Yes
#help-26
ruby meadow
exotic radish
$x+x+\frac {x}{2}+\frac {x}{4} +1 = 100\
2x+\frac {2x}{4}+\frac {x}{4}+1 = 100\
\frac {8x+2x+x+4}{4} = 100\
\
\
\frac {11x+4}{4} = 100\
11x+4=400\
11x=400-4\
x=36$
ruby meadow
That correct
Is it
exotic radish
Your a great tutor
Bet
Let's go to dms if u wanted
Btw
This was the geese problem
The answer is 36
thorny flameBOT
Plumbum
ruby meadow
Let's go to dms if u wanted
Bet
exotic radish
Wanna do .close here? @ruby meadow
topaz sinewBOT
@ruby meadow Has your question been resolved?
sleek ruin
topaz sinewBOT
sleek ruin
I tried doing this
sudden spade
The first bits of information just say the base is this
So we're looking at that middle region
topaz sinewBOT
@sleek ruin Has your question been resolved?
sudden spade
Hmm I get the same as u
sleek ruin
So we're looking at that middle region
As far as I know, it's supposed to be f(x)-g(x) as the side and then square it?
sudden spade
Yeah I mean ur integral to me seems logical but it isn't given as an option on that list
I'm guessing u haven't covered double integrals?
sleek ruin
Not to mention this is supposed go be done with a calculator
sleek ruin
I'm guessing u haven't covered double integrals?
Not sure
sudden spade
My initial thought was double integrals
sleek ruin
My initial thought was double integrals
ok I got it figured out
your not supposed to do e^x - 1 because the area under e^x stops at x = 0
sleek ruin
My initial thought was double integrals
the side is (e^x-0)^2 from 0 to 1
1 is used to find the end of the definite integral
neon iron
Hi, can anyone help me with this? I have taken the log of both sides of the equation and got (x+3)log2=(x-1)log6
topaz sinewBOT
Hi, can anyone help me with this? I have taken the log of both sides of the equa...
neon iron
is the next step xlog(2)+3log(2)=xlog6-log6?
leaden tusk
that works, now solve for x
neon iron
This is the bit I am stuck on š
leaden tusk
get all terms with x in them to one side, and the rest to the other side
leaden tusk
you have a sign error, but you're close
neon iron
which one?
leaden tusk
take a look back at what you kept on the same side
you moved the xlog6 to the other side, and changed its sign
you moved the 3log2 to the other side, and changed its sign
neon iron
oh I thought if it changes side, the sign changes?
leaden tusk
no no, you only had one mistake before
leaden tusk
you kept the -log6 on the same side
it was changing the sign while keeping this on the same side
everything else was right
leaden tusk
is the next step xlog(2)+3log(2)=xlog6-log6?
take a step back to here
and rewrite it on paper or something to make sure you're getting all your signs right
leaden tusk
yep
neon iron
and 3log2 to the right?
leaden tusk
yep
leaden tusk
it doesn't matter, as long as you get the sign right
neon iron
I'm not sure what the signs are
bc if they change sides, doesnt that make them both minus?
leaden tusk
the ones you switched were positive, so yes, they would become negative
leaden tusk
you fixed your original error and made more lol
neon iron
lmao this is so hard over message š¤£
leaden tusk
so is it xlog2-xlog6=log6-3log2?
the only thing i am saying is wrong with this is the fact that you changed the sign of log6, but didn't move it to the other side
neon iron
I'm so confused now haha
leaden tusk
is the next step xlog(2)+3log(2)=xlog6-log6?
you had this originally
where xlog(2) is positive, 3log(2) is positive, xlog(6) is positive, and -log(6) is negative
you kept xlog(2) on its side and log(6) on its side
therefore they should keep their signs
xlog(2) will stay positive, -log(6) will stay negative
you switched the sides of 3log(2) and xlog(6)
since they were both positive, they will now both be negative
neon iron
so -3log(2) and -xlog6
leaden tusk
yes, those will be negative
neon iron
xlog2-xlog6=-3log2-log6
leaden tusk
it's the left hand side
you're just factoring an x out
if you had 6x+3x and factored an x out, you'd have x(6+3)
you're just taking it outside of both terms while multiplying the entire thing by x
neon iron
is it x(log2-log6)?
neon iron
how would you do that?
leaden tusk
the way you'd do it any other way
you have x(log(2)-log(6)) = -3log(2)-log(6)
it's just as if you had 6x=3 and you had to solve for x
all those logarithms are just numbers
neon iron
is it xlog10(3)?
leaden tusk
?
neon iron
ahh I am confused
neon iron
Can someone please help me with this question
topaz sinewBOT
Can someone please help me with this question
wide berry
Can someone please help me with this question
Find the partial derivatives, and then solve the equations.
