It’d take time
#help-28
torn jolt
in general, there is no easy way to find determinants
worldly jacinth
I mean like a property
torn jolt
if you keep row reducing, you can find the rank of the matrix which would help
torn jolt
yeah
worldly jacinth
So it is zero
torn jolt
yes
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timid magnet
I understand the lemma and it makes sense, but I have no clue on how to start proving this. I added the definition used in this book for more context
timid magnet
ivory cairn
Consider that there's two parts of the sequence
the infinite terms after K and the finite number of terms before K
You know the terms after K are all bounded by a number. gamma
Can you show that there is a bound on the finite number of terms before K?
timid magnet
Are the terms before K bound by the term xi where i=K?
ivory cairn
not necessarily
look at something like 23, 100, 54, 97, pi, 1/2, 1/4, 1/8, 1.16,....
after K=5, they're all bounded by 1, can you find a bound on the first 5 terms?
timid magnet
The first 5 terms would be bound by the max of those 5, so 100?
So can I proof this lemma by saying that the part before i = K, the finite set is bounded by its maximum element. The part after and including i = K is an infinite set but is bounded by some number. This means that the whole sequence is bounded by the max of max(finite set) and the bound of the infinite set?
<@&286206848099549185>
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void quiver
if i want to find the speed of the function, i would find the integral of the function?
fleet briar
if i want to find the speed of the function, i would find the integral of the fu...
No
You find the differential
The integral of distance gives you nothing useful
void quiver
woulnt the differential give me velocity?
vagrant cypress
Could someone walk me through this?
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long quarry
Hello. I have this problem here. Trying to find dy/dx of the initial problem (1st line). I need to take d/dx of both sides, and that involves chain rule for the left side here, but I believe I did it wrong, as nothing in terms of dy/dx came from it
quaint prawn
honestly, I can't tell what you were getting at with your work there. But the process would be to take the derivative of x of everything. For sin(x) you will got cos(x) . For cos(y) , well first the derivative of cos is -sin, so you will get -sin(y) but then apply the chain rule, multiply by the derivative of y with respect to x (which is dy/dx) and you get -siny dy/dx. Then continue the process on the right hand side of your equation. Derivative of 7x is 7, derivative of -2y is -2 dy/dx
and then solve for dy/dx
long quarry
Ok. I don't understand how the derivative of -2y is -2 dy/dx. Why is that?
quaint prawn
well -2 is a constant so it stays, and then you have to take the derivative of y with respect to x
which is dy/dx
long quarry
Ok, that makes sense, thank you
quaint prawn
no problem
long quarry
I am still confused on the left though. So I know the chain rule is f'(g(x))g'(x), so I wrote out f(x), g(x), f'(x), & g'(x). So those are incorrect from what I know now
quaint prawn
you are incorrectly applying the chain rule
on the left hand side the functions are seperated by addition, so you do their derivatives seperately
first take the derivative of sin(x)
long quarry
Ah
quaint prawn
that does not require chain rule
then take the derivative of cos(y)
this does require chain rule, and you must account for the derivative of the inner function "y"
long quarry
Hang on. I don't understand then why chain rule applies when taking the derivative of cos(y). Wouldn't it just be -sin(y)?
quaint prawn
Well , the reason the chain rule "didn't appear" for sin(x)
is because the inner function was just x
so the chain rule would be multiplication by 1
which we don't need to write out
or do
but when the function is y
and we are taking the derivative with respect to x (not respect to y)
the derivative isn't 1
it is whatever dy/dx is
long quarry
Gotcha, that makes more sense now
quaint prawn
no problem
long quarry
So what would my f(x) and g(x) be? I usually base those off of what is happening to x
Would I base it around what's happening to y?
quaint prawn
there is no need to writing out f(x) and g(x) every time you apply the chain rule, you should get used to what it is actually doing without having to write out every step
but
if it helps you out
f(x) would be cos(y)
and g(x) would be y
so f'(x) would be -sin(y)
and g'(x) would be dy/dx
and that is the only place where it is necessary
for this problem
long quarry
Gotcha. Why is f(x) the one that is cos(y)? I would think f(x) and g(x) would swap here
Or would that just produce the same result?
