Ill get back to you
#help-0
alpine sable
north hamlet
Ok
wide raven
till then you might look up IBP
north hamlet
I took dv =1
U=lnx
Found du=dx/x
And idk how to get v
north hamlet
Yeah
alpine sable
what do you think the dv is
north hamlet
dx or 1
alpine sable
what do you think the integral of dx is? which is remember, just 1 (dx)
north hamlet
Int dx is x
alpine sable
north hamlet
Is the answer xlnx-x+c?
north hamlet
x
alpine sable
x
yes, good job
now you have your u, du, v, and dv
now place them in the IBP formula which is
wide raven
Is the answer xlnx-x+c?
you did it!
alpine sable
Is the answer xlnx-x+c?
yes
good job
also, don't forget to place the absolute sign between the x after the natural log
alpine sable
xln|x|-x+c
north hamlet
I can finallynsleep
alpine sable
š
wide raven
good job
next acorn
hey guys I have a probability problem
lone heartBOT
hey guys I have a probability problem
next acorn
gimme a sec I have to translate it
so there's a meterologist that says there is rain 90% of the time of when there actually is rain
and says there is rain also 15% of the time of when there is no rain
so I wrote P(M+ | R+) = 0.9
and P(M+ | R-) = 0.15
where M+ means the meterologist predicts rain
and R+ meaning there is rain
and viceversa
dawn birch
would use R and ~R but continue
next acorn
now, it tells me that when asked, the meterologist says there's going to be rain 80% of the time
and it's asking me what's the probability that there will be rain if the meterologist predicts sunny weather
so P(R+ | M-)
in a previous point I already calculated sensitivity as 0.07
and specificity as 0.85
I tried drawing the table and getting the values from that but it doesn't seem to work
from the sensitivity I found 7/125
and then I did 0,8-7/125 to find the other thing in the table
now, my idea was to calculate the probability of it raining by dividing 7/125 by 0,9
but it doesn't work according to the solution I have
On top of the page is my reasoning for this
(from right to left)
dawn birch
aight so hereās my idea
P is predicting rain and R is rain
we know P is 80% of the time so P takes up 0.8 of the 1 space
15% of the time without rain he predicts rain
so 0.15(1-R)
90% of the time with rain he predicts rain
so 0.9R
since the size of P is 0.8
0.8 = 0.15(1 - R) + 0.9R
R = 13/15
what you want is the last section of the R circle
R without P
next acorn
wait a sec I'll try to understand
dawn birch
ok
next acorn
ok well
this is exactly what I have in my solution and I totally understand this
but
I still don't get what I'm doing wrong
dawn birch
the last section we know is 0.1R but we want to find it as a percent of 1-P
so we solve x(1-P) = 0.1R with P = 0.8 and R = 13/15
0.2x = 13/150 gives x = 13/30
,w 13/30 * 100
ocean sealBOT
dawn birch
43%
dawn birch
lol
next acorn
can you tell what's wrong with my method?
dawn birch
idk what sensitivity or specificity is
dawn birch
ok
next acorn
that's predictive value
sensitivity is P(M+ | R+)
so it's just 0,9
predictive value is 0,07 though and I have that in my solution as well
so I know that's correct
I used that to calculate P+ and M+, do you think that step is correct?
("and" meaning the union of P+ and M+)
dawn birch
well what did u get for the size of the union
next acorn
7/125
dawn birch
lol
dawn birch
the union here is 0.9R and R is 13/15 so it should be size 39/50
dawn birch
yes
dawn birch
what was your P(R+|M+) again
next acorn
should be 0,07 but I'm thinking now that this is only true for the previous point
I'm checking the formula right now and it looks like it depends on the probability of rain
so it makes sense that it would change
I think that's the reason
dawn birch
in this pic the size of R given that itās in P is xP = 0.9R i believe
,w calc (13/15)/(0.8) * 0.9
ocean sealBOT
dawn birch
97% seems more reasonable than 7%
next acorn
you mean just based on real meterologists?
dawn birch
yeah the other numbers are fairly realistic
dawn birch
the rain chance is a little high but whatever
next acorn
in the previous example it was talking about a desert
where it rained only 5 years in 400 years
dawn birch
lol
next acorn
it makes sense that the meterologist would be much worse at predicting rain in that situation
dawn birch
yes
next acorn
well thanks man
dawn birch
no problem
ocean sealBOT
B. Eens
lone heartBOT
stuck echo
**B. Eens**
Oh, my mistake. This is my problem.
tawny schooner
Man you are making it way too complicated
It's easy using a simple Geometric series sum
Let me send you the solution
lone heartBOT
Available help channel!
tawny schooner
**B. Eens**
lone heartBOT
tacit arch
Let me send you the solution
try not to give away ENTIRE solutions
stuck echo
Oh. This makes a lot of sense. Thanks :D
.close
@tawny schooner you have to close the channel :/
lone heartBOT
Available help channel!
left frigate
How does
3^x * 2^(x-1) simplify into 0.5 * 6^x?
lone heartBOT
How does
`3^x * 2^(x-1)` simplify into `0.5 * 6^x`?
left frigate
I don't understand where the x-1 exponent goes
tacit arch
$a^{x-y} = \frac{a^{x} }{a^y}$
ocean sealBOT
riemann
left frigate
Thank you! I'm so confused why my book doesn't provide these rules before the problems make use of them, it's getting frustrating
Thank you so much
.close
coarse wedge
lone heartBOT
coarse wedge
How this one wrong?
tacit arch
try plotting this
tacit arch
Like this?
