show me ur process too
#help-0
tired axle
cinder sundial
wait multiply those y and x
tired axle
not quite
just the numbers
just multiply across
the "y" stay the same
just the whole numbers change
well only the numerator to be exact
cinder sundial
wdym
cinder sundial
ohhh
tired axle
LOL
craggy steeple
are u done now
craggy steeple
ouch
craggy steeple
and u are done and u have ur new ratio
saw the word done
expected u guys to be done
xd
cinder sundial
oh i forgot
tired axle
so change that real quick
cinder sundial
tired axle
x
cinder sundial
Should I put it in parentheses
tired axle
dont forget the x
if u want sure
but no need
-2x
the "x" did not go away
just the "-1"
cinder sundial
tired axle
yes
no need for ()
but other than that
looks good to me
and that is ur new ratio
craggy steeple
:D
cinder sundial
And actually
cinder sundial
There’s another
tired axle
LOL
craggy steeple
..
cinder sundial
With that xy
craggy steeple
die
tired axle
delete that plz ^
kk
@craggy steeple u can dm me ur quiestion
i can help 2 at once
no problem
cinder sundial
its like 5:3 to 5/3
tired axle
?????
cinder sundial
emmm
tired axle
yes 5:3 does =5/3
cinder sundial
yes
tired axle
so what is the question asking?
jagged imp
express one variable in terms of the other using 8x+5y=4x-y and then the ratio is only in one variable
cinder sundial
no its to find the x and y
tired axle
so then
cinder sundial
then use the x and y to those other question
tired axle
do the same exact thing we jsut did
for the first quesiton
and apply it to this new qeustion (apply the methods)
tired axle
im still confused
on that the question is asking LOL
is it saying" use the x and y we just found and plug it into this new ratio then simplily?"
cinder sundial
what
tired axle
so u plugged in everything what
cinder sundial
i have no idea
cinder sundial
should i find the value of x and y
tired axle
its not asking for that doe???/
u just said it wants to be simplified
and then put into a fraction
am i correect?
cinder sundial
yes
tired axle
ok
cinder sundial
but its weird
tired axle
so then do this
cinder sundial
left the x and y undone
tired axle
if that is just what its asking then i do not see why not?
u can always have a (equation with x and y terms in it/ same thing )
cinder sundial
really i can have a x and y in equation and its normal
tired axle
i mean im just going by what ur directions are
and they do not seem clear to me
if only they were translated exactly to english
im not entirely sure with asain culture and rules of how they do math
meaning
what if ":" really means =
tired axle
i have no idea
cinder sundial
i have no idea what im doing
tired axle
yes ^
dont forget
the
y in the first term
and the x in the last term
u keep forgetting them
cinder sundial
can i simplify them
tired axle
only 3 of them yes
tired axle
yes
get rid of them 1's
they make it look sloppy
even doe its still correct
and then merge them into a fraction
cinder sundial
tired axle
i dont understand
tired axle
u just told me that all we had to do is plug in the x and y we found in the way beginning
cinder sundial
yes
cinder sundial
but i wonder if it have an true value
cinder sundial
tired axle
because doing that will make the directions unclear and wrongf
cinder sundial
does they have an true value
cinder sundial
god
cinder sundial
my bad
tired axle
so what ur saying now is
tired axle
"using the first x and y we found, plug it in the new ratio and then solve for x and y again"
is that what ur asking
???
cinder sundial
yes
tired axle
wow
ok so i have work tomorw LOL and i dont want to be here for another hour
because if that question is asking that
u will be here for a while
LOL
cinder sundial
omg
cinder sundial
it is hard question right
cinder sundial
god
cinder sundial
god
tired axle
write out ur ratio
then put an equal signs
and put all ur "x's" on one side
and same for "y's"
then solve for them both
same process
just longer equations
cinder sundial
god
tired axle
thus makiing it a little bit more difficult
but same exact process!
just with extra terms
cinder sundial
ok let me try
cinder sundial
so x and y does have an true value
tired axle
cinder sundial
like an number
cinder sundial
ok
cinder sundial
why we dont get -2/3
cinder sundial
do we left sth
tired axle
meaning x and y could be a interger or rational number
orrrrrr can be a number with a variable
anyways im gonna go
good lucky
cinder sundial
ok
tired axle
ciao!
cinder sundial
i will, thank you
@ionic jewel wdym, y = 1
could you just give me the answer, so i can have an direction.