quaint prawn
I referred to f(x) as the outer function and g(x) as the inner function, I am not sure exactly what notation/method you use to write it down, but I recommend you ease off of using it
chain rule is just when you have a composition of functions, or multiple functions inside of eachother
it is called chain rule because you do a chain of derivatives
derivative of the outer function, times the derivative of the inner function
along the chain for as many as you have
long quarry
I usually do the opposite. Would those be the same then, if I defined f(x) as y and g(x) as cos(y)?
quaint prawn
I'm not sure why you would do that, or really what you are asking
if the notation is confusing you I recommend you stop using it
Can I just give you a few examples quickly?
long quarry
I'm just asking if my notation is the same as yours in the end. You defined f(x) as cos(y), and g(x) as y. If I were to swap what f(x) and g(x) were defined as, would I get the same answer?
And sure.
quaint prawn
I don't think that you would
so
,, f(x)=(\cos{y})^{2}
if we had something like this
glossy valveBOT
AustinU
quaint prawn
and you had to take the derivative of it
long quarry
Sure
quaint prawn
we have 3 functions here
the outermost is squaring
middle is cosine
and inner is y
so do the outermost first
2(cos(y))^(2-1)
long quarry
I haven't dealt with a middle function yet, this will be interesting
quaint prawn
which is just 2(cos(y))
and then you move to the next function
so derivative of cos(y) is -sin(y)
2(cos(y))*-sin(y)
long quarry
then innermost is dy/dx
quaint prawn
and then you move to the innermost
yup
and you
get
2(cos(y)) * -sin(y) * dy/dx
See how we did like a chain of derivatives
start from the outside, go to the inside
long quarry
So you just find the derivatives of all the functions, then multiply them together?
quaint prawn
kind of yes, but the order matters
that is what the chain rule is at its core
take the derivative of the outer function, multiply it by the derivative of the inner function
so if you have
f(g(x))
its derivative is f'(g(x)) * g'(x)
long quarry
Gotcha, let me try and apply that to cos(y) then with respect to x
So forgetting what f(x) and g(x)
The outtermost function is cos(y)
The derivative of which is -sin(y)
Then the innermost function is y, whose derivative is dy/dx
So multiplying those together would get -sin(y) * dy/dx, would that be correct?
long quarry
I think I will be doing chain rule like that from now on then, that was easier on my brain
Thank you very much for teaching me that
long quarry
I think I got it from here then, thank you so much again
quaint prawn
yah no problem, feel free to DM me if you need more help in the future
long quarry
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daring epoch
how many perfect squares leave remainder 3 if divided by 11
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how many perfect squares leave remainder 3 if divided by 11
@daring epoch Has your question been resolved?
worthy tree
how many perfect squares leave remainder 3 if divided by 11
you can express it as n² = 3 mod 11
replace n by :
11 k
11 k + 1
11 k + 2
11 k + 3
.
.
.
11 k + 10
and see if the hold for them
@daring epoch
quaint prawn
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quaint prawn
Could someone confirm that is correct?
stable heart
yeah that looks right
quaint prawn
ok thanks
worthy tree
that's what i found too
glossy valveBOT
AustinU
quaint prawn
<@&286206848099549185>
I am hoping someone can check my work for these two problems?
