you don't even need to do that, you can just plug and chug from the options they gave you
#help-42
finite oasis
polar bison
it's easier to use variable separable 1 step
primal bear
is there a name you can give to this type of DE
stuck sail
Remove the constant C by writing e^c *e^(x^3/3)
hearty tusk
like this?
stuck sail
like this?
Ye
primal bear
like this?
you should write a step before this
hearty tusk
?
primal bear
just write a $y=e^{\left( \frac{x^3}3 + C\right)}$ thing
potent lotusBOT
Percy
hearty tusk
isnt it same?
primal bear
it is
hearty tusk
then why
show your work
potent lotusBOT
Percy
primal bear
but skipping the middle step is kinda weird
anyway if this isnt work thatll be corrected its a-ok
calm coralBOT
calm coralBOT
Available help channel!
digital scaffold
Help
digital scaffold
<@&286206848099549185>
pallid halo
what did you try so far?
digital scaffold
what did you try so far?
I tried to do this
But now I do not know how to calculate the integration for 1/2pi * e^-(x2+y2)/2
pallid halo
try polar coordinates?
digital scaffold
no no no, I dont know these things
pallid halo
well then do the substitution you mentioned above, it's equivalent
digital scaffold
hmm but how do I write dx dy in terms of rho and theta?
Like if it were single variable, its ez
pallid halo
dx dy would be a da dtheta using your variable a
digital scaffold
how??
pallid halo
well you could compute the jacobian of the transformation in the usual way
or make a geometric argument
digital scaffold
well you could compute the jacobian of the transformation in the usual way
don't know this too
pallid halo
well have you done two dimensional integrals using polar coordinates before?
if so, how did you do it?
this is usually covered in multivariable calculus, did you take it yet?
digital scaffold
No, we have this course next sem
pallid halo
ok
you could use a "physics" type of geometric argument for now
see for example this figure
pallid halo
the region marked dA has area approximately equal to (dr) times (r d theta) if dr is small
pallid halo
yea don't sweat it too much, you will learn it properly in multivariable calculus
digital scaffold
So is it out of scope for now? As I have a quiz tomorrow
pallid halo
yea i mean i think you're gonna have to use polar coordinates to make this tractable but i could be wrong
it's nasty in xy coordinates
pallid halo
np
is this question from your course or are you doing like extra problems that you found elsewhere?
digital scaffold
is this question from your course or are you doing like extra problems that you ...
It was in the course texbook
pallid halo
hmm ok, would be interesting to see what their intended solution is
maybe they're assuming you already know some MVC?
digital scaffold
maybe they're assuming you already know some MVC?
Maybe, but our course had no pre reqs as such, only SVC and Linear Algebra
digital scaffold
ya
carmine umbra
Can anyone help me
calm coralBOT
pallid halo
yw
pallid halo
Can anyone help me
you can open your own channel, see #❓how-to-get-help
calm coralBOT
Available help channel!
median cloak
Convince me
calm coralBOT
Convince me
grand glacier
Are you sure it‘s ab=8 and not ab=-8?
Because if it‘s ab=8, then your solutions don‘t work
median cloak
ab=-8
grand glacier
Okay then yeah your solutions are correct
velvet osprey
Is (a,b)=(-4,2) or (2,-4) the only two solutions
do you think there are others? why or why not?
median cloak
do you think there are others? why or why not?
I doubt that there are solutions contain a and b being fractions
median cloak
do you think there are others? why or why not?
And How do you know there are only two solutions?
When it can be more than two
velvet osprey
ok, there are multiple different ways to explain this
do you know how to solve quadratic equations?
also known as equations of the 2nd degree?
velvet osprey
ok then a and b are roots of the equation x^2+2x-8=0
based on their known sum and product
median cloak
ok then a and b are roots of the equation x^2+2x-8=0
It is 4 or -2=x, should the equation hold
median cloak
but -4 and 2
You are right
So there’s two solutions based on our analysis and knowledge of quadratic equations
What about the another way to determine the number of solutions?
velvet osprey
"the another" -> "another"
anyway, ok
take the equation a+b=-2 and square both sides. you will get:
a^2 + b^2 + 2ab = 4
winter elbow
velvet osprey
in the equation ab = -8, multiply both sides by -4 and get:
-4ab = 32
add these equations together:
a^2 + b^2 + 2ab - 4ab = 4 + 32
a^2 + b^2 - 2ab = 36
(a-b)^2 = 36
@median cloak do you understand up to here?
median cloak
Sure, they are simple computation
velvet osprey
yes now
here comes the big insight
from (a-b)^2 = 36, we get that a-b=6 OR a-b=-6.
velvet osprey
and then we have in each case a system of two linear equations in two unknowns
ah
sorry i made a big typo
3 times
no, 4
ok fixed everything now
velvet osprey
And given ab=-8
we do not need that anymore!
median cloak
Sure
velvet osprey
ok, now the other case:
a+b=-2
a-b=-6
median cloak
It is the other way around:a=-4, b=2
Is that it?