8x+5y=4x-y
find the x and y, and x,y can't be the 0
ionic jewel
this is right
cinder sundial
here
ionic jewel
yeah that's the exact same answer you got
note how it says y=-2x/3
that's what you got
cinder sundial
and x=?
ionic jewel
you solved it yourself
cinder sundial
but i cant understand
ionic jewel
right here you have both
ionic jewel
one solution to the problem is x=3 and y=-2 but it's not the only solution
cinder sundial
i have no idea, i got x=-3y/2 and y=-2x/3 earlier
why x became 3 and y=-2
i want an number, i dont want those xy
what should i do
8x+5y=4x-y
find the x and y, and x,y can't be 0
ionic jewel
why x became 3 and y=-2
this is one possible solution it's not the only one
there are an infinite number of things x and y can be
ionic jewel
i have no idea, i got x=-3y/2 and y=-2x/3 earlier
this is the absolute correct answer
cinder sundial
could you show me why x=-3y/2 = 3
vale wigeon
can i see the original question
cinder sundial
sure
vale wigeon
i might not be here long
cinder sundial
8x+5y=4x-y
find the x and y, and x,y can't be 0
vale wigeon
is that it?
cinder sundial
still have another and another with those x y applied
vale wigeon
the equation 8x + 5y = 4x - y has infinitely many solutions.
cinder sundial
5x:3y=
vale wigeon
even when you exclude the zero solution (x=y=0)
wait
can i see the whole problem? just to be sure?
cinder sundial
vale wigeon
,rccw
ocean sealBOT
vale wigeon
what does the : mean?
vale wigeon
okay
jagged imp
i assume the task is to simplify that ratio given 8x+5y=4x-y
i :think: this is the task
vale wigeon
well... bunny and you arrived at 2x = -3y earlier, right?
which would make x : y = -3 : 2
vale wigeon
what did you get
cinder sundial
x=-3y/2 and y=-2x/3
vale wigeon
these two are the same
and both are the same as 2x = -3y
from x=-3y/2 you can divide both sides by y to get x/y = -3/2
cinder sundial
x=-3y/2 divided by y=2
cinder sundial
x should become 2
vale wigeon
never said x had to be 2 either
cinder sundial
oh im confusing
like what you get x : y = -3 : 2
from x=-3y/2 and y=-2x/3
like if you took away the 3y, then its 2 for x
vale wigeon
"took away the 3y"?
cinder sundial
yes
vale wigeon
you can't just remove symbols from an equation like that. this is like ripping out a patient's heart and lungs during surgery.
$x = -\frac{3y}{2}$
divide both sides by $y$
$\frac{x}{y} = -\frac{3y}{2y}$
ocean sealBOT
Ann
vale wigeon
and that's okay!
cinder sundial
ok
vale wigeon
x and y are unknown by themselves, but that's ok
cinder sundial
then 5x:3y=
vale wigeon
what's important is we know the ratio between them, namely x : y = -3 : 2
cinder sundial
ok
vale wigeon
then 5x : 3y = -15 : 6, which can be simplified to -5 : 2
cinder sundial
what it called btw, from x=-3y/2 and y=-2x/3 to x : y = -3 : 2
whats the process called
vale wigeon
i don't know of a special name for it. to me it's just some algebraic moves
cinder sundial
i never see x=numbers with y
vale wigeon
by the way, you keep saying "x=-3y/2 and y=-2x/3" as if they're not literally the same equation in different forms
vale wigeon
you don't understand how to get from one to the other?
vale wigeon
$x = -\frac{3y}{2}$
multiply both sides by 2
$2x = -3y$
divide both sides by $-3$
$-\frac{2x}{3} = y$
ocean sealBOT
Ann
vale wigeon
this is one of several paths you could take (the others are almost the same as this but with very small differences)
cinder sundial
ohh
vale wigeon
$-\frac{3y}{2} \times 2 \neq -\frac{3y \times 2}{2 \times 2}$
ocean sealBOT
Ann
vale wigeon
this isn't how multiplying a fraction by a whole number works
cinder sundial
thats what u means
since 3y/2 muliply by 2 is 3y
so just take the buttom 2 away
vale wigeon
that's what you mean
cinder sundial
thank you
why i have to mulyiply 2 then divide them with 3
why you choose 2 and 3, and why you do that
becuz x=-3y/"2" and y=-2x/"3"
vale wigeon
my goal here is to go from x = -3y/2 to y = (something)
cinder sundial
yes
vale wigeon
that's what i'm doing
cinder sundial
thats what i need
vale wigeon
yeah
that's why i'm doing things that will get y to be alone
honestly? i could've done this in one step: multiply both sides by -2/3
cinder sundial
do you multiply those x and y by 2 then divide them with 3
becuz i got x=-3y/"2" and y=-2x/"3"
vale wigeon
do you multiply those x and y by 2 then divide them with 3
that's what i did in my previous explanation
cinder sundial
yes
2 and 3 is Denominator
of x and y
so you multiplied x by 2 then divided by 3
vale wigeon
i have to go now sorry
cinder sundial
**Ann**
can someone explain why Ann have to do this to get x : y = -3 : 2
like from x=-3y/2 and y=-2x/3 to x : y = -3 : 2
from my perspective, bcuz 2 and 3 is the Denominator of x=-3y/"2" and y=-2x/"3"
but why 2 is being used to multiplying and 3 is dividing
and what it called, the method
shell widget
@cinder sundial You have $x = \frac{-3y}{2}$
ocean sealBOT
Sup?