Hint: Plotting a constant angle is a ray. In this case a diagonal one
lone heartBOT
@coarse wedge Has your question been resolved?
alpine sable
do you remember the cartesian formula for a line?
coarse wedge
Ax + By + C = 0
alpine sable
for your line Īø=5pi/4, what is the y-intercept and the slope?
coarse wedge
Y = 0, slope is one
alpine sable
what does it look like when you draw it?
coarse wedge
Straight line
coarse wedge
radius
coarse wedge
circle
coarse wedge
(x - h)2 + y2 = 36
alpine sable
what is h?
coarse wedge
0
alpine sable
ok good
coarse wedge
so x^2 + y^2 = 36
alpine sable
yup
coarse wedge
Im confued about the 1 equals
Like that just means that there is aconstant radius for any angle
@alpine sable
alpine sable
Im confued about the 1 equals
make it 1= something then
either divide by 36
or subtract 35
native blaze
lone heartBOT
native blaze
I dont understand the above warning
is it saying the product law cannot or can be applied if the individual function limits dont exist?
alpine sable
is it saying the product law cannot or can be applied if the individual function...
cannot be applied
native blaze
so why does it say it equals 3, as opposed to saying it doesnt exist?
is it to show that it might compute, but u shouldnt be tricked by that?
alpine sable
so why does it say it equals 3, as opposed to saying it doesnt exist?
the rule lim (fg)=lim(f)lim(g) can't be applied unless we know lim(f) and lim(g) exist beforehand.
Here they computed the LHS of the rule : lim(fg) where f=x and g=3/x which is equal to 3, which is different from the RHS lim(f)lim(g) which doesn't exist
native blaze
how do you compute the lhs vs the rhs
alpine sable
how do you compute the lhs vs the rhs
like you would compute any limit
native blaze
but if the lhs and rhs are different, wont i get the same result for both sides if i jsut plug in x
alpine sable
so why does it say it equals 3, as opposed to saying it doesnt exist?
Squeeze theorem
Or well
Firstly
The graphs of the third limit and second limit would be different
The second limit, if graphed will make a rational function with a vertical asymptote at x=0
native blaze
if you plug in x=0 this gives a division by 0 in both sides
Im asking in general how you compute the limit of the lhs vs rhs
alpine sable
,w plot 3/x
Whereas third limit 3/x * x will make a straight line at x = 3 which is discontinuous at x= 0
ocean sealBOT
native blaze
ok i understand that now
alpine sable
,w plot 3/x * x
ocean sealBOT
native blaze
the rule lim (fg)=lim(f)lim(g) can't be applied unless we know lim(f) and lim(g)...
@alpine sable im not sure what this person meant by lhs and rhs
but i understand your point
alpine sable
the rule lim (fg)=lim(f)lim(g) can't be applied unless we know lim(f) and lim(g)...
NGL dude
I've never even heard of this rule
And I'm like
Doing multivariable calc
So idk what to say lmao
All ik is as long as the graph doesn't go to infinity you're Gucci
Or negative infinity
alpine sable
And I'm like
sounds like you have some reviewing to do
alpine sable
<@456226577798135808> im not sure what this person meant by lhs and rhs
the lhs of the rule
You can combine limits approaching the same value
alpine sable
You can combine limits approaching the same value
not sure what you mean by this
All right I'm gonna use L all right
Cuz I'm not gonna write lim and all that stuff
If L(f(x)) exists
L(g(x)) exists
L(f(x) \cdot g(x)) = L(f(x)) \cdot L(g(x))
native blaze
the lhs of the rule
ok i get you
alpine sable
But doesn't mean L(f(x) \cdot g(x)) won't exist if L(g(x)) doesn't exist
native blaze
.close
worthy python
In part (b) I'm having difficulty understanding why any nonzero ideal has a matrix with a nonzero entry in the upper left-hand corner.
lone heartBOT
In part (b) I'm having difficulty understanding why any nonzero ideal has a matr...
@worthy python Has your question been resolved?
serene junco
@worthy python This is a bit over my head but it looks like abstract algebra?
worthy python
yes, this is from Hungerford's book
serene junco
You'll probably have more luck in the university or advanced channels. These help channels are more geared toward early university at the most.
worthy python
ok, thank you
serene junco
native blaze
if i have lim a times lim b, but lim b doesnt exist, whats the answer?
agile salmon
oh i didnt see this but i got it now thanks
lone heartBOT
@native blaze Has your question been resolved?
native blaze
<@&286206848099549185>
if i have lim a times lim b, but lim b doesnt exist, whats the answer?
gray isle
depends
marsh rapids
It doesn't exist because it's not defined. You use something that doesn't have a value. You'd want to say it's lim of ab and that it can be defined that way, but this only holds when the limits exist. When you're dealing with something undefined, it's just undefined and that is that.
native blaze
.close
alpine sable
Hey can someone help me with this $$\int^{-1}_{-\infty} \frac{e^x}{x},dx$$
ocean sealBOT
idecanymore
alpine sable
Question says I'm supposed to evaluate it without the power series for $e^{x}$
ocean sealBOT
idecanymore
weary wyvern
Hey can someone help me with this $$\int^{-1}_{-\infty} \frac{e^x}{x}\,dx$$
first u=-x
weary wyvern
$\int_1^{\infty}\frac{1}{xe^x}\dd{x}$
ocean sealBOT
giannis_money
alpine sable
$\int_1^{\infty}\frac{1}{xe^x}\dd{x}$
Don't see how much has changed still
weary wyvern
looks better imo
alpine sable
It's just e^{-x}/x
weary wyvern
x = log u doesn't seem to help
marsh rapids
There is no elementary antiderivative btw
weary wyvern
Let $I(t) = \int_1^{\infty}\frac{e^{-tx}}{x}\dd{x}$
ocean sealBOT
giannis_money
weary wyvern
the answer is I(1)
weary wyvern
**giannis\_money**
differentiate both sides of this
weary wyvern
it would help if you showed your work
marsh rapids
That's what I thought
alpine sable
That's what I thought
Exactly why I said it doesn't work
marsh rapids
But there's a 2 in it no ?
weary wyvern
Congrats you made a loop
who me?
weary wyvern
i can see that
weary wyvern
ok, and?
marsh rapids
If you differentiate the inside you get (x+1)^2 e^-tx / x, so arguably there's a differential equation in there
alpine sable
If you differentiate the inside you get (x+1)^2 e^-tx / x, so arguably there's a...