The results tell there are only two solutions, and so be it.
Is that method differs from the former one but a little tweak on how to solve the these variables.
velvet osprey
well it is a big difference
i do not rely on knowledge of how to solve quadratics anymore
only on knowledge of what a square root is
and that any positive number has two square roots: one positive and one negative
calm coralBOT
@median cloak Has your question been resolved?
indigo spoke
hello i need help with mastering integration, like just any ways i can excel in it
leaden thunder
lot of practice problems
indigo spoke
hello i need help with mastering integration, like just any ways i can excel in ...
im planning to do the STEP exam for cambridge entrance exam and the integration questions are wild, so does anyone know how to become a god at it
leaden thunder
do easy problems first
indigo spoke
but like are there any formulas or stuff they teach outside of school for example
indigo spoke
or should i just be able to do any type of integration from the rules we learnt
primal bear
sure
indigo spoke
ancient grotto
Okay, have you tried anything?
indigo spoke
everything and i failed
ancient grotto
everything and i failed
You tried integration by parts on 2sqrt(1+x^3)?
indigo spoke
You tried integration by parts on 2sqrt(1+x^3)?
it doesnt really make much sense tho, cause theres no two functions multiplying with each other in that part
the 2 is just a constant
indigo spoke
but then i would assign 2 as U
and when i do the integral i dfiferentiate it no?
so in the end ill have to integrate the sqrt(1+x^3) anyway
ill try it with v maybe
ancient grotto
Hmm.
void kite
wait when you derivative the function under the root and intergrate the 2 will it not become substituion afterwards?
ancient grotto
,texsp $\begin{matrix}\quad &D&I\+&\sqrt{1+x^3}&2\-&\frac{3x^2}{2\sqrt{1+x^3}}&2x\end{matrix}$
potent lotusBOT
;(
indigo spoke
wait when you derivative the function under the root and intergrate the 2 will i...
ive been trying to integrate the sqrt(1+x^3) by itself but im getting to a dead end all the time
ancient grotto
wait when you derivative the function under the root and intergrate the 2 will i...
Huh?
ancient grotto
||integrate the 2.||
Hence, differentiate sqrt(1+x^3).
void kite
ive been trying to integrate the sqrt(1+x^3) by itself but im getting to a dead ...
pretend the root is 1/2 and just put it beside it and itll become like this after derivative|| 1/2(1+x^3)^-1/2*3x^2||
ancient grotto
pretend the root is 1/2 and just put it beside it and itll become like this afte...
||I’ve already suggested it. I also recommend you spoiler anything that involves the solution.||
void kite
||I’ve already suggested it. I also recommend you spoiler anything that involves...
sorry
indigo spoke
oh wait im tryin gi tnow
ok so when i integrate the 2(1+x^3)^1/2 individually i get another integral that matches the second part of the original
very weird
the second part of the integral is where im mainly confused abt tho
void kite
ok so when i integrate the 2(1+x^3)^1/2 individually i get another integral that...
do u mind showing your work?
i want to check something
indigo spoke
ill rewrite it hold on
void kite
tyt
ancient grotto
Oh, wait, I’m a dumbass. There’s a faster method.
ancient grotto
Try integration by parts in the second term.
void kite
yippe
indigo spoke
ancient grotto
,rccw
indigo spoke
the underlined part is from integrating the first part using parts
potent lotusBOT
ancient grotto
Nice.
void kite
thx
ancient grotto
Oh, fuck, is this product rule?
indigo spoke
ye thats what integration by parts is
ancient grotto
:angery:
indigo spoke
reverse product rule
ancient grotto
No, like, an exact form.
indigo spoke
kinda
ancient grotto
Notice what happens.
indigo spoke
ima try it myself and lyk if i get stuck
most likely will
alr thankfully this one was easy
it was pretty similar to the first part
yo how does integration by parts work if theres limits?
cause i only integrate half of it at first
vague vigil
yo how does integration by parts work if theres limits?
the same
dull coral
Hello, I've been asked to find N's contact details, but I'm not very convinced of my results. I'd just like you to check this before continuing my exercise.
calm coralBOT
Hello, I've been asked to find N's contact details, but I'm not very convinced o...