cinder sundial
i wanna x=-3y/2 and y=-2x/3 be a number without unknown
that proves x and y are same thing right
but ann said x : y = -3 : 2
i can't understand why
i have no idea bout all of it
shell widget
Oh
uncut osprey
If x and y are the same, why not plug in 1 into your 2 equations and see if they produce the same result?
shell widget
x : y = -3 : 2 means x/y = -3/2
basically the sign : means ratio
and ratio means divide
cinder sundial
i know, but from x=-3y/2 and y=-2x/3 to x : y = -3 : 2
i dont understand the process
even i have wrote it down in paper
shell widget
You have x = -3y/2 correct?
cinder sundial
yes
shell widget
y is being multiplied with -3 on the right side
you can bring the y to the left side, but then it comes in the denominator
btw
you don't need to go from x=-3y/2 and y=-2x/3 to x : y = -3 : 2
cinder sundial
but i wanna a exact number
shell widget
you cannot solve this
shell widget
Okay so first of all
you should know that the sign : means divide
thats all
so you have x : y = -3 : 2
that means x/y = -3/2
okay?
uncut osprey
that's honestly a very strange problem
ionic jewel
How big is “countably infinite”.
it's a term that means you can map each element in your infinite set to an integer with none in your set left over
as an example every real number is not countably infinite becuause there are infinite real numbers per integer
obviously this isn't a technical definition but it's a way to think about it
alpine sable
shouldnt the break even point be lower?
It's $1.30 per cup and the fixed costs is $56,640
56640/1.30 = 43,569 cups
56640 cups * 1.3 = 73,362
So I only need to sell 73,362 cups to cover costs of $56,640
?
<@&286206848099549185>
vale wigeon
56640 < 73362...
alpine sable
Hi Ann
vale wigeon
your break-even point is like 57k cups
you say it should be lower but then state a higher value, about 73k
what gives?
alpine sable
the formula i have, it gives 56640?
alpine sable
yes
vale wigeon
so with each cup sold, you gain $1 profit
your profit is $1 per cup
do you understand this
yes or no
alpine sable
makes sense now
alpine sable
when profit =56640 i break even
vale wigeon
yes
alpine sable
I was thinking i have a profit of $1.30 for each cup sold
vale wigeon
no, you have a revenue of 1.30 per cup sold
each customer gives you 1.30 when they buy a cup
but of that $1.30, thirty cents go to cover your production costs for the cup you just sold
and the dollar that remains goes in your pocket
alpine sable
1.30 is revenue, 0.30 is variable costs than $1 is gross profit?
vale wigeon
it counts towards gross profit
but gross profit itself is all the money that goes in your pocket
vale wigeon
i'm tempted to say no, but also all this terminology being thrown around is kinda talking its toll on me
alpine sable
thanks Ann
quartz tusk
Why is 0 not a composite number ? . It has more than one factor
Probably infinite
Also are there any negative composite numbers ?
rich basin
The definition of a composite number requires it to have a multiplicative inverse, which 0 does not have.
cloud matrix
0 cannot be written as a product of primes
coral pagoda
Also true
charred flint
cuz it doesn't have a unique factorization
coral pagoda
Alright, now we're just saying fancier words to represent the same thing :p
vale wigeon
The definition of a composite number requires it to have a multiplicative invers...
by that logic, 4 isn't composite since it d doesn't have an inverse in Z
rich basin
It is a positive integer that has at least one divisor other than 1 and itself.