My solution to the second image is the latex directly above
nvm
.close
long quarry
Continuing a problem from before, moved here to reference a message
long quarry
Gotcha, let me try and apply that to cos(y) then with respect to x
So around here is where I recently learned how to do the chain rule in a different thinking method @simple totem
long quarry
x+y
simple totem
so f'(x) = ?
long quarry
So cos(x+y), gotcha
simple totem
yes
long quarry
I made that more complicated in my brain than it needed to be
Ok, I think I got it now. I'll keep moving along with these practice problems and do more practice
Thanks for the help
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torn jolt
Reopen
solar olive
I mean yeah but did you try solving it, which part of it are u stuck on?
solar olive
Lemme solve n check
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Well I got a answer
Show your work, and if possible, explain where you are stuck.
torn jolt
solar olive
yea cause it's v^2 so if the value of v is 5, u'd need to take 5^2
glossy valveBOT
Tammy
solar olive
yup
light sonnet
Wait I dnt understand
On your paper, you wrote v^2 in the denominator, but you only did 5, but not 5^2
torn jolt
Well it says as the square of v
solar olive
yeah, the value of v is given, not v^2, so u'd need to take the square urself
solar olive
yes
torn jolt
That why
solar olive
try solving with that and see if u get it
solar olive
At what?
solar olive
Oh why'd you remove the k
torn jolt
Wait did u already get it ??
solar olive
Yeah
torn jolt
Is it 0.57?
solar olive
In variance firstly you need to get the answer of k and then u can find what the actual question asks
no?
torn jolt
Is what I have there so far correct
solar olive
not rlly, u're moving straight to R, u need to find k first
move the values around so that you get k on one side and the other values on the other side of the equals mark
torn jolt
Right
solar olive
try solving and lemme know then
solar olive
how
torn jolt
solar olive
remember it's v squared
light sonnet
You keep forgetting, it's v**^2**
torn jolt
Right so 16
solar olive
yeah
torn jolt
5.25?
solar olive
okay
torn jolt
solar olive
alr lemme
torn jolt
Ight bet bet
torn jolt
Not yet still reading
solar olive
do u understand it?
solar olive
the time, it's given in hours, u need to convert that to minutes first
torn jolt
540?
solar olive
yea
torn jolt
Wait
solar olive
now find k
solar olive
because we always convert it to minutes
unless the question asks for hours
minutes is like the standard, otherwise just writing 9 wouldnt tell us whether we're talking about hours or minutes so it's just understood to be in minutes
torn jolt
Ans 60?
torn jolt
minutes is like the standard, otherwise just writing 9 wouldnt tell us whether w...
Ohhhh okay
solar olive
not .2 of an hour
it says 6.2 hours
convert 6.2 hrs into minutes just like u did last time
torn jolt
So 372?
solar olive
yeah
torn jolt
40?
torn jolt
Okayy
torn jolt
Ohh okay then
I can send it to u later
To check
I got an answer but
Close
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floral rampart
When I get to my second derivitive, I know to plug in x for 3. How do I determine what to plug y in for?
Do I plug x=3 into my original formula and to determine what my plug in for my y value should be?
simple totem
yes
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livid locust
Prove that for $ x > y > 0$, and $x, y, \in R$, $|\frac{1}{x}| + |\frac{1}{y}| \ge \frac{x-y}{xy}$
glossy valveBOT
chromium
junior willow
Prove that for $ x > y > 0$, and $x, y, \in R$, $|\frac{1}{x}| + |\frac{1}{y}| \...
multiply by xy and u have $|y|+|x| \ge x-y$
glossy valveBOT
4321
junior willow
and then u alr know that x and y are positive so idk what the abs value was for in the first place but
so then u can add y and u have $2y \ge 0$
glossy valveBOT
4321
glossy valveBOT
4321
livid locust
tf
you're not meant to prove
x > y > 0
you're not meant to directly use the proofs statement either
and assume anything there is true
this needs to be proved
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quick grotto
yo, what is arctan(-infinity)?
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yo, what is arctan(-infinity)?
quick grotto
apparently it's pi/2 but how?
trail barn
so infinity in general is not a number, but you can just think of it as a really really big one, and if you stay large everything works roughly the same, that's the answer
that's a bit poorly worded but I'll explain for this concrete example later
so you want an angle so that opposite over adjacent is really large, because that's what tan is
a diagram
explanation with this example, as long as the right/opposite side is really big, the hypotenuse is basically vertical regardless of how big we go
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twin herald
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twin herald
Hi guys, for some reasons I keep getting error for this qs
even though I applied the correct formula
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open crystal
Which parenthesis can I use in this situation?