For the converse, for part i, assume y=x and show that the partials agree.
For the converse for part ii, assume y=-x and show that the given equation holds
neon iron
Thank you
topaz sinewBOT
@neon iron Has your question been resolved?
wide berry
@Person who writes trichotomy law. This source https://web.math.ucsb.edu/~moore/2axiomsforreals.pdf says it's trichotomy axiom. See O1 page 4.
topaz sinewBOT
\@Person who writes trichotomy law. This source https://web.math.ucsb.edu/~moore...
wide berry
.close
junior nimbus
I don't understand where the equation in blue came from
topaz sinewBOT
I don't understand where the equation in blue came from
knotty ledge
$cos^{2}(\theta) + sin^{2}(\theta) = 1$
thorny flameBOT
iCaird
unique tundra
**iCaird**
you can derive this identity from the pythagorean theorem
junior nimbus
sine of theta is equal to the length of the opposite side
yeah that makes sense
the x is the opposite side, right?
topaz sinewBOT
@junior nimbus Has your question been resolved?
sweet shard
the x is the opposite side, right?
if the hypotenuse is length one then yes
junior nimbus
ok so where does the equation come from
topaz sinewBOT
junior nimbus
.reopen
topaz sinewBOT
ā
jade cobalt
Hello how I do integral for (2x+1) x (x^2 + x -2)^-0.5
topaz sinewBOT
Hello how I do integral for (2x+1) x (x^2 + x -2)^-0.5
thorny flameBOT
āamonov
jade cobalt
Listen our teacher didnāt taught us everything):
Due to lack of time
Or his teaching is bad ether way
And idk about substitutions
jade cobalt
I did once before
But there stuff like
Lin or Len idk what itās called
And stuff we donāt need
And some letter look like e
Some complex stuff
restive inlet
log? ln?
jade cobalt
I donāt really remember but ppl advices me to learn it
restive inlet
integration by substitution isn't exclusive to stuff with logs and exponentials
the principle can be applied in many situations including stuff like this
jade cobalt
Should I just learn the basics
jade cobalt
**āamonov**
Like how to do this integral
restive inlet
and if you know this principle, only then should you consider shortcuts
try starting with substitution
like
u = x^2+x-2
restive inlet
yes
jade cobalt
ok and xd ?
restive inlet
wdym by xd?
jade cobalt
Donāt have any idea what to do with it
jade cobalt
wdym by xd?
Donāt mind it
restive inlet
do you know the basic structure of doing integration by substation?
restive inlet
look it up again
jade cobalt
Kk I donāt need to know Lin and e and stuff like this right
restive inlet
no, you don't need logs for this question
jade cobalt
I wonder why our teacher didnāt teach us this /:
Iāve been studying for days and I feel like no progress
Makes me really sad ):
restive inlet
since you recognised that
2x+1 is the derivative of (x^2+x-2)
so starting with
u = x^2+x-2
is a decent idea
that gets you
du/dx = 2x + 1
and/or
du = (2x+1) dx
and you can apply that to get your integral in terms of u
jade cobalt
Iāll go and see the integral by substitutions again
restive inlet
(and something that's simpler to integrate)
jade cobalt
And remember how it was xd
The problem is Arabic videos r little bit
And if I want to watch English there is a lot of complicated expressions I canāt understand ;-;
Iāll just go and try
Thx u
.close
lilac torrent
yo how would one make a progression formula like: 1 * day = 1 on day 1 2 on day 2. I want to know how many I would have in total on day 50.
topaz sinewBOT
yo how would one make a progression formula like: 1 * day = 1 on day 1 2 on day ...
tiny wolf
what
lilac torrent
formula for cookies = Day * 2
Day 1 | 2 | 3 | 4 | 5
cookies 2 | 6 | 12 | 20 | 30 (shown in total)
cookies gotten at the day (day, number 1, 2 | 2, 4 | 3, 6 | 4, 8 | 5, 10
how many would I have by day 50 in total?
topaz sinewBOT
formula for cookies = Day * 2
Day 1 | 2 | 3 | 4 | 5
cookies ...
knotty ledge
on day 1 you have 2 cookies. on day 2 you have 2 + 2*2 = 6 cookies. on day 3 you have 6 + 2*3 = 12 cookies. Do you see any pattern here?