vale wigeon
if you mean positive then say positive
quartz tusk
Ah
rich basin
by that logic, 4 isn't composite since it d doesn't have an inverse in Z
I suppose moving out of Z to find the inverse is not pretty, but is it wrong?
vale wigeon
nowhere in the defn of a composite integer does it say it should have a multiplicative inverse
i mean tbh, zero is special, bc every number is a divisor of zero.
rich basin
True, I may have taken "divisor" too liberally.
cloud matrix
check the definition of relatively prime
quartz tusk
I know about it
cloud matrix
you can answer that yourself tbh
quartz tusk
But my question was that since one is negative nand other is positive there GCD Or HCF is not 1
Thus they are not relatively prime
Further the pair (3,5) is as they have 1 as HCF
Which leads me to conclusion that relatively prime are defined over same type of integers i.e either positive or negative
cloud matrix
In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that evenly divides both of them is 1. One says also a is prime to b or a is coprime with b. Consequently, any prime number that divides one of a or b does not divide the other.
quartz tusk
@cloud matrix what about -3 and -5 ?
cloud matrix
look up coprime's properties on wiki
vale wigeon
gcd(-3, 5) = 1 yes
cloud matrix
"The greatest common divisor (gcd) of two integers is the same as the gcd of their absolute values. Therefore, the function can just replace negative integers by their negatives, which are positive."
quartz tusk
Thanks man
Also just a little more
Can we define factors of 0 ?
For the purpose of finding whether (0,5) as re relatively prime or not .
@cloud matrix
One more thing
quartz tusk
"The greatest common divisor (gcd) of two integers is the same as the gcd of the...
As your said this about GCD. Is it true for LCM too ?
Like LCM of (3,5), (-3,5) and (-3,-5) is 15 ?
quartz tusk
@thorn kindle thanks , just a bit more . So whenever mentioning factors , we are talking about factors of absolute values . Is it ? .
Like factors of -20 is same as that of 20 . ??
thorn kindle
yes. +-
quartz tusk
+- ??@thorn kindle
quartz tusk
Oh . Thanks
But this also raises a doubt . Since we have disregarded -ve signs for lcm and hcf of given numbers ( we have used there absolute values only ) doesn't this makes it wrong to say that 15 is LCM of (-3,5) as 15 is multiple of 5 but it's not multiple of -3 ?.
tight locust
-3 * -5 = 15
quartz tusk
So this means negative numbers are also multiples ?
tight locust
yep
quartz tusk
Man looks like o was sleeping under a rock .
I am so thankful for all your support - Bernie Sanders. Lol
But thanks to all .
grand light
rancid flume
substitute x for x-16
alpine sable
the answer is not correct
I mean, the graph for the function you said above doesn't match the graph in the answers.
rigid smelt
it would be better if you said what your answer was
alpine sable
I don't have an answer I just don't know how to get the function
If I know that g(x) equals f(x-16)
f(x) = 1/sqrt(-x)
rigid smelt
substitute x for x-16
they just showed you how you can get the answer
alpine sable
they just showed you how you can get the answer
that's wrong
rigid smelt
again
you need to write your answer
so i know if you did it correctly
and btw, they are right
alpine sable
Cool, now how?
rigid smelt
you sub (x-16) into places where x are present
alpine sable
I know
alpine sable
g(x) = 1/sqrt(16-x)
rigid smelt
yes
alpine sable
its wrong
alpine sable
It's not a textbook. It's an old exam.
rigid smelt
sure, still what is the "assumingly correct" answer
alpine sable
Oh never mind it's right I had a typo while writing the func on Desmos. Thanks for the help
main meadow
hi! im just getting started on discrete math, not really sure what x and y refers to in this qn
tired creek
theyre elements of A_n
ashen spear
Hello, how can I solve this polynomial problem using the box method?
(c+7)(c+9)
Is it c^2+16c or something else.
cloud matrix
whats up with this weird way of calculating 3rd order determinants?
everything looks so random
<@&286206848099549185>
stable pecan
^ This series of videos will help you appreciate why we calculate determinants the way we do and make it seem non-random so it makes sense
A determinant is basically a unique number associated with a square matrix. If you want to understand why we define how to calculate determinants the way we do, I highly recommend the playlist.
stable pecan
A good way of thanking will be helping others out here when you can
cloud matrix
FOR SURE! 🙌
fast jay
If we have 4 red socks, 6 blue and 8 white in a drawer, what is the probability of getting a red pair given that we take 2 socks.
Why can't we just take (4c2)/(18c2)?