@dull coral Has your question been resolved?
dull coral
.close
calm coralBOT
dawn jay
I NEED MATH HELP
calm coralBOT
Available help channel!
eternal shard
I NEED MATH HELP
.you were too fast
eager crown
Can anyone help me to prove that for a, b,c real positives
$8(a^3 + b^3 + c^3) >= (a+b)^3 + (b+c)^3 + (c+a)^3$
potent lotusBOT
Gust4vooo
eager crown
I tried $8(a^3 + b^3 + c^3) = (2a)^3 + (2b)^3 + (2c)^3$ and letting a>=b>=c but did not work and i tried expanding too and did not work and idk what to do
potent lotusBOT
Gust4vooo
sweet stag
no need
just expand (a+b)^3 & (a+c)^3 & (b+c)^3
simplify what u can simplify
and use a^3 +b^3 >= ab(a+b) for you to do the proof its fairly easy @eager crown
open hazel
**Gust4vooo**
Expand then use Muirhead u have 24 terms in both sides and (3,0,0) majorizes (2,1,0)
eager crown
Expand then use Muirhead u have 24 terms in both sides and (3,0,0) majorizes (2,...
Sorry idk what Muirhead is?
eager crown
simplify what u can simplify
I will try
open hazel
Sorry idk what Muirhead is?
Google it it's a powerful tool in inequalities
eager crown
Okk
eager crown
and use a^3 +b^3 >= ab(a+b) for you to do the proof its fairly easy <@5871254259...
Ooo i did it
gentle stream
Expand then use Muirhead u have 24 terms in both sides and (3,0,0) majorizes (2,...
lmao ofc muirhead my beloved
eager crown
But i did not know about that inequality, i proved it to myself tho
gentle stream
Can anyone help me to prove that for a, b,c real positives
$8(a^3 + b^3 + c^3) >...
there's probably a nice alternate approach where you take a+b+c = 1
eager crown
there's probably a nice alternate approach where you take a+b+c = 1
Hmmm i never understand why u can normalize
Or for example let abc = 1
May u explain pleaseee?
gentle stream
Hmmm i never understand why u can normalize
it's because the inequality is homogenous
if i multiply all of a,b,c by k
then the inequality stays the same
eager crown
Oh then you can cancel
gentle stream
(as in if the inequality is true for (a,b,c), then it's also true for (ka, kb, kc) (k > 0) )
so that means i can always scale a,b,c and assume that a+b+c = 1 say
open hazel
there's probably a nice alternate approach where you take a+b+c = 1
Yes cause symetric and homogene
gentle stream
Like when u can just consider a, b, c coprime?
they're not necessarily integers
eager crown
Yeah
gentle stream
but yeah it's similar to the thing that u do in NT problems
eager crown
Ohh ok
So if their sum is k u can just divide all them by k right?
Same for product ig, u can divide all by cubic root of k
gentle stream
anyway then u're proving 8a^3 + 8b^3 + 8c^3 >= (1-a)^3 + (1-b)^3 + (1-c)^3 and there's probably gonna be a way to do that using jensen or tangent line trick or smth
open hazel
anyway then u're proving 8a^3 + 8b^3 + 8c^3 >= (1-a)^3 + (1-b)^3 + (1-c)^3 and t...
What function
U consider?
eager crown
Google it it's a powerful tool in inequalities
Let me take a look at this
And also what is tangent line trick?
gentle stream
What function
i didn't really think too much about it lol, like some form of f(x) = x^3 or f(x) = (1-x)^3
open hazel
And also what is tangent line trick?
with the line y=f'(x_0)(x-x_0)+f(x_0)
eager crown
Cauchy Schwarz Inequality?
Maybe, but how?
eager crown
with the line y=f'(x_0)(x-x_0)+f(x_0)
Damn u guys are smart
Using calculus and functions at inequality problem
eager crown
I am studying for my countrys olympiad
I was better last year tho
Lost my knowledge
open hazel
I am studying for my countrys olympiad
Which country?
open hazel
How old are y?
eager crown
16
open hazel
U still have time
eager crown
I hope
My problem is that i see a problem and try one single thing and if it does not work then i just keep staring at it and cant think about anything else
Then i just go and see the solution 😭
I am talking too much about myself sorry
high lotus
I thought of using Cauchy Schwarz for both LHS and RHS. Could be fumbling.
eager crown
Wow
open hazel
My problem is that i see a problem and try one single thing and if it does not w...
Normal
open hazel
Work lot of problems
calm coralBOT
@eager crown Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
pure breach
If for all real $x$, for which $\frac{x+a}{x^2+bx+c^2}$ is defined, it attains all real values, then which of the following must necessarily hold true?
potent lotusBOT
rak³en
pure breach
quick question
the denominator cannot be 0 (i think thats what is givenz0
so i dont need to consider b^2-4c^2<0 right
also if i set $y = \frac{x+a}{x^2+bx+c^2}$ then I find that $(b^2-4c^2)y^2 + 2(2a-b)y+1 \geq 0$
potent lotusBOT
rak³en
pure breach
now for the last thing to be true we need D=0 and b^2-4c^2>0 right
for some reason my workbook has used D<0??? which makes 0 sense
fickle hearth
<@&268886789983436800>
fickle hearth
now for the last thing to be true we need D=0 and b^2-4c^2>0 right
What last thing?
