girder
Hello!
lone heartBOT
@lunar girder Has your question been resolved?
lunar girder
.close
lone heartBOT
@covert tapir Has your question been resolved?
lime halo
lone heartBOT
solemn juniper
Cool question, thanks for sharing
lime halo
I need help
tidal rivet
theres 2 of each side for the box
calculate the given 3 sides
it should be twice of that
lone heartBOT
@lime halo Has your question been resolved?
celest hearth
How do you solve this ? I know how to do it if there's only one || on the left but not if there's 2
tacit arch
do a sign chart analysis for separate cases to remove the absolute values.
celest hearth
do a sign chart analysis for separate cases to remove the absolute values.
What's a sign chart analysis?
tacit arch
on the real line, find where each of the individual absolute values change signs
they're different for each so you'll have 3 combinations
for example for x > 2, you know both terms are positive
so you just solve for (x-2) + (2x+3) = 6
do the same for x<-1/2 and -1/2 < x < 2
by combinations i mean (x-2) - (2x+3) or -(x-2) + (2x+3) or -(x-2) - (2x+3)
should only be 3 unless i made a mistake
celest hearth
I still don't understand, can you please draw it for me?
tacit arch
no
draw it yourself and share it here
something like that
but instead of - + -, you replace it with (x-2) or -(x-2)
similarly for the 2x+3 term
celest hearth
Ah so that's what you meant by real line
lone heartBOT
@celest hearth Has your question been resolved?
grizzled cliff
Hey guys
ocean sealBOT
grizzled cliff
I think?
trim wagon
yea ig, idk if i don’t see what you’ve done
grizzled cliff
is this right
trim wagon
yes
trim wagon
is this the next step?
well you’re skipping some terms but ig yea
and now write numerator in form of (1-sin^2)
autumn pasture
helloo
grizzled cliff
oh hi
autumn pasture
are you trying to show the left hand side?
grizzled cliff
yes
autumn pasture
$\frac{sinC - sin(C) cos^{2}(C)}{cos^{2}C}$
trim wagon
you ate some terms
ocean sealBOT
duckiescute!
trim wagon
also
autumn pasture
I think it should be that
grizzled cliff
oh
autumn pasture
then you factor out sinC
grizzled cliff
oh yeah I saw my mistake
autumn pasture
grizzled cliff
I turned 1-sin(C) into cos^2(C)
autumn pasture
oh how did you get 1-sin(C)
grizzled cliff
I think I ended up adding it instead 💀
autumn pasture
ohh hahaha
grizzled cliff
**duckiescute!**
wait where'd cos^2(C) come from
autumn pasture
making the denominator the same
autumn pasture
okayy
grizzled cliff
okay so left hand side
changed into sin and cos
should I make that -sin(C)/1 actually
or
hm
nah
okay
grizzled cliff
yes
autumn pasture
what denominator does it have
autumn pasture
right
grizzled cliff
uhh
autumn pasture
the one with -
grizzled cliff
oh 1
autumn pasture
we want it to have the same denominator as the one on the left
what’s the denominator
for the left
grizzled cliff
cos(C)
autumn pasture
cos^2(C)
grizzled cliff
oh huh
autumn pasture
cosC x cosC = cos^2 C
grizzled cliff
do I multiply it already
autumn pasture
yes
autumn pasture
why multiplied?
ocean sealBOT
duckiescute!
ocean sealBOT
duckiescute!
grizzled cliff
yeah
autumn pasture
so to make common denominator
grizzled cliff
oh
autumn pasture
we multiply it’s numerator and denominator by 4
grizzled cliff
so we multiply both the numerator and denominator
autumn pasture
what do we multiply the numerator and denominator by
grizzled cliff
by cos^2(C)
grizzled cliff
YES
autumn pasture
grizzled cliff
so this?