Where's the of (x+1)^2 coming from?
marsh rapids
If you differentiate the inside you get (x+1)^2 e^-tx / x, so arguably there's a...
Nvm
marsh rapids
Where's the of (x+1)^2 coming from?
Quotient rule
alpine sable
Nvm
You differentiate in terms of t
Not in terms of x
It's a partial differential on the RHS
marsh rapids
I'll go to sleep then
alpine sable
If you did it in terms of x, you'd just get integral of -xte^(-tx)-e^(-tx)/x^2
alpine sable
I'll go to sleep then
Lmao
alpine sable
If you did it in terms of x, you'd just get integral of -xte^(-tx)-e^(-tx)/x^2
Which would be even more useless
No offense
marsh rapids
If you differentiate the inside you get (x+1)^2 e^-tx / x, so arguably there's a...
It does make a diff eq though
I'(t) = -t I(t)
weary wyvern
$I'(t) = \frac{-e^{-t}}{t}$
ocean sealBOT
giannis_money
alpine sable
I'(t) implies $\frac{dI}{dt}$
ocean sealBOT
idecanymore
alpine sable
You can't just differentiate in terms of t on the left side and in terms of x on the right side and call it a differential equation
@marsh rapids
weary wyvern
$I(1) = -\int_1^{\infty} I'(x) \dd{x}$
alpine sable
$I(1) = -\int_1^{\infty} I'(x) \dd{x}$
Uhh wut
alpine sable
$I(1) = -\int_1^{\infty} I'(x) \dd{x}$
What exactly did you parametrize
I'm so confused
What's the 1
Value of t?
weary wyvern
**giannis\_money**
lhs is from this
weary wyvern
**giannis\_money**
rhs is from that and this
weary wyvern
mate the rhs is a number
ocean sealBOT
giannis_money
weary wyvern
ok just realised i meant to say this, which is a tautology
alpine sable
mate the rhs is a number
The RHS is a number but
When we began we defined $$I(t=1) = \int^{\infty}_{1} \frac{e^-x}{x},dx$$
When we differentiated in terms of t, we found.
$$I'(t) =- \frac{e^-t}{t}$$
$$I(t) = \int \frac{-e^{-t}}{t},dt$$
alpine sable
ok just realised i meant to say this, which is a tautology
Exactly
It's not helping still which is kinda my point
ocean sealBOT
idecanymore
weary wyvern
It's not helping still which is kinda my point
good job for figuring that out
weary wyvern
you should really try to take a less pessimistic approach to maths. what you think doesn't help, might help in the future
alpine sable
you should really try to take a less pessimistic approach to maths. what you thi...
What
weary wyvern
literally what do you not understand
weary wyvern
alright help yourself, i'm not helping you
alpine sable
Bcz the only two ways I knew are not working?
alpine sable
alright help yourself, i'm not helping you
Ok
All right
Just putting it again, in case anyone else sees
Q: Evaluate the following improper integral without using any power series.
$$\int ^{-1}_{-\infty} \frac{e^{x}}{x},dx$$
ocean sealBOT
idecanymore
alpine sable
Methods already tried : Feynman's and using a complex integral
Don't seem to be working
I thought complex might help since then I can use the identity $e^{ix} = \cos(x)+i\sin(x)$ since I already have found the $\frac{\sin(x)}{x}$ for $0$ to $\infty$ before and just changing the 0 to a 1 wouldn't be too hard but it's not working
ocean sealBOT
idecanymore
alpine sable
Or at least that didn't work when I tried it last
tacit arch
it's divergent around x=0 so you have to use cauchy principal value
alpine sable
I thought complex might help since then I can use the identity $e^{ix} = \cos(x)...
The integral for sin(x)/x*
alpine sable
it's divergent around x=0 so you have to use cauchy principal value
Ik it's divergent around 0
That's why I was gonna just approximate 0 to 1, subtract it from pi/2
For sin(x)/x
Cos(x)/x idk why I couldn't figure it out from 1 to infty
tacit arch
That's why I was gonna just approximate 0 to 1, subtract it from pi/2
is pi/2 what you get from cauchy's principal value?
alpine sable
is pi/2 what you get from cauchy's principal value?
I'm gonna be honest, I haven't done cauchys principal value formally
So idk what it is
I've heard of it
tacit arch
that's the only way you can do the integral without estimating
alpine sable
And it's used to figure out improper integrals which don't have a certain integral
alpine sable
that's the only way you can do the integral without estimating
But the pi/2 for sin(x)/x was correct afaik
Checked from Wolfram sooo
tacit arch
yea but you just exchanged one unsolved problem for pi/2 + another unsolved problem
alpine sable
yea but you just exchanged one unsolved problem for pi/2 + another unsolved prob...
Yeah but 0 to 1 is a v small interval
tacit arch
cos(x)/x is also divergent at x=0 so you again need cauchy principal value
alpine sable
So I thought I could just approximate it
alpine sable
cos(x)/x is also divergent at x=0 so you again need cauchy principal value
I was figuring that one out from 1 to infty
So I need cauchy's principal ig
@tacit arch is there any way I can do it without that?
Cuz I haven't done it per say so I'll try to cover it first now obviously
tacit arch
**idecanymore**
what class is this even for? the power series doesn't even converge
if you haven't been taught the tools, i doubt you're supposed to actually do this problem
maybe you made a mistake along the way here
alpine sable
what class is this even for? the power series doesn't even converge
I found the q on the internet
Didn't get it from a class
alpine sable
if you haven't been taught the tools, i doubt you're supposed to actually do thi...