nimble harbor
for some reason my workbook has used D<0??? which makes 0 sense
it makes sense
because D<0 allows the quadratic to have no solution
pure breach
What last thing?
the last quadratic inequality in y
pure breach
because D<0 allows the quadratic to have no solution
but its >=0
nimble harbor
if no solution, then there is no such case that the denominator is zero
pure breach
if no solution, then there is no such case that the denominator is zero
the denominator is never 0 that is given
pure breach
**rak³en**
=0 arises from me assuming that the quadratic in x will have have a D>=0 - it can have a repeated root, can it not
pure breach
then it wont be defined there
yeah so that isnt included in the domain
nimble harbor
but its for all real x?
nimble harbor
i dont understand. if there is a root at the bottom, then (x+a)/(x^2 + bx + c^2) must be undefined at that root. In such case, it wouldn't hold for all real x? So, shouldnt the only condition be that D<0?
pure breach
i dont understand. if there is a root at the bottom, then (x+a)/(x^2 + bx + c^2)...
ITS NOT ALL REAL X
<@&286206848099549185>
pale cedar
so i dont need to consider b^2-4c^2<0 right
velvet osprey
eh hold up
pale cedar
your function is defined precisely when b^2-4c^2<0
velvet osprey
you have a function f(x)=(x+a)/(x^2+bx+c^2)
you want it to be defined everywhere & surjective
pale cedar
so you meant that you dont need to consider b^2-4c^2>=0?
velvet osprey
and you have a set of answer options for conditions on a, b and c
primal bear
here we go
velvet osprey
but you are getting sth that does not match any
pure breach
here we go
this happened in the morning lol
velvet osprey
@pure breach is that right
primal bear
!show maybe
calm coralBOT
Show your work, and if possible, explain where you are stuck.
velvet osprey
yes
pure breach
alr i will do both
velvet osprey
and a ss of the original q
pure breach
and a ss of the original q
no no i wrote in the exact words its in my workbook
i only skipped the options
velvet osprey
wait hold up
If for all real $x$, for which $\frac{x+a}{x^2+bx+c^2}$ is defined, it attains all real values, then which of the following must necessarily hold true?
potent lotusBOT
Ann
velvet osprey
that's your thing?
pure breach
i getting different option than given :\
velvet osprey
i think there is some wording based fuckery happening here
pure breach
ok see here's the thing
mhm
pure breach
i think there is some wording based fuckery happening here
LOL i have been trying to deal with em all day
velvet osprey
then in fact we cannot possibly have the range be R
pure breach
if denom is a quadratic that's never zero
its 0 we just remove the pts its 0 at thats what it means
i am 99% sure
velvet osprey
oh so there is no req of being defined on R
and we are just looking for surjectivity
anyway do send the options still
pure breach
pretty much
pure breach
anyway do send the options still
the ones that matter to us our:
A) b^2 > 4c^2 and a^2+c^2>=ab
B) b^2 > 4c^2 and a^2+c^2<ab
the remaining two are for the case b^2<4c^2 and are therefore irrelevant
pure breach
so you need to ascertain the sign of a^2 + c^2 - ab
see the problem is
i getting 0
for that
pure breach
yes
velvet osprey
ok show work then
pure breach
yes
pure breach
mhm
pure breach
the ones that matter to us our:
A) b^2 > 4c^2 and a^2+c^2>=ab
B) b^2 > 4c^2 and ...
the answer is B by the way
velvet osprey
new discr=0 would mean the y quadratic achieves a minimum value of 0
velvet osprey
because if its D<0 it wont fit > or = to 0 since it will never be 0
it will fit
pure breach
new discr=0 would mean the y quadratic achieves a minimum value of 0
which is what we want no?
velvet osprey
a requirement for a function to be >=0 can be satisfied by it being positive everywhere
pure breach
a requirement for a function to be >=0 can be satisfied by it being positive eve...
but we always set =0 for >=0...........