sturdy oracle
Well this seems to be a summation problem, right
$\sum_{n=1}^{50}2n$
I hate everything
thorny flameBOT
Umbraleviathan
thorny flameBOT
Umbraleviathan
thorny flameBOT
Umbraleviathan
sturdy oracle
@lilac torrent hopes this helps
lilac torrent
Ok
neon iron
Im not sure how to start this
neon iron
<@&286206848099549185>
knotty ledge
You need a point that lies on both planes, and then the direction of the line, the cross product should help here
neon iron
.close
echo spoke
so how to do this one
topaz sinewBOT
so how to do this one
neon iron
Bunas, soy Gian Marco Arteaga
Estoy estudiando proyecciĆ³n y componentes vectoriales.
Tengo dudas en descomponer vectores en R3. Quisiera saber si podemos debatir mi incognita por este medio.
mint perch
I am not understanding how to split up factorials and such
topaz sinewBOT
I am not understanding how to split up factorials and such
mint perch
My teacher wrote (n-1)! as (n-1)(n-2)!
Is it that (n-1)! goes all the way to infinity and it was written as (n-1)(n-2)! because the numerator had an (n-2)! to cancel out
mint perch
You just multiple stuff going down
mint perch
3!
pseudo bear
Which is?
mint perch
6
pseudo bear
What is (n - 1)(n - 2)!?
mint perch
2
pseudo bear
No.
mint perch
6 i mean
pseudo bear
Right, so they're the same.
It can be seen more clearly here.
3! = 3 Ā· 2 Ā· 1
3 Ā· 2! = 3 Ā· 2 Ā· 1
3! is all the numbers from 1 to 3 multiplied.
2! is all the numbers from 1 to 2 multiplied, and then with 3 in there, it's all the numbers from 1 to 3 multiplied.
So, n(n - 1)! = n!
Does it make sense why?
mint perch
I think I just didn't see that they gave an n value on the bottom of the e looking thing
E
pseudo bear
Ī is capital pi and does the same thing, except it's the product (pi for product) instead of sum.
mint perch
Could you help with tis problem
its originally infinity on top of summation and n=0 on bottom
pseudo bear
OK, so multiply the fractions.
mint perch
I spit up the 10 to (10)^2n and (10)^1
pseudo bear
Did you multiply the fractions?
mint perch
No sir
pseudo bear
OK, multiply them together.
pseudo bear
You might as well have everything together so that you can reduce properly rather than reducing both, multiplying them, and reducing the product.
mint perch
but idk how to do it with the (2n+1)! and (2n+2)!
pseudo bear
Well, 2n + 2 is how many higher than 2n + 1?
pseudo bear
So, separate out the highest 1 factors from (2n + 2)!
mint perch
You mean i can just take out a 2 so 2(n+1) ?
pseudo bear
No.
Factorial is a product.
The things in the product are factors.
Like 1 Ā· 2 Ā· 3 Ā· 4 has factors 1, 2, 3, and 4.
(2n + 2)! has factors 1, 2, 3, 4, āÆ, 2n + 1, and 2n + 2.
What is the highest factor?
mint perch
4
pseudo bear
No.
pseudo bear
Right.
mint perch
oh
pseudo bear
So, you have 1 Ā· 2 Ā· 3 Ā· 4 āÆ (2n + 1) Ā· (2n + 2)
mint perch
2n+2(2n+1)
pseudo bear
Separate out the highest one factor.
mint perch
And then i can cancel out the (2n+1)?
pseudo bear
1 Ā· 2 Ā· 3 Ā· 4 āÆ (2n + 1) Ā· (2n + 2)
[1 Ā· 2 Ā· 3 Ā· 4 āÆ (2n + 1)] and [(2n + 2)]
(2n + 1)! and (2n + 2).
pseudo bear
No, that's incorrect.
mint perch
Lol sorry im dumb
pseudo bear
You didn't factor the powers of 10 correctly.
mint perch
I think im missing a 10 on the top
pseudo bear
Yes.
Then you can reduce the fraction and move the negative sign in front, where it can be eliminated due to the absolute value.
The sign is irrelevant because of the absolute value.
pseudo bear
Well, you didn't fully reduce the fraction.
pseudo bear
And, no you can't put that in front of the limit.
The absolute value sign has to be taken into consideration.