Ik I'm not
Doing it purely for fun
tacit arch
the instructions are poorly worded then since you can't even calculate the integral using power series
or is that something you made up?
alpine sable
or is that something you made up?
You can get an indefinite answer tho
Ofc bounding to infty, it won't converge so it's useless
alpine sable
or is that something you made up?
Nope, I asked my schoolteacher and she first did say that you'd use the power series but the question specifically said no power series
tacit arch
Nope, I asked my schoolteacher and she first did say that you'd use the power se...
show the original question
alpine sable
or is that something you made up?
No?
tacit arch
url would be best
alpine sable
show the original question
I saw it months ago, I don't have it anymore
tacit arch
how do you know you remembered it correctly if you saw it months ago?
alpine sable
I've been stuck on this problem for 4-6 months
alpine sable
how do you know you remembered it correctly if you saw it months ago?
Bcz the question was pretty short? It's barely like 10 words
And the integral's written like 90 times in my notebook bcz I kept retrying the same method over n over thinking I was doing something wrong
alpine sable
I've been stuck on this problem for 4-6 months
Also this?
Before that I was stuck on this one which was allegedly taken from the Putnam
$\int^{1}_{0} \frac{1}{\ln(x)} + \frac{1}{1-x},dx $
I saw it on flammys channel I think
@tacit arch ?
You there?
tacit arch
So I need cauchy's principal ig
do this
tacit arch
alpine sable
Ty
tacit arch
alpine sable
https://math.libretexts.org/Bookshelves/Analysis/Complex_Variables_with_Applicat...
Residue theorem is in complex analysis, right?
Or real?
Some people told me to finish multivariable first before going to analysis
tacit arch
yea complex. some complex analysis books might cover it, but not all
alpine sable
yea complex. some complex analysis books might cover it, but not all
I've got Serge Lang's one
tacit arch
complex analysis is just multivariable calculus with different notation
alpine sable
complex analysis is just multivariable calculus with different notation
š yeah but rn I struggle with multivariable calc
tacit arch
alpine sable
<:catshrug:563818735085944843>
So do unis usually do complex analysis after real or does the order not matter?
tacit arch
i took complex before real analysis
alpine sable
Ooh
Fancy
I thought the opposite was like
Mandatory
Tho real analysis looks v boring to me so I wanted to do complex before it
alpine sable
i took complex before real analysis
Would u suggest doing complex before real?
tacit arch
ask your math department's undergrad advisor, not some internet stranger
alpine sable
ask your math department's undergrad advisor, not some internet stranger
I'm not in college...
I'm in school
Ik I'm not supposed to study it but I want to
So I ask people online
Who have done it before
Thx anyways
.close
summer mortar
guys how do i do this continuity problem? its has to be bound times infinitesmy right?
lone heartBOT
guys how do i do this continuity problem? its has to be bound times infinitesmy ...
@summer mortar Has your question been resolved?
lone heartBOT
@summer mortar Has your question been resolved?
summer mortar
<@&286206848099549185>
lone heartBOT
@summer mortar Has your question been resolved?
vocal hawk
summer mortar
i have been asked to analyse the contuinity if the ecuation i shared on the point (0,0)
the answer is supposed to be a yes, but i cannot make the limit be equal to 0
it looks like an infinitesimy times a bound funtion but i cannot work it out
elfin snow
maybe ask in #real-complex-analysis
naive valley
Indeed $\left|\frac{x^2 - y^2}{x^2 + y^2}\right|$ is bounded on its domain $(x,y) \neq (0,0)$. Also note that $|y| \leq \sqrt{x^2 + y^2}$, which means that $y \to 0$ as $(x,y) \to (0,0)$. What can you conclude?
ocean sealBOT
Bungo
lone heartBOT
@summer mortar Has your question been resolved?
summer mortar
i dont understand how did you get the moduls, can you explain it to me? i know that $\frac{x^2 + y^2}{x^2 + y^2}$ is bounded, but i dont get how is $\frac{x^2 - y^2}{x^2 + y^2}$ thats the problem
ocean sealBOT
juanfran
naive valley
i dont understand how did you get the moduls, can you explain it to me? i know t...
one way to obtain a bound: $\left|\frac{x^2 - y^2}{x^2 + y^2}\right| = \left|\frac{x^2}{x^2 + y^2} - \frac{y^2}{{x^2 + y^2}}\right| \leq \left|\frac{x^2}{x^2 + y^2}\right| + \left|\frac{y^2}{x^2 + y^2}\right| \leq 1 + 1 = 2$
ocean sealBOT
Bungo
naive valley
i might have misinterpreted, i thought you said you already found that it was bounded
summer mortar
no problem. I imagine the solution has to be somewhat related to that but yeah i dont know if its bound or not, the actual answer in the practice is " the function is continuous" and i dont understand how
so the limit for (x,y)->(0,0) has to be 0 but i cant make it work
oh im so sorry, i was rambling and i didnt even notice that you already answer it above
naive valley
yeah i was about to repeat the argument
summer mortar
yeah sorry lol, let me think it on paper
naive valley
so you have the product of two factors, one is bounded and the other goes to zero
that's enough to conclude that the limit of the product is zero
if you get stuck with concluding that, feel free to ask, and i can give a hint
lone heartBOT
lone heartBOT
Available help channel!
olive spade
help I have this equation a^3 + b^3 = c^3 Can anyone find a valid set of non-zero integers for a, b and c thx
lone heartBOT
help I have this equation a^3 + b^3 = c^3 Can anyone find a valid set of non-zer...