😭
velvet osprey
for the function f(t)=t^2+1 it is true that f(t)>=0 for all t
0 is a lower bound for it
pure breach
why do conditions change for every question
velvet osprey
even if not sharp
velvet osprey
but we always set =0 for >=0...........
weh???
pure breach
well okay that makes sense
velvet osprey
can you show a q where going from quad>=0 to discr**=**0 was legit
pure breach
weh???
theres a couple questions in my other workbook that involve setting d=0 in cases where we have to solve >=0 for all x
pure breach
can you show a q where going from quad>=0 to discr**=**0 was legit
yes i can
heres one
wow slow photo
but wtever
velvet osprey
oh but
this time it actually says 0 should be exactly the min value
in the case of your original q it doesn't
pure breach
this time it actually says 0 should be exactly the min value
so the statments x in [0, infinity] and x>=0 are different?
velvet osprey
mmmmm
no. too far abstracted.
here are two stmts that actually are diff
- f(x) in [0,infty) for all x
- range of f(x) is [0,infty)
pure breach
no. too far abstracted.
uh okay
velvet osprey
2 strictly implies 1
pure breach
1. f(x) in [0,infty) for all x
2. range of f(x) is [0,infty)
how are they different 
pure breach
2 strictly implies 1
but 1 doesnt?
velvet osprey
1 does not imply 2 no
pure breach
velvet osprey
f(x)=x^2+1 satisfies 1 but not 2
you cannot find a real x for which the ineq x^2+1>=0 is violated
pure breach
welp my teacher has given the same question but with 1 and we still did the same thing ...
AH I HATE JEE
velvet osprey
then that was wrong
pure breach
I HATE IT
pure breach
then that was wrong
no see it was condition 1 but i still used d=0
in 1 its supposed d<0 right
pure breach
d <= 0
well then it wont fit either option
because u'd have
b^2>4c^2 and a^2+c^2<=ab
and it definiely doesnt look like B
velvet osprey
oh is it < and not <=
pure breach
which is the answer
velvet osprey
uhhhhhhhhhhh.
pure breach
oh is it < and not <=
well see it should be <=0
pure breach
uhhhhhhhhhhh.
I KNOWWWWWWWW ITS SO GOD DAM IRRITATING
velvet osprey
ok this might already be in typo territory tho
pure breach
- i cant contact a teacher rn, more like no ones responding rn
pure breach
ok this might already be in typo territory tho
i say the entire workbook is mistyped
okay next question
under the assumption this was is a typo
@velvet osprey it isnt written but please assume that this version of R doesnt contain the points where our function DNE
velvet osprey
it should be that discr of denom should be <0
pure breach
it should be that discr of denom should be <0
no it cant, because then the top cant attain 0
they have the same D
velvet osprey
they do?
pure breach
i have went over this in the morning alr
pure breach
fr
pure breach
it should be that discr of denom should be <0
we just assume that the x for which a+3x-4x^2=0 are not in our domain
pure breach
yeah this one looks like a wrong question
theres 5 more like this ...
pure breach
ok yeah idk how to recover from typos or w/e
the problem is i cant solve it even under this domain assumption
the algebra is giving me stupid results
more like i cant even do it
its so god damn messy
and wolfram confirms that my steps are right.
wait nevermind.
oh god thats crazy how tf i am i supposed to guess that
.close
calm coralBOT
calm coralBOT
Available help channel!
hexed void
I wanted to know if I have to equate the equation to get their intersection points or should I just see them from the graph .
I did see them from the graph but the answer didn't match and is my graphic Okey
calm coralBOT
I wanted to know if I have to equate the equation to get their intersection poin...
@hexed void Has your question been resolved?
limber spire
I wanted to know if I have to equate the equation to get their intersection poin...
usually I don't think the graph is to be sacled
calm coralBOT
calm coralBOT
Available help channel!
patent phoenix
how are there 2 asymptotes for this function?
calm coralBOT
how are there 2 asymptotes for this function?
patent phoenix
ik x = 1 is the vertical asymptote but what else
inland dagger
An asymptote is a line linked to a certain limit
If a line is not vertical, in what other way can it be then ?
@patent phoenix
calm coralBOT
@patent phoenix Has your question been resolved?
patent phoenix
If a line is not vertical, in what other way can it be then ?
huh?
i dont understand
oh
i thought there would be a horizontal asymptote at y = 0
but thats not ture
inland dagger
But yeah a horizontal asymptote
Who knows maybe, what limit would it correspond to ?
inland dagger
So what could it be if it's not vertical nor horizontal ?
patent phoenix
So what could it be if it's not vertical nor horizontal ?
oblique
but doesnt that only exist when the degree of the numerator is just 1 higher tan degree of denom?
calm coralBOT
patent phoenix
.reopen
calm coralBOT
✅
patent phoenix
bruh
pearl iron
how are there 2 asymptotes for this function?