I understand the other method for calculating it with conditional probability but why is this wrong?
stable pecan
Are we replacing the socks after taking them?
fast jay
No, not putting it back.
stable pecan
Your method is correct then
fast jay
Oh I misread the question lmao, thanks!
stable pecan
Assume the number of bacteria at any instance is x
how will we express the rate of change in the number of bacteria with respect to time?
quaint ivy
dx/dt?
stable pecan
yup
Also, the number of bacteria is already y according to the equation, we didn't need to assume it, sorry
Now integrate dy/dt=ky
What do you get?
quaint ivy
I'm not sure how to
As in I know how to integrate things, just not what I should be integrating with respects to here
stable pecan
Have you heard of integration by variable seperation method?
quaint ivy
Should I have multiplied both sides by k before raising both sides with e?
stable pecan
yes
quaint ivy
Alright, I fixed that, and got y=Ce^(kt). I'm not sure what to do from there to solve for k though
And/or if I need to solve for C first somehow
stable pecan
Well, the question has given you 2 values of y and t
try substituting them in
to find k and C
quaint ivy
I think that's what I'm really stuck on, I'm not sure how to solve for both given that there's 2
And substituting in one of the two sets of y/t will either leave things in terms of k or in terms of C
stable pecan
I think that's what I'm really stuck on, I'm not sure how to solve for both give...
You will be able to get 2 equations in terms of C and k
Substitute y=123,t=1 for 1st eqn
then y=357,t=3 for 2nd
Now try
quaint ivy
I'm not quite sure what to do from here
I imagine this is something related to a system of equations, but it's been like 4-5 years since I've had to use techniques to solve for these lol
stable pecan
You need to do something to remove one constant from the equations. Which operation (+,-,*,/) can you perform?
quaint ivy
Would I be able to divide the top equation by the bottom?
stable pecan
Why not?
Try it
Experimenting and playing around is always a good idea when you don't know what to do exactly
quaint ivy
I hope the order of the work isn't too confusing, I ran out of page space lol
I don't believe this is one of the answers unfortunately ):
Though it's entirely possible by algebra is just wrong somewhere
upbeat gorge
Also there’s a slight mistake
stable pecan
You need to find k and c
then substitute them in the original equation of y
upbeat gorge
Remember $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
ocean sealBOT
CST
stable pecan
Also there’s a slight mistake
I think that's just a typo?
quaint ivy
Oh shoot, I didn't notice I forgot to carry the sqrt over
Yeah, that was a typo, but I wouldn't have noticed it otherwise
stable pecan
I think that's just a typo?
But yeah
upbeat gorge
I think that's just a typo?
I’ve been very careful about typos
Ever since I lost a contest due to writing 1404.5g instead of 1404g
stable pecan
I’ve been very careful about typos
Ever since I lost a contest due to writing 14...
I have gotten so many 99/100 due to my silly mistakes as well
quaint ivy
Wait, which step/equation would I plug that K value back into to solve for Y?
Since all of them have C in it
upbeat gorge
Your choice
stable pecan
y=Ce^(kt)
stable pecan
Your choice
they are basically the same
quaint ivy
How would I solve for y since C is there though?
quaint ivy
Ahh
I solved for C, but what would I use for t when solving for y? Since I have C and K
stable pecan
I think the question is incomplete as they haven't mentioned the time at which we have to calculate the rate of growth (which increases as time increases)
But try putting both 1 and 3 for t and see if the option matches
quaint ivy
None of it matches :/
I think I'm doing this wrong
Can we possibly eliminate C since y=1 at time 0?
or at least I assume it is, I have no idea
stable pecan
I think the question is incomplete
quaint ivy
Unfortunately I won't even be able to see the answer or whether I got it right or wrong lol. I'll just put in a random answer, but thanks otherwise!
stable pecan
You are welcome ^^
teal fox
I imagine this is something related to a system of equations, but it's been like...
ln
oh you got it
nvm
teal fox
can you fig out the equation using the hint? after that, you just differentiate it for the RATE of change
umbral pecan
can i calculate employee turnover rate by no. of people who left / total employees (including current employees and those who left)?
teal fox
can i calculate employee turnover rate by no. of people who left / total employe...
not 100% sure never done this topic but logically thinking seems right
umbral pecan
not 100% sure never done this topic but logically thinking seems right
i did some searching, and the formula involves number of people are the start and at the end divided by 2 to find the average, however i only have data of those who left and active
thank you
teal fox
i did some searching, and the formula involves number of people are the start an...