□ { [ ( ) ] } □
I want to use parenthesis in '□'
fervent lava
for what equation or question do you want to use parenthesis for?
wild sleet
they showed it
that's the exact "expression" they want to use them in
double round makes sense
or like, bold round?
open crystal
Like (( { [ ( ) ] } ))?
tiny shoal
Show that ln((e^x-1)/(e^x+1)) = 1 if and only if e^2x-2e^x-1 = 0
tiny shoal
I don’t know where to start this question i have never come across a question that looks like that
vast fossil
If
[
\ln(\frac{e^x-1}{e^x+1}) = 1
]
Then
[
\frac{e^x-1}{e^x+1} = e
]
Right?
glossy valveBOT
A Lonely Bean
tiny shoal
**A Lonely Bean**
But yes this is true
vast fossil
I found that e^x = (1+e)/(1-e)
You could plug that into e^(2x) - 2e^x - 1 = 0 and see if the equation is true
vast fossil
Put (1 + e)/(1 - e) instead of e^x and (1 + e)^2/(1 - e)^2 instead of e^(2x)
tiny shoal
Hold on a second Let me do that
vast fossil
Or just solve e^(2x) - 2e^x - 1 = 0
tiny shoal
Or just solve e^(2x) - 2e^x - 1 = 0
x=ln(1+ square root of 2)
vast fossil
I highly doubt that it's the same as (1 + e)/(1 - e)
tiny shoal
I highly doubt that it's the same as (1 + e)/(1 - e)
?
vast fossil
1 + sqrt2 isn't the same as (1 + e)/(1 - e)
So the statement is false as long as you've done everything correctly
vast fossil
Show that ln((e^x-1)/(e^x+1)) = 1 if and only if e^2x-2e^x-1 = 0
That's what the statement is saying 
Ight let me try
tiny shoal
Ok ok
vast fossil
I got e^x = (1 + e)/(1 - e) as the solution to the first equation as well
Let's now see the second equation
e^(2x) - 2e^x + 1 = 2
e^x = 1 + sqrt2
The solutions don't match up
tiny shoal
Nevermind i found the answer
vast fossil
Show that ln((e^x-1)/(e^x+1)) = 1 if and only if e^2x-2e^x-1 = 0
So this statement is false
tiny shoal
I found it was true
Because
When you resolve e^2x-2e^x-1=0
You find that x = ln(1+ sqrt 2)
vast fossil
Right
tiny shoal
And when in f’(x) you replace x by ln(1+ sqrt 2) it equals 1
vast fossil
Why f'(x)?
tiny shoal
Because i have to show that f’(x) = 1
vast fossil
And what's f'(x)?
tiny shoal
And f’(x) = (2e^x)/(e^2x-1)
So you just replace x by the solution of the other equation and you find 1
vast fossil
You were sayng ln((e^x + 1)/(e^x - 1)) though
tiny shoal
That’s something else i think sorry if i drove you on the wrong path but you helped me find the answer still so thank you
vast fossil
Alright
tiny shoal
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rotund blade
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next venture
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next venture
how do I continue after expanding the (2x - 1/x)^8
sharp flame
What's the question
swift sequoia
uuh
swift sequoia
how do I continue after expanding the (2x - 1/x)^8
expand or factor
sharp flame
Lol
swift sequoia
aah
autumn kestrel
are u aware of binomial expansion?
sharp flame
Sure
sharp flame
In ascending powers of x?
next venture
yep
sharp flame
independent term of x
Wait the independent term or the first three terms
autumn kestrel
mostly these questions have to do with finding out the coefficient of x^t
next venture
independent term i think
i had a question on it
and idk how to do
first 3 term is easy
sharp flame
And what would be the power of x if the term is independent of x?