Try simplifying the fraction out
pearl iron
but doesnt that only exist when the degree of the numerator is just 1 higher tan...
it just has to be higher
patent phoenix
Try simplifying the fraction out
is that possible
it doesnt cancle out tho
i got x^2/3 (x+2)/(x-1)
but i dont see anyting
pearl iron
is that possible
yes
pearl iron
but i dont see anyting
$\frac{x^{\frac{5}{3}}+2x^{\frac{2}{3}}}{x-1} = \frac{x^{\frac{5}{3}}-x^{\frac{2}{3}}+3x^{\frac{2}{3}}}{x-1}$
potent lotusBOT
Kaikhosru Shapurji Sorabji
patent phoenix
WHAT
pearl iron
or just polynomial long division it
$= \frac{x^{\frac{2}{3}}\left(x-1\right)+3x^{\frac{2}{3}}}{x-1}$
potent lotusBOT
Kaikhosru Shapurji Sorabji
patent phoenix
or just polynomial long division it
oh okay
ya i got that
so is the asymptote at y = x^2/3?
pearl iron
so is the asymptote at y = x^2/3?
yes
patent phoenix
wait so the degree doesnt need to be higher by 1 for it to have an oblique asymptote?
patent phoenix
never mind
huh
pearl iron
wait so the degree doesnt need to be higher by 1 for it to have an oblique asymp...
yes
it just has to be higher
patent phoenix
o,fg
omfg
i have another question
@pearl iron is this a point of inflection or not
bc
f'(2) DNE
not differntiable
but
f''(2) concavity changes and f(2) exist
remote mural
sorry to jump in but um im pretty sure its still an inflection point since there is a change in concavity
and it exists - i believe an inflection point can exist without differentiality
patent phoenix
and it exists - i believe an inflection point can exist without differentiality
oh really
and no worries thank you
im confused cuz my teacher said f'(x) must exist at that point too 😭
patent phoenix
oh okay 😭
remote mural
😭
patent phoenix
hopefully someone else can verify too, i asked chatgpt and deepseek (said the same thing as google) but im just so scared she'll mark it wrong or smth
remote mural
hopefully someone else can verify too, i asked chatgpt and deepseek (said the sa...
if thats the case you could also try talking to her before handing it in or smth
or email
try to not sound cocky tho cuz like "heh! 🤓 teach ur WRONG" prolly will not be received well... 😭 😭
patent phoenix
lmfaooo
remote mural
fatal mistake i have seen smn make 💀
patent phoenix
yea okay tyty
calm coralBOT
@patent phoenix Has your question been resolved?
sharp ledge
calm coralBOT
remote mural
Don’t really know how to get started
First, all the forces on the forearm should add up to 0
Next, total torque should add up to 0
So first draw all the forces
And their distances from center of mass
(After breaking them down into horizontal and vertical components)
calm coralBOT
@sharp ledge Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
deft arrow
,rotate
potent lotusBOT
edgy leaf
correct
calm coralBOT
Available help channel!
outer sedge
In the solution, they set the bounds for z to be 0 to 4-3r^2, r from 0 to 1, and theta from 0 to 2pi, I am kinda confused here, what happens to the inequalities 1<=z<=4 and 0<=z<=1, why did they just ignore those constraints?
calm coralBOT
In the solution, they set the bounds for z to be 0 to 4-3r^2, r from 0 to 1, and...
@outer sedge Has your question been resolved?
outer sedge
I'm gonna repost my question because of a timeout:
In the solution, they set the bounds for z to be 0 to 4-3r^2, r from 0 to 1, and theta from 0 to 2pi, I am kinda confused here, what happens to the inequalities 1<=z<=4 and 0<=z<=1, why did they just ignore those constraints?
nocturne heron
if z<=4-3r^3, the maximal value of z is 4 (when r=0) and the minimal value of z is 1 (when r=1) so you have 1 <= z <= 4
calm coralBOT
@outer sedge Has your question been resolved?
calm coralBOT
@outer sedge Has your question been resolved?
marsh arrow
Miroslav and Zlata said all the natural numbers from 1 to 1000 in ascending order. After every second number, he made a short pause, during which Zlata said the sum of the last two numbers that Miroslav said.
Thus, the numbers were first said:
1, 2, 3, 3, 4, 7, 5, 6, 11, ...
16.1 Determine the number that was said between the numbers 24 and 25.
16.2 The number C was said as the 90th number in the sequence, which was then said again.
Determine the number that was said immediately before the number C was said for the second time.
16.3 Determine the largest number that was said twice among the first 150 numbers that were said.
calm coralBOT
Miroslav and Zlata said all the natural numbers from 1 to 1000 in ascending orde...
@marsh arrow Has your question been resolved?
marsh arrow
Yes
versed sluice
So the 90th number is the 'their sum' of the 30th group
marsh arrow
How do we get their sum
versed sluice
The 1st group, has 1 and 2
2nd has 3, 4
3rd has 5, 6
See the pattern
The 1st number of nth group is the nth odd number, and the 2nd number is the nth even number
You know what would be the 30th odd and even numbers?
marsh arrow
28, 30
calm coralBOT
@marsh arrow Has your question been resolved?
slender socket
how can I find iqr if I can't be sure of any of the values for the histogram?