@olive spade Has your question been resolved?
keen pasture
help I have this equation a^3 + b^3 = c^3 Can anyone find a valid set of non-zer...
No
glossy current
tacit arch
It's not too difficult to prove this if you know number theory
pliant hazel
lone heartBOT
pliant hazel
Hello, can anyone help me to denote |x| = max{x, -x} ? As I get it x is like some kind of operation as explained later.
olive spade
:C
lone heartBOT
@pliant hazel Has your question been resolved?
remote heron
Hello, can anyone help me to denote |x| = max{x, -x} ? As I get it x is like...
denote?
x is just some value
pliant hazel
I don't get it why it is explained so hard. Abs of x or -x is x. I see max{} for the first time.
remote heron
I don't get it why it is explained so hard. Abs of x or -x is x. I see max{} for...
its just rigor
its not always helpful
max just means maximum
pliant hazel
Thank you. I'm trying to study by myself and want to know every detail, but sometimes it doesn't make sense
remote heron
Thank you. I'm trying to study by myself and want to know every detail, but some...
it depends on the author if they give a necessary amount of detail to be honest
sometimes stuff is just there because it was included
lone heartBOT
@pliant hazel Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
can someone help explain to me how to do 1 b)
i am pretty sure for 1 a) the odd number of steps dont count as u have to end on the first rung
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
rose sigil
can someone help explain to me how to do 1 b)
if catalan paths are what I think... have you tried making a correspondence by associating moves up in catalan paths with moves up on the ladder, and moves to the right in catalan paths with moves down on the ladder?
alpine sable
Catalan paths?
rose sigil
so like for example, if n = 3, the up up right right up right catalan path corresponds to up up down down up down ladder path
alpine sable
Oh I see
rose sigil
I'm guessing catalan paths are paths from (0,0) to (n,n) on the integer lattice that don't go outside the smallest square containing (0,0) to (n,n), and don't cross its bottom left to top right diagonal
lunar galleon
I was given |xĀ²-9| = |xĀ²-5| to solve for x. I "broke down" the absolute value brackets by making one side positive and the other negative, so xĀ²-9 = -(xĀ²-5) which I then correctly solved and got Ā±ā7. I know what absolute values are, but I wonder how making one side positive and the other negative "broke" the brackets down and enables me to solve the equation
lone heartBOT
I was given |xĀ²-9| = |xĀ²-5| to solve for x. I "broke down" the absolute value br...
lone heartBOT
@lunar galleon Has your question been resolved?
lone heartBOT
@lunar galleon Has your question been resolved?
lone heartBOT
@lunar galleon Has your question been resolved?
tidal lantern
By breaking the bracket you assumed that x^2-something was positive or negative, you got two solution because two intervals where x is leads to the same equation
lone heartBOT
@lunar galleon Has your question been resolved?
trim wagon
You see there will be 4 cases actually
Case1: +(xĀ²-9) = +(xĀ²-5)
Case2: -(xĀ²-9) = +(xĀ²-5)
Case3: +(xĀ²-9) = -(xĀ²-5)
Case4: -(xĀ²-9) = -(xĀ²-5)
But you see case 1 & 4 donāt results anything useful because xĀ² cancels out and we get no solution
lunar galleon
You see there will be 4 cases actually
Case1: +(xĀ²-9) = +(xĀ²-5)
Case2: -(xĀ²-9) ...
I thought only case 2 and 3 is valid? as in, you add Ā± to the equation to break the brackets. Multiplying both sides with +1 or -1 does nothing, or in other words, does not break that absolute value bracket
lunar galleon
By breaking the bracket you assumed that x^2-something was positive or negative,...
Hmm I get that, but not really what I'm looking for
trim wagon
I thought only case 2 and 3 is valid? as in, you add Ā± to the equation to break ...
Yes you are right, case 1 & 4 are invalid, and can you see why? ||5=/=9||
lunar galleon
ye
lunar galleon
aight I figured it out after analysing the graphs in more detail š
a +positive part of one of the equations f(x) intersects with the -negative part of the other equation g(x)
thats why you use the negative value of one of the equations and the positive value of the other
lone heartBOT
lone heartBOT
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misty cedar
I'm trying to do the extra credit part. Since V=pi.r^2.h, dV depends on both h and r but I can't just find the change for h and find the change for r on the previous equation i get, it doesn't make sense for me at least. Also dV = 2pi.r.h.dr and also dV = pi.r.dh, I know I have to express the change like this but no idea how to combine 2
lunar galleon
Hmm I think this has something to do with the chain rule
last ether
Well let's look
You know that $V = Ļr^2h$, so let's derive that with respect to time
ocean sealBOT
Umbraleviathan
last ether
$$\frac{dV}{dt} = Ļ\left(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\right)$$
ocean sealBOT
Umbraleviathan
misty cedar
hmm
I'm sorry if this sounds dumb but
how do you derive it with respect to time, V doesn't depend on t
last ether
Well I'm assuming it changes with respect to time
misty cedar
oh
last ether
I mean logically, an object takes time to morph
I highly doubt it'll just spontaneously combust into a different shape lol
misty cedar
this expression is the same as dV = 2pi.r.h.dr, dV = pi.r.dh adding these two together
so let's say for a cylinder with h = 2 and r = 3
last ether
Uh yeah, you can think of it that way if you're thinking partials
misty cedar
that changes to h = 3 and r = 4
misty cedar
the difference is 30pi
but this formula $$\frac{dV}{dt} = Ļ\left(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\right)$$
ocean sealBOT
Resit
misty cedar
gives 40pi if i'm not wrong
misty cedar
ok pi(2.3.1.2 + 9.1) then
misty cedar
but the change in volume was 30pi
last ether
Using what
last ether
this expression is the same as dV = 2pi.r.h.dr, dV = pi.r.dh adding these two to...