swift sequoia
use the properties of the exponent
undone kettle
I think 5th term will be independent of x of the expansion (2x - 1/x)^8
next venture
Wait the independent term or the first three terms
8-2r
sharp flame
?
undone kettle
Yes
next venture
yeh
swift sequoia
(x+3)(2x^2-1/x)
sharp flame
In this case however, you need to find a term with power of x 0 and -1 assuming they both exist
next venture
(x+3)(2x^2-1/x)
???????????????
sharp flame
And them up
swift sequoia
use the properties of the exponent
.
sharp flame
I think I'll let jk handle it, ping me if you need me
undone kettle
Use binomial theorem for this question
next venture
okay
swift sequoia
(x+3)(2x^2-1/x)
then use this to calculate
next venture
how tho
i got 1120 for the term independent of x
do i sub it in
1120 times (x+3)?
sounds wrong
swift sequoia
wait its (x+3)(2x^2 -1/x)^8
next venture
yea
swift sequoia
then
undone kettle
Take general term first :
undone kettle
Do you know how to solve 8C4?
undone kettle
Okay
next venture
yep
sharp flame
,w C(8, 4)
glossy valveBOT
swift sequoia
(x+3)(2x^2 -1)^8/x^8
undone kettle
next venture
ye
the question now is
how to sub in the term independent of x into (x+3)
do i just do it directly
undone kettle
(3 + x ) (1120)
3360 + 1120 x
undone kettle
do i just do it directly
Yes
undone kettle
Yes
undone kettle
Nope
undone kettle
👍 np
next venture
thank youuu
undone kettle
i always panic when these questions come out
I myself haven’t practiced this chp much 💀
next venture
omg
undone kettle
If it’s done then close this ticket
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opaque cedar
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dire rampart
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dire rampart
Idk how to solve iii
short vector
Ok so
l is parallel to the tangent at point P, meaning it has the same slope (gradient)
Since in the previous question you showed that it was 4, l is of the form y = 4x + b
But you also know it intersects the curve at x = -2
dire rampart
but shouldnt I use the tangent at p
short vector
For?
dire rampart
the gradient
which is the negative reciprocal of the original gradient of point p
-1/4
short vector
That would be perpendicular to the tangent
The gradient almost by definition is already the number m such that y = mx + b is tangent to that point
dire rampart
I'm very foncused
short vector
Look
dire rampart
is it asking for the tangent of the curve or the tangent of the gradient of the curve ??
short vector
Here is the graph
short vector
So the number you found earlier tells you the gradient
Which was 4
And we want the line to be at (1,0)
So it’s y - 0 = 4(x - 1)
dire rampart
ohh ok
short vector
If we try at 0 for example, 6(0)^2 + 6(0) - 8 = -8
And the point is 0, 3
So y - 3 = -8(x - 0)
If you don’t use P’s y value, the line is properly angled but not in the right place
The equation “6x^2 + 6x - 8” just tells you the angle it needs to be at that x value
And you have to subtract by the x and y to get it in the right place
Back to the question, the first sentence is “the line l is parallel to the tangent to the curve at point P”. For two lines to be parallel, they have the same gradient, and we know that the tangent line to point P has a gradient of 4 (from 6(1)^2 + 6(1) - 8) so we know that l must also have a gradient of 4
We also know that the curve touches l at x = -2, but at x = -2 the curve has a y value 15, so we can write y - 15 = 4(x + 2)
Here the green line is the tangent at P
And the red line is the one parallel to it
That touches at x = -2
dire rampart
We also know that the curve touches l at x = -2, but at x = -2 the curve has a y...
hold up where'd you get 15 from?
short vector
Same way you got 3 for x = 0
f(-2) = (2(-2) - 1)(-2 + 3)(-2 - 1)
= (-5)(1)(-3)
= 15
If you know the x value is -2, then you can also know what they y value of the curve will be
And just based on observation, (iv.) will also be true, but you can easily check by just making sure that 6(-2)^2 + 6(-2) - 8 is 4
dire rampart
ahh ok sorry im slow at catching up lol
short vector
Np
If you have any questions about any part, feel free to ask
Even if it’s something simple
dire rampart
so equation for l is y=4x+23, correct?
dire rampart
but for iv it's asking to prove that it's the tangent not the gradient
short vector
?