slender socket
let say I wanted to count the 8. The values are betweeen 5 and 9
slender socket
yes
velvet osprey
ok so that column says 8 people paid between 5 and 7 USD(?) for their meal
slender socket
yes
so thats where my question lies. How can I accurately calculate the iqr if I don't know the exact values
unreal isle
id like to interject and specify the words of the question say "COULD BE"
slender socket
I am still confused though on the process of estimating the iqr
unreal isle
I am still confused though on the process of estimating the iqr
lemme walk u through it, so can you define the IQR?
slender socket
difference between q3 and q1
unreal isle
alright so in a total frequency of 100 people our q1 and q3 would lie at what frequencies?
slender socket
25 and 75
unreal isle
perfect now from the histogram can you tell me in which INTERVALS would these fall?
slender socket
q1 is between 9 and 11 and q3 is between 15 and 17
unreal isle
oops sorry went afk for a sec
unreal isle
q1 is between 9 and 11 and q3 is between 15 and 17
perfect so real quick can we find the max and min possible iqrs?
slender socket
one sec
unreal isle
u good
unreal isle
for a max iqr
you want to take the max value of q3 and min value of q1
vice versa for min iqr
does that make sense
slender socket
so smallest and biggest spread
unreal isle
yep
slender socket
so 4 and 8
unreal isle
perfect! so now we have
4 < IQR < 8
or simple, iqr is between 4 and 8
from the options given can you deduce it now
slender socket
so 5 is our answer
unreal isle
yep
slender socket
ok thank you so much
unreal isle
np
slender socket
.close
worn hedge
,rotate
potent lotusBOT
worn hedge
After cross multiplication how did they get to this simplified form
Is it even worth expanding
leaden thunder
Is it even worth expanding
yes expand
wise crescent
this is what i get
leaden thunder
!nosols
calm coralBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
calm coralBOT
@worn hedge Has your question been resolved?
torn hemlock
Is a function still able to be classified as odd or even if f(0) exists and is nonzero?
torn hemlock
Well it can be even
glass heart
f(-x)=-f(x) for odd functions. so f(-0)=-f(0), aka f(0)=0
torn hemlock
Okay, so you can't have an odd function where f(0) is not zero, right?
edgy leaf
yes
torn hemlock
Like this could not be odd nor even, since it is 1 at zero, but otherwise odd?
edgy leaf
yups it is neither even nor odd
torn hemlock
For Fourier series am I supposed to ignore zero?
tranquil wasp
me trying to comprehend what is happening here
glass heart
you mean for the integrals involved?
the value at a specific point doesnt change the integral
torn hemlock
I'm a bit confused because in an example in class the professor noted that this function was odd from (-2,0) U (0,2)
edgy leaf
I'm a bit confused because in an example in class the professor noted that this ...
0 is excluded so yes
sharp narwhal
For Fourier series am I supposed to ignore zero?
the defintion of odd/even is the same regardless of if ur doing fourier series
swift laurel
if a function is odd you can use only sin terms, and if it's even only cosines
sharp narwhal
But why would that be relevant?
maybe cuz then integral on (-2, 2) is 0
torn hemlock
the defintion of odd/even is the same regardless of if ur doing fourier series
I know, but for questions regarding it should/can I make a domain that excludes 0?
Or am I just lost
sharp narwhal
the domain is the domain
glass heart
if a function is odd you can use only sin terms, and if it's even only cosines
its not that you cant use the other terms. the coefficients just end up being 0
sharp narwhal
but changing it at a point doesn't change the integral
sharp narwhal
u should change ur language
from "can i make the domain this"
"can i count this as that"
like try to be precise
torn hemlock
I'm sorry, I don't really know how to be more clear.
torn hemlock
In order to solve the problem, am I able to make a domain that exlcudes 0 to solve as though it were odd?
torn hemlock
like the domain is what it is u can't change it
Yeah but I could like solve around it, no?
Like integrate -2 to 0 and 0 to 2
Uh no cause then its not odd on those domains
.close
strong mulch
can anyone here sit ith me for a fe hours to help me get my algebra 2 ork done? right noq im on logarithms and im not sure my next units but its all algebra 2 and im really behind so i just need help catching up
making sure my ork is right
etc
i might forget simple concepts so please be patient ith me
strong mulch
right noq, im on this
from here, i subtract 15 and divide by 3, but then i dont kno hat "in terms of R" means
like
a= R(yadayada)?
leaden thunder
more like a = f(R), where f is a function
strong mulch
hered the ln come from?
for context i just started logarithms
im not super familiar ith them at all
gleaming kelp
hered the ln come from?
ln is log_e
leaden thunder
strong mulch
ohhhhhhhhhh okay
leaden thunder
i don't know how you learn about logs without learning about e
strong mulch
i don't know how you learn about logs without learning about e
no i just forgot
hat e meant
ivelearned it
i just forget
strong mulch
can anyone here sit ith me for a fe hours to help me get my algebra 2 ork done? ...