Using this still gets you 21Ļ
misty cedar
Using this still gets you 21Ļ
yeah i know but shouldn't it be 30 pi with these values
last ether
Lemme check
I mean it should but idk why it's not
Ayo @tacit arch did I goof something up
last ether
**Umbraleviathan**
With this
tacit arch
You know that $V = Ļr^2h$, so let's derive that with respect to time
Yes right here
The correct word is differentiate
last ether
Okay well that's just word moment
But then we're getting 21pi as opposed to a suggested 30pi given r = 3 -> 4 and h: 2 -> 3
tacit arch
But then we're getting 21pi as opposed to a suggested 30pi given r = 3 -> 4 and ...
Where does it say h changes from 2 to 3
last ether
He's giving a hypothetical
last ether
r = 3 h = 2 becomes r = 4 h =3
Here
tacit arch
So r should be 3 and h should be 2 iirc
r is 2 and h is 3
misty cedar
for r = 2 and h = 3 the volume is 12pi
for r = 3 and h = 4 the volume becomes 36pi the difference is 24 pi
so dV should be 24pi right
dV = 2pi.r.h.dr + p.r^2.dh
should i use the initial h and r to find the change or the later
using the initial values gives 16pi and using the later values gives 33pi
in both cases it isn't 24pi
misty cedar
r is 2 and h is 3
.
last ether
Yeh no that's weird idk why it's not working usually this is how it works unless im forgetting something
lunar galleon
can you say that dr/dt = -0.1 ?
misty cedar
for r = 2 and h = 3 the volume is 12pi
for r = 3 and h = 4 the volume becomes 36...
you can use these for simplicity
lunar galleon
logically it should be dr/dt = -0.1 dt but š©
misty cedar
you can say that since volume can shrink i guess
lunar galleon
but how can u say that when r = 3 , h = 4 ?
misty cedar
i just gave another example for simplicity you don't have to use the values on the question
for r = 2 and h = 3
for r = 3 and h = 4
here dr/dt and dh/dt is 1
lunar galleon
ah I see
well I am using the chain rule to try and get a solution where dh comes into play in dV/dr
dV/dr = dV/dh ā¢ dh/dr
and to get dh/dr we need the dr/dt
dh/dr = dh/dt ā¢ dt/dr
at least thats what I'd try to do
lunar galleon
its just (dr/dt)^-1
since id expect to get a real number value from dr/dt, dt/dr would just be the 1/(dr/dt)
and since from the question dr is the only value given id try to work with that
ionic flint
hi
ionic flint
anyone here have matlab knowledge and willing to help?
worn fox
lone heartBOT
@ionic flint Has your question been resolved?
ionic flint
its actually a test got some help with first questions
tacit arch
its actually a test got some help with first questions
don't cheat on tests
ripe rain
split sphinx
Q: Plane sells 10% more tickets than capacity. 10% of clients cancel flight last minute (they cancel independently of each other). There are n seats on plane.
(a) All tickets are sold, including the extra 10%, find the expected number of people who actually take the plane.
(b) Use a suitable chernoff bound to estimate the probability that plane is over its capacity, and show this converges to 0 as n goes to infinity
A: For a, the probability that someone takes their seat= 0.9, total number of trials is 1.10n, so expectation is 0.9 x 1.10n = 0.99n (because we have a binomial situation here)
B: I know we have to find P ( X > n) where X is number of people that show up, and then i have the following chernoff bounds give in my notes, but i don't know how to connect the two things. (also for similar questions we've done we sometimes use chernoff + booles inequality together)
split sphinx
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split sphinx
<@&286206848099549185>
lone heartBOT
@split sphinx Has your question been resolved?
lone heartBOT
@split sphinx Has your question been resolved?
lone heartBOT
@split sphinx Has your question been resolved?
lone heartBOT
@split sphinx Has your question been resolved?
remote heron
i am looking 
stay open
i lied, im not sure what a chernoff bound is
@split sphinx you may try the stats server
all I see is $P(x \geq a) \leq e^{-at}M_x (t)$ as a bound
ocean sealBOT
jan Niku
remote heron
does that mean you use the mgf for binomial 
alpine sable
Choose whether inductive or deductive. What is the next term in the sequence 1,4,9,16,25,__. The next number is 36.
alpine sable
My answer is inductive.
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
alpine sable
.close
native blaze
e^x^2 is different than (e^x)^2 right
lone heartBOT
e^x^2 is different than (e^x)^2 right
native blaze
because in the second case the 2 can be multiplied by exponent x
is my reasoning here correct?
somber wedge
Correct, e^(x^2) is different to (e^x)^2 = e^2x
Keep in mind that this is because, unlike addition or multiplication, exponentiation isn't associative ( e.g. (a^b)^c =/= a^(b^c) )
lone heartBOT
lone heartBOT
Available help channel!
faint whale
(x-1)^2 should be x^2 + 1 +2x
As b is -1 but i used an app to find the answer it say it should be x^2 + 1 -2x and a teacher on youtube did that too
faint whale
What is the right answer?
wide raven
karmic rapids
(x-1)^2 should be x^2 + 1 +2x
As b is -1 but i used an app to find the answer it...
,, (a-b)^2 = a^2 - 2ab + b^2
ocean sealBOT
illuminator3
faint whale
(x)^2 - 2(x)(-1) +(-1)^2=x^2 +2x +1
True?
faint whale
You dont take it as -1?
karmic rapids
no, if b were -1 then it'd be $(x + (-1))^2$
ocean sealBOT
illuminator3
sullen river
answer:
1186 to 2370 with growth factor 1.189 after 4 years
my answer:
1186 to 5640.616 with growth factor 1.189 after 4 years.
i did 1186 x 1.189 x 4 (which obviously is incorrect)
what is the math i need to do thanks?```maybe exponential functions
somber wedge
```idiot at math here
answer:
1186 to 2370 with growth factor 1.189 after 4 yea...