yeah so how would you find that ?
maybe some more searching will find it hahah
umbral pecan
I'm not sure, I don't think the dataset gives enough information, hence : turnover rate by no. of people who left / total employees (including current employees and those who left)
teal fox
I'm not sure, I don't think the dataset gives enough information, hence : turno...
yep, sounds about right to me, no other way to do it imo - keep me updated when you find out the correct answer though, would love to know the right way for these small lil things in case i might need it later on
small helm
Lets say I say the cartesian equation of a plane is -6x -6y + 3z + 15, what does that actually mean?
stable pecan
Lets say I say the cartesian equation of a plane is -6x -6y + 3z + 15, what does...
that's not an equation
It's not equating anything
small helm
sorry -6x -6y + 3z + 15 = 0
stable pecan
If you plot all the solutions (values of (x,y,z)) of that equation in a cartesian coordinate system, you will get a plane
small helm
will that equation have 3 solutions? Cause don't you need 3 points to plot a plane?
small helm
ok
rich basin
a solution will be a set of 3 values
Not sure I follow. What would be the other two points for the solution (0,0,-5)?
rich basin
Yes, but I didn't understand "a solution will be a set of 3 points".
copper umbra
Yes, but I didn't understand "a solution will be a set of 3 points".
I guess he meant x,y,z coordinates
stable pecan
Yes, but I didn't understand "a solution will be a set of 3 points".
accident, sorry
I meant values
It's fixed now
stable pecan
I guess he meant x,y,z coordinates
*they
small helm
Yeah I get it now it's just a 2D representation of all the values that satisfy that equation, just like how the line y = x is a line of values that satisfies that equation
cinder sundial
do you guys have any idea, where should i getting started with
i just forgot how to solve question like that
0.4=4/10 if my memory serves me right
alpine sable
find out what the left side of the equation is. Then divide that from 0,4
cinder sundial
6/7 for left side
cinder sundial
when i subtract a fraction, i just like subtract it right
dont have to make it equivalent
or i have to before i subtractin them
alpine sable
you mean like 1/4 - 1/2?
cinder sundial
alpine sable
yeah just like addition just subtract at the end
alpine sable
cinder sundial
yes
alpine sable
ya like that
cinder sundial
square = x
cinder sundial
im trippin again, i dont know what am i doing rn
just forgot what i did before
let me rewrite it
alpine sable
forget the subtraction stuff
cinder sundial
so i dont have to do that
alpine sable
yeah just solve for x
Here’s a step by step of what you’ve done so far
let's say box = x
cinder sundial
u wanna me to take the riciprocal then multiply them
cinder sundial
yes
alpine sable
same thing
alpine sable
thank you so much <@456226577798135808>
np
sage jacinth
Just wondering if would this be a valid way of using L.H's rule? My end answer is apparently correct, but my method seems completely wrong.
alpine sable
what really pops out at first is that you didn't made a simple cancellation 2x/2x=1.
some tips, your working is a little bit messy as in there are too many arrows/changes of direction, i'd recommend trying to keep this linear, to make it easier to read, go line by line from left to right, you'll waste even less space and it'll be more organised.
if you insist on using L'Hôp on this, simply using it at first sight works as well and may be easier than what you did
can't you solve that by saying that the x on top and the x on the bottom are both to the power of 1 since there's the square root and then just not counting the 1 because infinity-1 is still infinity
so you'd get x/x which is 1
this is how my teacher taught me to solve this at least
velvet pelican
Dividing by x works aswell for more rigour
alpine sable
can't you solve that by saying that the x on top and the x on the bottom are bot...
yes, you can do that as well, and i'd recommend doing this, but they were doubting on how to use L'Hôp not any other method.
the question was directed to L'Hôp
gotcha
can I jump in with another question?
or I should go to another channel?
i'd go in another channel just in case thet pop up with doubts
and i'm not done yet
aight
thanks
and i'm not a fan of your notation/syntax, while you're doing a substitution f(x)=x/sqrt(x²+1), you are missusing/ignoring the actual limit you were finding, you need to be respectful to what you're finding as well on all of the steps.