Oh
So to check if it’s the tangent
You need two things
- Same gradient
- Same place
dire rampart
oh yeah the tangent is the gradient at a point
short vector
But you already made sure it was in the same place at x = -2 because that was what the previous question asked of you
“It touches the curve at x= -2
dire rampart
ahh ok
short vector
You can always check again tho
dire rampart
I think what tripped me up is the fact that the gradient for the cubic is a quadratic and not a straight line
dire rampart
and we keep treating it like a line
short vector
Yeah
It’s the formula for the gradient of a line
Not the line itself
That’s a good thing to remember
dire rampart
but then shouldnt the gradient at p be a quadratic
otherwise we should have found d2y/dx
dire rampart
oh yeah i meant the equation for it
dire rampart
wait wait never mind I get it now haha
thank you so much for your help I get it now :)
short vector
Np :)
dire rampart
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torn jolt
If "x^4+mx^2+nx^3+4x+4" is equal to a square number, what is the minumum value of the sum (m+n) ?
torn jolt
I've tried to factor out the polynomial and tried to find some identities like opening of the (x+y)^2, (x+y)^3 or something like that, but the result is nothing but a mess. It gotta be about factoring and identities but I just couldn't see what to do.
glossy valveBOT
torn jolt
So we get m+n= 4k+6k^2 ?
sharp flame
Yup
torn jolt
And minumum value of thatvwould be 2
sharp flame
Now maybe use derivatives to find the lowest value of that function
sharp flame
And minumum value of thatvwould be 2
Would it 
sharp flame
I don't think it needs to be an integer?
torn jolt
But the expression is equal to a square number so if it equals to (x+k)^4, then...
sharp flame
It equals a square number?
torn jolt
Yes
sharp flame
Which means it's a perfect square for all values of x huh
Which means (x + k)^4 won't work
torn jolt
Yeah
And also i dont think were gonna need derivatives
Because its under the topic of factorization
sharp flame
Have you tried assuming a general equation like (x^2 + ax)^2 and then comparing coefficients
,w expand (x^2 + ax)^2
glossy valveBOT
sharp flame
Although this doesn't give us an x term
torn jolt
Yep
sharp flame
,w expand (x^2 + ax + b)^2
glossy valveBOT
glossy valveBOT
NEONPerseus
sharp flame
This seems to be somewhat consistent
m = a^2 + 2b
n = 2a
4 = 2ab
4 = b^2
But this gives us a concrete value for m + n doesn't it
sharp flame
What did you do
torn jolt
we need the minumum of m+n
Gave b -2 and a will be -1
And that would give us min. value of sum
sharp flame
I was thinking about that but I'm not sure if it's right
Which is why I didn't say it
Actually I think it should be right
Because a quartic as a perfect square should be factorable into two identical quadratics
torn jolt
Yes its right
sharp flame
,w factorize x^4 -2x^3 -3x^2 + 4x + 4
glossy valveBOT
sharp flame
Yup seems good
torn jolt
But how do you manage to equal the expression to (x^2+ax+b)^2
Like they didnt teach us a thing likemthis in this topic
sharp flame
But how do you manage to equal the expression to (x^2+ax+b)^2
It said that it's a perfect square
If it is a perfect square it should be factorable into two identical factors
And for a quartic that would have to be two quadratics
Since the two quadratics multiplied together would give us a quartic
torn jolt
Yeah right thanks I would keep in mind that👍
sharp flame
Just remember comparing coefficients like this is pretty powerful
torn jolt
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tranquil glacier
Guys i need help here
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Guys i need help here
tranquil glacier
i need to turn in today...
proven jay
is it math?