Do you know about compound interest?
sullen river
not really. could you explain pls?
somber wedge
So what they mean by a growth factor of 1.189 is that in the first year the amount increases by a scale of 1.189
e.g. the amount after one year is 1186*1.189
But when we consider the amount we will have after the second year, we can think of it as the amount we have after the first times our scalar again
e.g. we need to account for the amount we gained in the first year
So we would do that by taking our first year and * it by the scalar again (1186*1.189)*1.189
This means we would get for our second year our initial value * the scalar to the power of time
e.g. initial * growth factor ^ time
Does that make sense?
sweet vault
how do you find the asymptotes of g(x) = e^x + e^-x
lone heartBOT
how do you find the asymptotes of g(x) = e^x + e^-x
fallen verge
take limits at infinity for horizontal
sweet vault
take limits at infinity for horizontal
im just getting infinity + 0 though
fallen verge
the vertical asymptotes are a little harder but it can be show none exists
fallen verge
im just getting infinity + 0 though
so what can you conclude?
sweet vault
are there really no horizontal asymptotes?
fallen verge
yes
sweet vault
how would i know how to graph it then
fallen verge
try graphing the two together then adding them
most of the additions past -1 and 1 become negligible
sweet vault
most of the additions past -1 and 1 become negligible
what do you mean by that
sweet vault
but doesnt -1<= x <=1 look different to the actual graph
fallen verge
the actual graph is in red
sweet vault
yeah
fallen verge
the green and purple hug the graph at parts
fallen verge
š
lone heartBOT
Available help channel!
next oyster
lone heartBOT
next oyster
how would i start this question?
tacit arch
,rccw
ocean sealBOT
lone heartBOT
@next oyster Has your question been resolved?
next oyster
what do i plug into the calculator or what do i do to find the angle?
lone heartBOT
@next oyster Has your question been resolved?
next oyster
thank you @true mason for helping me
meager patio
If I have a cross product like AxB=C can I say that CxA=B and BxC=A?
meager patio
yes exactly š thank you
worn fox
If you don't, you get a negative
meager patio
yea like BxA=-C
worn fox
You got it
meager patio
permutations
odd number of permutations i need to change sign even number of permutations i keep the sign
good guess?
worn fox
I think your language is a bit mixed here
We can do an odd number of permutations, I.e. one cycle and not have to change sign
You may be thinking of the word transpositions instead
(Switching two elements)
meager patio
yes that's what i mean
so transposition=permuations of 2 elements and keeping everything else in the same spot
worn fox
Yep!
native gull
Hi people, I'm new to discord, I'll ask when i have problems.Take care beautiful people š
lone heartBOT
Hi people, I'm new to discord, I'll ask when i have problems.Take care beautiful...
@native gull Has your question been resolved?
native gull
lone heartBOT
lone heartBOT
Available help channel!
elfin lark
uneven canyon
Does this notation mean that every element in Matrix A is 2?
surreal meteor
I'm getting the feeling that this isn't 16-1/2
because that would be 15.5, so what am i missing haha?
grave island
I'm getting the feeling that this isn't 16-1/2
mate
thats indices
do we know our indices rules
surreal meteor
Det er min kanal broski
š det jo bare et simpelt dumt spĆørgsmĆ„l hahaha
surreal meteor
Ja, det min fejl sƄ brormand
surreal meteor
do we know our indices rules
yep LOL I didn't notice it was 16^-1/2 š Thanks man
uneven canyon
.close
lone heartBOT
surreal meteor
.close
lone heartBOT
Available help channel!
true skiff
Hi! can someone help me with this? I am stuck at last part. It says that every divisor of n! occurs when n=3 so that includes 2 but i cant find a polynomial in 3 (commuting) variables which only gives 2 distinct polynomials (including itself) on permuting variables
novel night
One insight is: the polynomial will have to be invariant under a cyclic permutation like (123) and not be invariant under any transposition like (12). So step 1 would be to look for polynomials that are invariant under cyclic permutations.
And a nice way to get an invariant polynomial is to take the sum (or average if you prefer) over the relevant permutations.
lone heartBOT
@true skiff Has your question been resolved?
Available help channel!
Available help channel!
autumn mountain
if i had to sketch a velocity time graph for this problem how would i find all the specific measurements: A ball is dropped from a height of 5m, it bounces to half the height of the previous bounce each time. You may assume the velocity reverse direction instantly when it hits the ground
kindred dagger
if i had to sketch a velocity time graph for this problem how would i find all t...
This is more of a physics question https://discord.gg/physics
autumn mountain
This is more of a physics question https://discord.gg/physics
ah, mb
wasn't sure if physics came under maths or not
kindred dagger
small beginning of research, when the ball is at its maximum height at each bounce, its speed is zero
autumn mountain
small beginning of research, when the ball is at its maximum height at each boun...