@sage jacinth
sage jacinth
and i'm not a fan of your notation/syntax, while you're doing a substitution f(x...
thank you for this. if i wanted to use l'hopital from step one i would just get the reciprocal of the original, right? i think it would still be in an indeterminant form after substitution. would it just be better to just not use L.H's rule?
paper temple
ocean sealBOT
dim vine
If I'm tryna work out the area under the graph, do I do the integral 2 -1 (function) or the integral for 2 0 and the integral for 0 -1 combined
tight locust
if the antiderivative is known then it doesn't matter
otherwise if you're doing a reimann sum or something to that effect then yes split it into two regions
sand kiln
How do I solve out matrix 𝑌 in the matrix equation 2𝐴𝑌 = 𝐵 + 3𝑌
chrome salmon
How do I solve out matrix 𝑌 in the matrix equation 2𝐴𝑌 = 𝐵 + 3𝑌
Wdym break out
sand kiln
solve out*
vapid viper
hello... is someone able to help me with this question please
cunning cape
In differential equations, are the so called "Ansatz" just something that mathematicians have come across by luck and have no real proof?
static crypt
ok so i want to find the infinite series of [8-9sqrt(n)]/n^3. how would i do that?
i tried using limit comparison with 1/n^(5/2) but i realized it wouldn't work because of the negative
alpine sable
thank you for this. if i wanted to use l'hopital from step one i would just get ...
just saw this, you'd get 2sqrt(x²+1)/x and yeah this leads nowhere, this is a bad example to use L'Hôp anyways. but yeah i wouldn't recommend using it either and you can consider some algebraic manipulations like dividing by x on numerator and denominator, or not do this, and consider another method that consists of when talking about infinity-wise, the constant terms like 1 can be pulled, as the leading terms will be the ones who will mark for the behaviour on the ends, so you can solve for =lim x->+∞ x/sqrt(x²) which easily simplifies to something.
@sage jacinth
nocturne gazelle
if im given dense disjoint subsets of a rectangle R C R^n where R is the union of the two subsets. how can i show a function in R->R is integrable
the function is
g(x) = 1 if x is in A, and = 0 if x is in B
shouldnt this be NOT integrable?
sage jacinth
thanks!
white obsidian
white obsidian
In differential equations, are the so called "Ansatz" just something that mathem...
"Ansatz" is just the german word for approach or wdym?
nocturne gazelle
<@&286206848099549185>
white obsidian
dude please follow the rules
alpine sable
https://gyazo.com/54c2dc34929ae9d6faa593dedc1755d5
Would anyone be able to help me get through this problem? (ignore the random answers was pasting while bored)
nocturne gazelle
@white obsidian i waited 15mins man
white obsidian
.07 minus .58 is 15 minutes? also you overposted the question before.
nocturne gazelle
nope i didnt
i posted another q
so thats cap
also, look at the time of the original message
sage jacinth
@alpine sable The radius is just the hypotenuse of the right triangle, and the 2.64 is the horizontal distance (2nd side of the right triangle). You can compare the ratios for a. cos(theta) = adj/hyp = 2.64/sqrt(2.64^2+1.81^2). For B i think it is 1.81/hypotenuse and the sin(theta) = opp/hyp = 1.81/sqrt(2.64^2+1.81^2). Keep in mind theta is the angle formed by the x axis and the terminal side. Also think about the range of sin and cos (they cannot exceed 1). I just realized that they gave you the radius from the start after writing this, but I'll leave the work so you can see how they got it. Hopefully that helps!
,w plot sin(x) and cos(x)
ocean sealBOT
sage jacinth
note the ranges of these two functions
alpine sable
<@456226577798135808> The radius is just the hypotenuse of the right triangle, a...
ty
sage jacinth
yup no problem
white obsidian
also, look at the time of the original message
white obsidian
there is none
tight locust
@nocturne gazelle try asking questions that people actually know how to answer next time
90% of the people here (me included) don't even know what a disjoint subset is
maybe ask about something a bit simpler like systems of linear equations or trig functions
i'm really good at systems of linear equations
ionic jewel
i was going to answer but then he had to go and be rude about it
there's a good few people here that know higher level math, it will just take longer to get an answer
thorn kindle
apparently there's this other math server that's for super advanced people
they kick you on sight if you're not smart enough
ionic jewel
they kick you on sight if you're not smart enough
... that doesn't sound true
there's the competitive math server but j don't get kicked
just use a calculator my dude
thorn kindle
i went there and i got kicked instantly
ionic jewel
this is a nightmare by hand
thorn kindle
apparently they don't take kindly to questions about integrals
ionic jewel
i mean you can get the characteristic polynomial by hand
but boy does that not look fun
sure use wolfram or mathmatica or something
lemme do it here
tight locust
that looks like a pain in the ass to even type
too many grouping symbols
i hate matrixes
can you try typing it in the form {{a,b,c},{d,e,f}...}
ionic jewel
,w eigenvalues [[0.83, -0.67, 0.18, 0.3],[-.67, 0.83, -0.34, -0.19], [0.18,-0.34,0.83,.46],[.3,-.19,.46,.83]]
check my input matrix
tight locust
you forgot the lambas
ionic jewel
you forgot the lambas
yea but i don't need them
tight locust
also you didn't even type it in right
ionic jewel
i just skipped that part and went straight to solving for eigenvalues which is what he needs anyways
tight locust
even ignoring the lambdas
ionic jewel
yeah I'm on mobile it's a bit of a pain, please correct it
tight locust
0.83 - lambda does not equal 0.84
ocean sealBOT
alpine sable
My teacher never taught us this and I’m just beyond confused
ionic jewel
My teacher never taught us this and I’m just beyond confused
1/x + 1/(x+1) = -11/30
solve for x
alpine sable
1/x + 1/(x+1) = -11/30
Uhuh.