As I said, the absolute value makes the sign inside irrelevant.
pseudo bear
If you want to.
pseudo bear
Well, what expression do you have now?
mint perch
lim as n approaches infinity of n+1/50
pseudo bear
OK, and what's the limit of that?
mint perch
infinity
pseudo bear
Right.
mint perch
So it diverges
pseudo bear
You're doing a series?
mint perch
yes
pseudo bear
Is this like the ratio test or something?
pseudo bear
Talking in here reminds me of it.
Like I see people asking about the ratio test, and then I look it up.
I saw it when I took the second calculus course, but that was a long while ago.
So I just refreshed my memory when others asked about ratio tests.
mint perch
Wow
I can't really remember what I did in the beginning of calc 2 and I'm taking it right now
pseudo bear
You can look back at a homework problem or two from earlier in your book if you want to refresh it.
mint perch
Ya but there is stuff like partial fraction decomposition, trig sub, trig integrals
pseudo bear
Yeah, the trigonometry stuff gets me because I don't remember much beyond basic trigonometry.
mint perch
Honestly I find all this stuff with limits and series way harder than that stuff though
You don't even use any of your fancy tricks to find integrals anymore
pseudo bear
Yeah, this is around the time when you learn power series and stuff.
Like taking a function and getting a series that calculates it.
There's integrals and then this later stuff like series divergence and getting a Taylor or Maclaurin series for a function.
pseudo bear
It's kind of interesting if you want to know how to calculate sine without a calculator, I guess.
mint perch
That is what my professor was going on about
pseudo bear
You get its power series, and you plug x into the first few terms, and you get an approximate answer.
mint perch
He was talking about how calculators only know how to +,-,*,/
pseudo bear
Yeah, some of the cheaper ones are like that.
Older CPUs.
I think, but I'm not sure, that they might have figured out how to do things like log and sine in circuitry rather than writing a program that only uses the basic four operations.
But I haven't really looked into it.
Log and exp are needed for things like arbitrary exponents.
On a calculator.
mint perch
Idk what arbitrary exponents are
pseudo bear
Oh, like any exponent you can think of.
Arbitrary means anything that works.
Like an arbitrary integer is any integer.
An arbitrary exponent is just some real number.
pseudo bear
Yes, TI-89 and TI nSpire can.
Cell phones can with things like MathStudio (http://mathstud.io).
mint perch
But we still have to do it by hand
pseudo bear
Yeah, doing it by hand is good.
You have to teach a computer a lot of tricks to get some integrals.
And there are some tricks that people know that computers don't yet.
mint perch
It seems like the expensive calculator could do all that?
south rose
And there are some tricks that people know that computers don't yet.
Do you know any examples like that?
Very interesting
pseudo bear
No, I've heard of examples, but I don't remember them.
pseudo bear
No problem
neon iron
topaz sinewBOT
neon iron
guys
im strugglin with lhopitals
how is this 0 * (-infinity)?
i get ln(1) is 0
but how is tan(pi * x / 2) = - infinity?
wide igloo
Do you know the domain for tan or cot @neon iron
Remember than tan(x) is the same as sin(x)/cos(x)
And you canāt divide by 0 so tan(x) is undefined for all cos(x) = 0 right
neon iron
And you canāt divide by 0 so tan(x) is undefined for all cos(x) = 0 right
right
sinx / cosx
wide igloo
Ye
wide igloo
Well
neon iron
does that mean its infinite?
neon iron
right
i got up to there, but after getting 1 / 0
i didnt know how that was - infinite
neon iron
right
approach from right
ahh
got it
thank u..
š„ŗ
lots of info.. too know
does it work
if i make the problem into a fraction and evaluate like that?
like tan = 1 / cot?
wide igloo
For lāhr ye
neon iron
its the same?
kk imma just do that for the trig stuff
seems more intuitive
for lhopitals
thanks
.close
bold tusk
Can someone Tell me if I have Done right ?
topaz sinewBOT
Can someone Tell me if I have Done right ?
vale jacinth
Correct
vale jacinth
vale jacinth
Yeah
bold tusk
And the Numbers are the edges
vale jacinth
The order of vertices I passed
vale jacinth
Sure
bold tusk
You need to find 25^99 mod 24
What does this mean
vale jacinth
a=b mod n means n divides a-b
bold tusk
Hmmm
vale jacinth
What you need to do
Is to prove yourself by definition that
a=b mod n, c=d mod n, imply ac=bd mod n
(Hint: write ac-bd as sum of two things)
vale jacinth
(Hint: write ac-bd as sum of two things)
(a-b)c+b(c-d)
bold tusk
(25-24)
vale jacinth
Just 25=1 mod 24 gives you 25^99=1^99=1 mod 24
vale jacinth
a=b mod n, c=d mod n, imply ac=bd mod n
First you show this
As a result by induction we have a=b mod n implies a^r=b^r mod n
Then plug in n=24, a=25, b=1
r=99
bold tusk
Okay, Thank you šš¼
vale jacinth
Np
topaz sinewBOT
@bold tusk Has your question been resolved?