jade radish
this is stats
jade radish
Guys i need help here
also biases are things that impact the scenario but aren't the variables being controled... so if u think about that, u can just read and see what might be some biases
like for example
the first one
the director asked staff near their office
but didn't ask all the people in the company
also near their office during COVID-19 also is excluding those who are working remote, or hybrid and today they weren't in for ork
so that'd be a bias
This is called undercoverage
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@tranquil glacier Has your question been resolved?
median cedar
$ln²(x) - 2ln(x) - 4 =0$
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$ln²(x) - 2ln(x) - 4 =0$
glossy valveBOT
Amer
median cedar
teacher said it's positive after e³, i try to plug e⁴ for example but i find it negative :/
torn jolt
solve for x?
median cedar
i plug e⁴ and the answer is negative, it shouldn't
robust slate
teacher said it's positive after e³, i try to plug e⁴ for example but i find it ...
Send your working - mental math gives me 4
median cedar
(4)² - (4)² - 4 = -4
glossy valveBOT
Civil Service Pigeon
grave elm
median cedar
teacher said to always return a.lnx to lnx^a
heavy wolf
teacher said to always return a.lnx to lnx^a
That would still be ln((e^4)^2)
Which is equal to 8
heavy wolf
If you have x*ln(a) you aren’t taking the ln(a) to the power of x but rather the a term to the power of x
I do not, however I think YouTube would have some good videos on it
median cedar
If you have x*ln(a) you aren’t taking the ln(a) to the power of x but rather the...
makes sense
thanks
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hollow moth
is there a mistake in this:
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is there a mistake in this:
hollow moth
because N can be 0, and r can also be 0, right?
and 0^0 is undefined
should I assume it means N > 0?
smoky heron
It would not mean 0/0, for example: plug in r = 0, this would give 0^N+1 - 1 / 0 - 1 which is simply 0. If N = 0, (r-1) is independent of N meaning this would also not result in an undefined term.
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@hollow moth Has your question been resolved?
hollow moth
It would not mean 0/0, for example: plug in r = 0, this would give 0^N+1 - 1 / 0...
no but you can also plug in N = 0
oh wait
never mind, thank you!
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alpine chasm
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alpine chasm
Can someone help me understand why knowing that E(X^4) < inf is useful?
Is it just something that tells us that we can be ensured that E(X^2) is less than inf which is used throughout the task is less than infinity, hence it can be evaluated to a numerical value since its not infinite?
<@&286206848099549185>
fervent ocean
ok
fervent ocean
huh
what do you mean what do i mean ?
i was just asking if anyone needs help
im willing to help
alpine chasm
I asked a question regarding math and you responded with "ok".
alpine chasm
Oh I thought you wrote in the wrong channel
fervent ocean
i dont have time for peoples bullshit
alpine chasm
You woke up on the wrong side today?
Well Ima open a new chat to ask this question because the chat is now flooded with stuff that is irrelevant to the problem
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atomic blade
Just checking my terminology. The function f(x,y,z) = xyz is "odd"?
atomic blade
Well I mean
torn jolt
I thought odd was only defined on funcs of 1 variable
but ig you could define if f(x,y,z)=-f(-x,-y,-z) then f is odd
atomic blade
Like because I have to do $\int_{-1}^{1}\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{x^2+y^2}^{2-x^2-y^2} (xyz)\dd z \dd y \dd x$
glossy valveBOT
Umbraleviathan
torn jolt
you could say its odd when viewed as a function of x etc
atomic blade
Hm
I have to hand solve this integral ://
Shdhdhd
,w expand 1/2 xy (2-x^2 - y^2)^2 - (x^2 - y^2)^2)
HA doesn't make it any better
torn jolt
thats an even function wrt y :p
glossy valveBOT
atomic blade
Yeah no that's way too convulatedfor my course
fleet briar
I have to hand solve this integral ://
i guess spherical coordinates wouldnt work here
torn jolt
hmm
atomic blade
The surface is like an funky egg
torn jolt
🥚
atomic blade
Centered evenly around the z axis
Actually it's just bounded by x^2 + y^2 and 2 - x^2 - y^2
So it is an egg of some sort
Sadly I can't see a 4D plot
torn jolt
,w int from y=0 to y=sqrt(1-x^2) of (xy(2-x^2-y^2)^2/2-xy(x^2+y^2)^2/2) dy
glossy valveBOT
atomic blade
With a small ass space
Oh I could
But we're never expected to square a trinomial
In fact that was a guanratee in the course ....