I see, i'll try starting from that
thank you š
burnt ravine
You can make it using exponential form
x^n = exp(n log x)
for x > 0 you can distinct other cases as similar
fossil karma
Hi, how can I find the answer without using a calculator?
lone heartBOT
Hi, how can I find the answer without using a calculator?
alpine sable
are you familiar with long division
fossil karma
yes
gray isle
$11)\overline{8\red{.0000}}$
ocean sealBOT
āamonov
gray isle
introduce more trailing 0s as needed
alpine sable
how to get the inital value and common ratio based off of this exponetial table?
mortal trellis
what is F(6)/F(4) in terms of the common ratio?
alpine sable
what is F(6)/F(4) in terms of the common ratio?
wait how does that give common ratio
mortal trellis
I didn't say that it does
I just want you to express it in terms of the common ratio
alpine sable
I didn't say that it does
f(6)/f(4) = 2.25
mortal trellis
get your own help channel #āhow-to-get-help
how would you normally determine the common ratio
alpine sable
how would you normally determine the common ratio
u divide nth term from previous term
but this is btween every 2 terms
mortal trellis
assume we have some term f(4) and we know the common ratio r. what would f(5) be
alpine sable
assume we have some term f(4) and we know the common ratio r. what would f(5) be
f(4) * r = f(5) right
mortal trellis
yes
alpine sable
ohhh
alpine sable
so we go f(4) * r * r = f(6)
alpine sable
2.25
mortal trellis
and in terms of the common ratio r ?
alpine sable
1.125?
mortal trellis
so we go f(4) * r * r = f(6)
I just want that you divide this by f(4) on both sides
alpine sable
wait so r^2 = 2.25
mortal trellis
yes
alpine sable
oh
mortal trellis
then what is r?
ocean sealBOT
alpine sable
then what is r?
1.5 š
mortal trellis
that's just one of the options
we'll get to that
first tell me the other option that r could be
alpine sable
first tell me the other option that r could be
-1.5
mortal trellis
yes
so we know that f(1)*r= f(2)
we know f(2) and we know r (or at least we know it can only be one of two things)
what is f(1) ?
I don't know if you consider f(1) or f(0) as the initial value
alpine sable
+-96 is f(1)
alpine sable
I don't know if you consider f(1) or f(0) as the initial value
i think its f(0)
alpine sable
,w 96/1.5
ocean sealBOT
alpine sable
64?
alpine sable
in both cases for r btw
i think there was a constriction though where r>-0
mortal trellis
yeah that could be
agile condor
find all pairs (a;b) such that $(a+b)^7āa^7āb^7$ is divisible by $7^7$ but $ab(a+b)$ is not divisible par 7.
lone heartBOT
find all pairs (a;b) such that $(a+b)^7āa^7āb^7$ is divisible by $7^7$ but $ab(...
ocean sealBOT
what do i live for v2.0
agile condor
i found that $$(a+b)^7-a^7-b^7=7ab(a+b)(a^2+ab+b^2)^2$$
ocean sealBOT
what do i live for v2.0
agile condor
@oak perch
mortal trellis
so on the left we want 7 factors of 7. on the right we have one of them, so we need 6 more
ab(a+b) can't have a factor of 7, so they all have to come from (a^2+ab+b^2)^2
ocean sealBOT
what do i live for v2.0
mortal trellis
hmm I would probably start slow. first it has to be 0 mod 7, so that probably limits a and b (combined with the other assumption that ab(a+b) is not 0 mod 7)
lone heartBOT
@agile condor Has your question been resolved?
lone heartBOT
@agile condor Has your question been resolved?
oak perch
We can do it graduallyā¦ reduce how much we need to calculateā¦ but still very brutalā¦ like it =0 mod 7, so (a,b)=(1,2),(1,4),(2,4),(3,6),(5,6) mod 7ā¦ then we probably for all (a,b)= any one of those mod 7 for a,b from 1 to 48, solve that thing =0 mod 7^2, then obtain all cases, then do it last time?šš
oak perch
Me neitherš
Just in case, you know. When someone point a gun to our head force us to solve this in order to live , at least we are able to survive š¤£
agile condor
Just in case, you know. When someone point a gun to our head force us to solve t...
ig dying is better
essayons de factorizer $p(x)=(x+1)^7-x^7-1$ en regardant ses racines : on remarque
quāoutre 0 et 1, le nombre complexe $j=2^{2i\pi/3}$est aussi racine car $j + 1 = āj^2$de sorte que
$P(x)$ est divisible par $x(x + 1)(x^2+x+1)$ donc
$$(a+b)^7-a^7-b^7=7ab(a+b)(a^2+ab+b^2)^2$$On est ainsi amenĀ“e a rĀ“esoudre $a^2+ab+b^2 ā” 0\ mod \ 7^3$ $\implies$ $(a+\frac{b}{2})^2 ā”-3(\frac{b}{2})^2 \ mod \ 7^3$ laquelle possede des solutions si et seulement si le symbole de Legendre$(\frac{-3}{7^3})=1$ce que lāon
verifie aisement en utilisant la loi de reciprocite quadratique
ocean sealBOT
what do i live for v2.0
alpine sable
untested brute force code incoming
,tex \pgfkeys{/pgf/fpu}%
\foreach\a in {0,...,100} {\foreach\b in {0,...,\a}{%
\pgfmathsetmacro{\result}{equal(mod(\a^2+\a*\b+\b^2,343),0)}%
\pgfmathfloattofixed{\result}
\pgfkeys{/pgf/fpu=false}
\pgfmathparse{\pgfmathresult==0?1:0}
\ifnum0=\pgfmathresult{(\a,\b)\}\fi
}}
end
ocean sealBOT
Toby
alpine sable
(only up to 100 because latex throws a fit if it goes up to 342)
native gull
I need help sir(s)
ocean pelican
lone heartBOT
ocean pelican
hello can u help me I dont have any idea how can i solve this but i have answer for g(f(x)) = 1/(x-2) + 2
alpine sable
take LCM BROO
hallow vessel
so
i guess u have to expand the g(f(x))
and try and find a relationship
so write the g equation all over 1 denominator
alpine sable
after that sir what do i do
after that compare
hallow vessel
write the equation after putting everything over the same denominator
i feel like alpha u can work out quite easily
in fact I think even without expanding u can work out alpha and beta
ocean pelican
the lcm is 2(xā2)22(x-2)^2
ocean pelican
maybe I'll just close sorry guys my dumb brain stop working.Thanks for helping I'll try this tommorrow
.close
lone heartBOT
hallow vessel
@ocean pelican ping me tmw when u open a channel, im in bed rn