bold tusk
@vale jacinth
drifting swift
the first four numbers are a1, a2, a3 and a4 while you wrote down a2, a3, a4 and a5
topaz sinewBOT
@bold tusk Has your question been resolved?
bold tusk
the first four numbers are a1, a2, a3 and a4 while you wrote down a2, a3, a4 and...
What should I do then
dry oxide
vapid root
What is the domain of this in interval form
topaz sinewBOT
What is the domain of this in interval form
fluid phoenix
what have you tried?
topaz sinewBOT
@vapid root Has your question been resolved?
vapid root
what have you tried?
I got R-{plus/minus 2}intersection [-4,4]
fluid phoenix
that's correct but you can simplify that further
vapid root
Can you show me please how to do it
vapid root
[-4,4]?
vapid root
But we also we can't have -2
[-4,4]-{-2,2}
fluid phoenix
no
clear kindle
Wait
fluid phoenix
its x^2 not x in the denominator
clear kindle
Yeah my bad
vapid root
But we also we can't have -2
[-4,4]-{-2,2}
What do I do now?
fluid phoenix
But we also we can't have -2
[-4,4]-{-2,2}
yes I was taking it one step at a time
cuz that'd be easier to do
vapid root
So that's the answer?
fluid phoenix
it is the answer yes
vapid root
Someone from another server told me this
[-4, -2) U (2,4]
fluid phoenix
but you can express that as union of 3 intervals
fluid phoenix
Someone from another server told me this
[-4, -2) U (2,4]
this is wrong
at least its incomplete
vapid root
he edited and now gave this
[-4, -2) U (2,4] U (-2,2)
vapid root
Oh alright
fluid phoenix
this is how you express it as an union [-4, -2) U (2,4] U (-2,2)
did you understand though?
spiral briar
What would i do?
restive inlet
you haven't applied that PQ is parallel to SR
topaz sinewBOT
topaz sinewBOT
Available help channel!
topaz lynx
topaz sinewBOT
topaz lynx
if u square a complex number
that means modulus is squared
so mod is now 4 instead of 2
and it means each of the angles are doubled too, right?
but im confused how that works
its a hexagon.... if you double all the angles uh i have no clue how that would work?
fluid phoenix
its a hexagon.... if you double all the angles uh i have no clue how that would ...
keep in mind the angle that's doubled is the angle from the x-axis
topaz sinewBOT
@topaz lynx Has your question been resolved?
fluid phoenix
it's theta that doubles not phi
thorny flameBOT
azeem321
marsh mortar
The general form for the six vertices are $z=2e^{\frac{j\pi k}{3}}$ for $k \in {1,2,3,...6}$
thorny flameBOT
azeem321
marsh mortar
Now just square the general form
and split into triangles or something to find the area of the hexagon
topaz lynx
and split into triangles or something to find the area of the hexagon
my trouble is understanding how its still a hexagon if all the angles double?
oh wait maybe i get it
marsh mortar
when k=1 and you square it, you get 4cis(2pi/3)
when k=2 and you square it, you get 4cis(4pi/3)
when k=3 and you square it, you get 4cis(6pi/3)
We know a shape forms a hexagon, if the distance from a centre point (the origin) is the equal
and
the angle between each line segment is constant
topaz lynx
heres what im tryna do rn and its not working lmao
im tryna understand what graphically happens to the points
doesn't point 4 end up where point 1 is???
point 4 is 210 degrees
7/3pi
uh that dont seem right
it should be idk
so point 4 when you square it
(210 x 2) - 360 = 60 degrees????
but point 1, 30 x 2 = 60
marsh mortar
why dont you keep on with this
when k=1 and you square it, you get 4cis(2pi/3)
when k=2 and you square it, you get 4cis(4pi/3)
when k=3 and you square it, you get 4cis(6pi/3)
and see what shape it forms
topaz lynx
oh well it just makes a triangle thing
marsh mortar
yh
topaz lynx
equlateral triang
e
because the points overlap
is there any mathematical approach to this though?
imagine if we didnt start with a hexagon but an octagon
and you squared each of those points
how do we predict how many points the new shape will have?