ionic jewel
,w determinate [[0.83-λ,-0.67,0.18,0.30],[-0.67,0.83-λ,-0.34,-0.19],[0.18,-0.34,0.83-λ,0.46],[0.30,-0.19,0.46,0.83-λ]]
ocean sealBOT
ionic jewel
bruh
tight locust
lol there's your answer
ionic jewel
that's not right
tight locust
i think wa likes curly brackets
,w determinant of [[0.83-λ,-0.67,0.18,0.30],[-0.67,0.83-λ,-0.34,-0.19],[0.18,-0.34,0.83-λ,0.46],[0.30,-0.19,0.46,0.83-λ]]
ocean sealBOT
ionic jewel
there we go
tight locust
WOW!
alpine sable
1/x + 1/(x+1) = -11/30
When I do the math I got -5/11 and -6
ionic jewel
me and the boys failing to use wolfram
ionic jewel
When I do the math I got -5/11 and -6
those are not consecutive or integers
alpine sable
You are right
ionic jewel
also unless marcel is done ping me in a other channnel
ocean sealBOT
Requested by marcel#6496
alpine sable
those are not consecutive or integers
How do I do it.
ionic jewel
1/x + 1/(x+1) = -11/30
alpine sable
Yes but the numbers I get aren’t consecutive
alpine sable
I am
ocean sealBOT
nocturne gazelle
@tight locust lol what?
alpine sable
okay what do you get for x?
-5/11 and -6
tight locust
?
alpine sable
I have to find 2 integers
tight locust
I'm saying you're a bit too smart for this server. sorry @nocturne gazelle
tight locust
@solar mural it gave you the answer. a polynomial in terms of lambda
ionic jewel
just type in the characteristic polynomial into wolfram and itll solve it
nocturne gazelle
i followed the rules and just got shit on
by @white obsidian
so idk
@tight locust whats the other server
tight locust
idk you tell me
velvet pelican
You plug them into the matrix A-lambda*I
and then find non zero vectors such that (A-lambda*I)v = 0
fleet steeple
I understand what they say about the sequence
but what is the notation 1010(subscript 5)
tight locust
well you see
numbers are just sums of powers times coefficients
1234 (in base 10) = 1* 10^3 + 2*10^2 + 3*10^1 + 4*10^0
so what is 1010 (base 5)? i'll leave that exercise to you
cunning cape
"Ansatz" is just the german word for approach or wdym?
it is but when you solve differential equations often times you rely on an Ansatz (trial solution). So my question is, are those trial solutions found by accident or there's a proof behind them?
turbid idol
Yes in base 10! And now on base 5
fleet steeple
hmm base 5
1^5*3 + 2 times 5^?
wait before that how did they get 1010 subscript 5
tight locust
yeah
fleet steeple
ok
tight locust
i think you get it
fleet steeple
so 1010 written in base 5
wait
im not getting it lol
1 times 5^3 = 125
but how do you get
1010 frorm 125
tight locust
read what i wrote above
numbers in base n are sums of coefficients times the powers of n
glass lichen
$1010_5=(5^3+5)_{10}$
ocean sealBOT
moshill1
tight locust
or you could just give him the answer and not let him think about it at all
that's helpful
fleet steeple
i still dont understand what that means-
tight locust
1234 (in base 10) = 1* 10^3 + 2*10^2 + 3*10^1 + 4*10^0
fleet steeple
what would 1234 be in base 5
tight locust
the same thing