Verbatim
Bruh
Scam
torn jolt
interesting guarantee 
atomic blade
I hate squaring trinomials
torn jolt
I hate squaring trinomials
its squaring 3 binomials!!!1!!1
atomic blade
NO
torn jolt
torn jolt
But we're never expected to square a trinomial
u sub for x^2+y^2
atomic blade
Jacobians 💀
torn jolt
huh?
atomic blade
Oh wait
torn jolt
just treat it as a function in y
atomic blade
That's genius
torn jolt
ignore x until you finish the du integral
torn jolt
yeah
atomic blade
Wouldn't the u-bounds be 1 and 1
torn jolt
yes
atomic blade
Wait but
torn jolt
it only becomes zero when we do the dx integral
torn jolt
x^2+sqrt(1-x^2)^2=1
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torn jolt
LOL
atomic blade
FUCK
torn jolt
i saw that
torn jolt
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vague elbow
why doesnt the fibbonachi numbers have one of these patterns
vague elbow
what are you doing there
torn jolt
the red lines match the number from the top row to a number on the second row
torn jolt
what "thing"?
vague elbow
let me find it
spice orchid
i suspect method of differences for finding the nth term of a sequence is what youre talking about
vague elbow
spice orchid
that only works if the nth term is a polynomial in n, which fibonacci isnt
vague elbow
whats n
spice orchid
the nth number
vague elbow
is n a variable
spice orchid
yes
spice orchid
long story short fibonacci just isnt the right kind of sequence to apply that technique to
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vague elbow
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jade radish
it's closed already
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solar grail
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solar grail
I don't understand what steps are taken to get a^2-6a + 8
solar grail
Ohhhhh
a^2 +8 *(1) = 6a
Yeah that makes a lot of sense
thank you!
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pallid veldt
I need help with this, i keep getting the answer -13/20 and apparently it’s wrong, i even tried doing the decimal, by the way it’s pedmas.
atomic venture
thats the right answer though
kind jay
,w (1/8 * 3/4)/(5/8) - 4/5
polar valve
I need help with this, i keep getting the answer -13/20 and apparently it’s wron...
why should -13/20 be wrong?
kind jay
,w -13/20
pallid veldt
I did that
Decimal form didn’t work neither
Its like a pixel art
And it should show the rest of the picture
But it didn’t
See look
polar valve
come on, how should we know which question it was? and can you post the original question, not the screenshot of a calculator?
pallid veldt
that was the original question?
The number 6 is the last one i need on that damn page
As you could see.
polar valve
why should -13/20 be wrong?
Have you answered this?
pallid veldt
no
it should be wrong because it would show the rest of the among us character if i was right.
But I don’t know
polar valve
more than one user says -13/20 is right, wolframalpha.com says -13/20 is right. you can not explain in a convincing manner why it should be false.so i do not see a problem which i can help to solve. therefore: ok, i am out.
pallid veldt
What ever
I think its right
I turned it in
But can i ask another thing in this comment section
Because i need help with a finding the surface area of triangular prisms
But i have to find the nets triangular prisms surface area.
fiery valve
can someone explain this step to me
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can someone explain this step to me
atomic blade
For the numerator, change 4u + 1 to 4u + 2 - 1
Then split the fraction appropriately
fiery valve
For the numerator, change 4u + 1 to 4u + 2 - 1
oh wow
how do i practice for these type of fraction problem
i sometimes have trouble knowing how to find them