because in an exam i dont wanna be drawing this out
in here, it seems to be half but idk if thats co incidence, i could try it with octagon in a min but wondering if there is something algebraic
ig if you double each of the angles
its gonna half the amount of points, that kinda makes sense? is it always the case?
wonder what happens if i double this triangle
makes a differently oriented triangle if i double that
marsh mortar
If you experiment with it, I am sure you could find a pattern. However, is it a good use of time? I guess the examiner just expected the candidate to square all the vertices like above, notice that the 6 vertices form 3 vertices after the transformation because some are identical and then proceed to find the area of the triangle
topaz lynx
tbf that was an easier approach tbh lol
rather than thinking graphical angles just square the points and plot on a sketch
alright thanks
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
timid summit
topaz sinewBOT
heavy parrot
y varies inversely as x means y=k/x
Insert values of y and x to find k which is constant
Then use old k and new x to find new y
timid summit
ok
yeah I didnt knaow what inversly ment
so yould I subtract 5 or divide by 5
in the first equation
timid summit
so it would be k=5/5
heavy parrot
no no
timid summit
I would multiply 5 on each side
timid summit
so k would be 30
heavy parrot
I can't tell if ur trolling lol
heavy parrot
agreed
timid summit
damn š¦
ornate crow
The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series.
Find the sum of the first 30 terms of this series.
topaz sinewBOT
The sum of the first 48 terms of an arithmetic series is 4 times the sum of the ...
deft mirage
The sum of the first 48 terms of an arithmetic series is 4 times the sum of the ...
What are your thoughts on this question?
I would start by expressing the information of the question in terms of the arithmetic series formula. So
$a_n=a_1+(n-1)d$
thorny flameBOT
Social Capital Gainer
thorny flameBOT
Social Capital Gainer
deft mirage
You can then find and expression for a_1 in terms of d and use this to get an expression as the answer also in terms of d
topaz sinewBOT
@ornate crow Has your question been resolved?
proven monolith
Hey
proven monolith
What is the formula in this graph?
Values: (0,4) (1,12) (2,36) (3,108) (4,324)
topaz sinewBOT
@proven monolith Has your question been resolved?
proven monolith
<@&286206848099549185>
mint raft
What is the formula in this graph?
Values: (0,4) (1,12) (2,36) (3,108) (4,324)
looks like the y-coordinate is multiplying by 3 every time the x coordinate goes up by 1
does that give you a hint?
umbral oyster
But that's a straight line
Ye
topaz sinewBOT
@proven monolith Has your question been resolved?
patent oxide
What is the formula in this graph?
Values: (0,4) (1,12) (2,36) (3,108) (4,324)
Observe that the y coordinate is a multiple of 12
||one more hint - observe how these multiple of 12 correspond to the x values||
topaz sinewBOT
@proven monolith Has your question been resolved?
fossil zealot
i donāt understand the first step how it changed from a fraction to a non fraction everything else i get
topaz sinewBOT
i donāt understand the first step how it changed from a fraction to a non fracti...
fossil zealot
i donāt understand the first step how it changed from a fraction to a non fraction everything else i get
wheat grove
where?
restive inlet
{3/2}
median oak
Could anyone help me to find a special solution to the homogeneous case? I tried several things like x^2 and x^3 but didn't work out. Is there some kind of special trick to doing this that I'm unaware of??
topaz sinewBOT
Could anyone help me to find a special solution to the homogeneous case? I tried...
median oak
š„ŗ
vernal vale
how about power series 
is that overkill
that they say polynomial makes me want to try it
median oak
probably and I'm not sure how to do that...
thorny flameBOT
jan Niku (Shuri for Honorable)
median oak
k, I'm gonna try(I thought it would be a simple guess
vernal vale
it probably is
im just bad at ode 
well, its probably like some form
(t^2 - 2)*diff(y(t), t) - y(t)*(2*t - 2) + (- t^2 + 2*t)*diff(y(t), t, t) == 0
>> ySol(t) = dsolve(ode)
ySol(t) =
C1*t^2 + C2*exp(t)```
ySol(t) =
(t + 2)/(t - 2) - t^2/(t - 2) + C1*t^2 + C2*exp(t)
heres the final answer, if it helps
topaz sinewBOT
@median oak Has your question been resolved?
median oak
yeah I tried the Taylor series but I think my calculations went wrong, now I'm recalculating
I'm just bad at calculationsš
thanks anyway
vernal vale
its not gonna be nice anyways
its a bummer ramonov is helping savagex rn
i bet he knows exactly what form this is
median oak
I don't know who that is, sounds like a nice guy
vernal vale
you need real help lol
i mean from someone who knows what that means beyond recognizing barely the form
maybe
maybe you figured it out though
median oak
yeah I think I know how to solve this one,but I have another question so I figured I'd just ask it here:
edgy frigate
The hint definitely seems to me to suggest to try a power series to find one solution from which you can find the general solution by possibly reduction of order to find the second independent solution and then variation of parameters for particular solution.
median oak
Well technically it's not a "question", because I got stuck in calculations again in the first method the prof is asking us to use, but I'm not sure what the second method he is referring to....?
median oak
The hint definitely seems to me to suggest to try a power series to find one sol...
okk thank you, that's what I thought too, I didn't know how to solve the specific solution(but I do now), thanks for your reply anyway
median oak
Well technically it's not a "question", because I got stuck in calculations agai...
Again, this problem's calculation is just nasty....
vernal vale
isnt that just undetermined coefficients
median oak
should I convert it to cost instead
median oak
I'm sorry the prof only mentioned undetermined coefficients for five minutes
and I
I'm not sure what to do
vernal vale
first you need the solution of the homogeneous problem
i remember this
,w y'''-2y'+4y=0
thorny flameBOT
median oak
fuck I think I calculated the eigenvalues and vectors wrong
give me a sec
oh wait, it's correct, but I didn't simplify things
The instructor only covered one way to solve nth order ODE, which is using the exponential of the Jordan block but I couldn't calculate it(my attempt as above), so I'm a lil stuck
median oak
Is anyone there?
pale terrace
Ping helpers
topaz sinewBOT
@median oak Has your question been resolved?
topaz sinewBOT
@median oak Has your question been resolved?
eternal viper
topaz sinewBOT
eternal viper
Iām really stuck on the second case. Iāve tried changing to polar coordinates but it didnāt really help me
knotty ledge
why did polar coordinates not help you?
topaz sinewBOT
@eternal viper Has your question been resolved?
wide berry
I'll have to try again š
Can you show what you tried?
eternal viper
I tried again and got this
wide berry
I tried again and got this
That's not right. What is the integrand for large a?
eternal viper
sorry I don't understand your question. Where did I mess up?
topaz sinewBOT
@eternal viper Has your question been resolved?
topaz sinewBOT
@eternal viper Has your question been resolved?
wide berry
I tried again and got this
You have to split it.
Consider 0<r<1, and r>1 and then add them
wide berry
sorry I don't understand your question. Where did I mess up?
The integral becomes
$\int_0^{2\pi} \int_0^1 \dfrac{r^3}{r^{\alpha}} dr d\theta + \lim_{a \to \infty} \int_0^{2\pi} \int_1^a \dfrac{r}{r^{\alpha}} dr d\theta$
thorny flameBOT
1345631
wide berry
sorry I don't understand your question. Where did I mess up?
From this the cases to consider become clear.
For alpha = 4, it diverges.
For alpha = 2, it diverges.
For alpha not equal to 2 or 4, the first integral converges to 2pi/(4-alpha), and we only need to look at the second. This converges if 2 - alpha < 0, i.e 2 < alpha.
So the integral converges if 2 < alpha < 4, alpha > 4
eternal viper
.close
topaz sinewBOT
topaz sinewBOT
iron fog
is this correct?
worthy veldt
whats the method to do this
topaz sinewBOT
whats the method to do this
mellow venture
neon iron
hi. can someone verify my solution if I solved my problem correctly? i am trying to find the absolute extrema of a given function in a given interval
topaz sinewBOT
hi. can someone verify my solution if I solved my problem correctly? i am trying...
@neon iron Has your question been resolved?
neon iron
.close
neon iron
Could someone help me with this please
topaz sinewBOT
Could someone help me with this please
neon iron
ohh
neon iron
of the sum of the numbers in the ratio
I still don't quite understand
silver valve
you can assume that the actual number of red and blue marbles are 7x and 4x respectively for some x
then total number of marbles is 7x + 4x = 11x
since 11 is a factor, it must be a multiple of 11
mild pewter
yes
marsh mortar
topaz sinewBOT
marsh mortar
I am not so good with these questions
Can we treat it like a normal x^2 function
In which we know the function will be increasing from x=0
So why they said that $x_0>3$?
thorny flameBOT
azeem321
marsh mortar
Shouldn't it be $x_0>0$
thorny flameBOT
azeem321
topaz sinewBOT
@marsh mortar Has your question been resolved?
sudden spade
Your thinking about positivity they are talking about monotonically increasing/decreasing
You need to show that if $x_0=3$ then $x_{n+1}-x_n > 0$
thorny flameBOT
Max..
marsh mortar
,w graph (x^2+6)/5
thorny flameBOT
marsh mortar
Your thinking about positivity they are talking about monotonically increasing/d...
This is not monotonically increase from x=0?
sudden spade
It doesn't look like that. 1) It is not continuous we are dealing with a sequence. 2) It's not a function it's a recurrence relation. In a function we don't have a dependence on the previous term. In a recurrence relation you do.
A good example of this is $a_{n+1}=3a_n$
thorny flameBOT
Max..
topaz sinewBOT
marsh mortar
.reopen
topaz sinewBOT
ā
sudden spade
Let $a_0 = 1 \Rightarrow a_1 = 3 \cdot a_0 \Rightarrow a_1 = 3$ doing the same for $a_2,a_3..$ you get $a_0 = 1, a_1 = 3, a_2 = 9,a_3=27$
thorny flameBOT
Max..
sudden spade
Which is clearly not the same as $f(x)=3x$, it is actually $f(x) = 3^x$
thorny flameBOT
Max..
topaz sinewBOT
@marsh mortar Has your question been resolved?
marsh mortar
Does this make sense so far?
Yes. So I've seen the closed form for this thing and yeah it's $3^n$. Ok so the closed-form of a sequence is not necessarily the same function with subscript removed lol
thorny flameBOT
azeem321
sudden spade
Alright nice
Anyways back to the question we need to prove this function is increasing. In other words the $a_{n+1}$ term is bigger than the $a_n$ term
thorny flameBOT
Max..
sudden spade
And we need to show this is true for all n if $a_0=3$
thorny flameBOT
Max..
marsh mortar
hm maybe induction?
open bane
@sudden spade sorry interrupt this channel but I see that you are good at combinatorics. Can you please help me once you are free? I have a poker card problem that I am struggling with
marsh mortar
.close
tawdry chasm
topaz sinewBOT
tawdry chasm
So generally
a=.05
Sure, ok
But where is the .025 coming from
Is there a table to see this stuff?
Is it just made up and is actually a little prank, a little jape by some old mathematician?
pulsar falcon
0.05/2=0.025
sudden spade
hm maybe induction?
Yes
tawdry chasm
I swear my Excel is broken
p isn't even close to the correct number
Like what the fuck
I followed the video guide to the dotted i and the crossed t
tawdry chasm
āSample of thirtyā
?
pulsar falcon
? Those words are in what you sent
tawdry chasm
The sample size is 128
With a mean of 118.1
StnDev of 33.17
Went through the formulas to make sure I didn't miss a parenthesis (didn't), and made sure there wasn't a typo (there wasn't)
pulsar falcon
āSample of thirtyā
Here is a sample size
tawdry chasm
30 was written as "thirty", and my eyes glanced over it every time
@pulsar falcon Thank you, I wish I could have caught stuff like that myself, idk how I missed that hard
steady vale
topaz sinewBOT
steady vale
hello i need help idk where to start tbh but
i have this idk if it's right
y=-18(-3+6)(-3+4)
so far
idk what to do with it to make it into standard form
idk if i maybe did something wrong either
vale jacinth
vernal vale
lip 
vale jacinth
vernal vale
use a system of equations
LIP is easy but its uhh
conceptual
start with Ax^2+Bx+C=y
do you see how this gives you 3 equations of 3 unknowns from your given information?
steady vale
idek bruh i just know i use y=a(x-p)(x-q) then convert it to y=ax^2+bx+c
vernal vale
sure, start there
lets start at Y=A(x-p)(x-q)
what are p and q?
notice you are given two roots
steady vale
idk how to explain it but we use the y value of the ordered pair that's not a zero
vernal vale
okay
vernal vale
(-3, -18) is the point
steady vale
so sub -3 for x and -18 for a?
vernal vale
(-3, -18) "Being on the parabola" means that if you plug in -3 for x, youll get -18 for y
vernal vale
š
vernal vale
how do you solve an equation
youve picked a very bizarre place to give up seeing as all the hard work is done
$-18 = a(-3+6)(-3+4)$
thorny flameBOT
jan Niku (join us for @pomo)
vernal vale
what do they become?
thorny flameBOT
ariki
steady vale
so
steady vale
-6
vernal vale
-6 what?
steady vale
is a