read the end of this
the last sentence
its a big problem so i just put it in there as a arning to people "hey i forget these things" lol
okay i see
strong mulch
f(R) = ln(R-2)
i get this noq i think
gleaming kelp
right noq, im on this
u just have to isolate a, by taking off all the junk around it. subtracting 15 and dividing by 3 is a good start. at this point you should get rid of the log, do you remember how?
strong mulch
for context i just started logarithms
here
ive already done this but
idek if thats right
strong mulch
uhhhhhhhhhhhhh
i dont have it in that
format
i dont think
no
so hoq do i get it there?
unless
strong mulch
is it D 😭
gleaming kelp
i think its C
leaden thunder
every step should be justified
gleaming kelp
logarithms are inverse of exponentiation (well, one of the inverses). this is how you "undo" a log
strong mulch
Thats gonna be a struggle
Consiering
its not hole numbers and stuff im orking ith
gleaming kelp
ive already done this but
so that entire LHS is being lifted into the exponent of 10
strong mulch
10is my base
leaden thunder
this should be the next step
if you're just gonna guess and ignore this rule, you're not gonna learn what you need to do these types of problems
gleaming kelp
strong mulch
if you're just gonna guess and ignore this rule, you're not gonna learn what you...
If youre going to be ignorant, leave.
Ive literally said i ANT TO SOLVE IT
leaden thunder
Ive literally said i ANT TO SOLVE IT
wanting to solve it by guessing is still guessing
don't guess
strong mulch
wanting to solve it by guessing is still guessing
DUDE I SAID I AS GONNA ORK THROUGH IT
Leaveme alone
Donotinteract ith me anymore
gleaming kelp
i still dont understand it
we are just doing the same thing to both sides, but the point is that on the right hand side you can cancel out 10 and log_10, this is a log rule, and its indicative of the definition of logarithms
strong mulch
we are just doing the same thing to both sides, but the point is that on the rig...
oh okay i see
so basically i end up ith ((r-15)/3)_10=(a+2)?or
no log is
an operator
i forgor
is that right noq?
gleaming kelp
you are left with just a+2 on the right
strong mulch
ohhh dang okay
gleaming kelp
cuz thats the only thing left in the log
strong mulch
okay edited it
strong mulch
10^r-15/3 -2=a?
gleaming kelp
yurp
strong mulch
i see, thank you so much. so if i need to get rid of a log i just like
dothe _hatever the number of log itis?
gleaming kelp
yeh
strong mulch
like double the logover itself?
gleaming kelp
wdym double the log
gleaming kelp
well the log signifies that you are, in a sense, doing the opposite of what 10^x does
so they are meant to cancel
strong mulch
ooooooooooooooooooo
gleaming kelp
can anyone here sit ith me for a fe hours to help me get my algebra 2 ork done? ...
im willing to work through a couple more problems
strong mulch
hoq do i find the inverse of a function ith log in it?
gleaming kelp
im not sure what you mean, can you give an example?
strong mulch
i dont really have one besides modeling it off of my question and that feelslike cheating
gleaming kelp
right noq, im on this
to find the inverse of a function, in general, is going through a similar process to what you did here
you basically unwrap the input variable until its by its lonesome
which means you have to invert everything you come across
strong mulch
hats an input variable?
gleaming kelp
including the log, which we did
strong mulch
x?
gleaming kelp
here, the meaning of x has changed
x is essentially what y used to be
if that makes sense
strong mulch
qhy did people teach me that?
gleaming kelp
but it wouldnt be clear what it means
gleaming kelp
qhy did people teach me that?
well ok maybe its fine then
but usually people write it like how i did
because the inverse function is a DIFFERENT function
(usually)
strong mulch
i normally seeit that ay but
like
people tell meto rerite it sometimes as f(y)=x
it doesnt matter
not noq
this is qhat im trying to do
gleaming kelp
i normally seeit that ay but
like
people tell meto rerite it sometimes as f(y)=x
oh i think what they mean is to swap x and y
strong mulch
and like
i dont knoq hoq a log affects this
strong mulch
oh i think what they mean is to swap x and y
yes
gleaming kelp
you could swap at any point so its not really important (you are just changing names)
gleaming kelp
this is qhat im trying to do
ok so lets start with this
so here we want to solve for y
again, we are met with a silly little log, so we have to do the same trick
strong mulch
oo oo!
gleaming kelp
this time the base is 2
gleaming kelp
im not sure what x_2 means, if you mean to say 2^x then yes
strong mulch
im not sure what x_2 means, if you mean to say 2^x then yes
the make it go loer number
the uhhh
loq exponent looking thing
gleaming kelp
x with subscript 2 doesnt really mean anything here, the subscript is only used on the log
strong mulch
like this ^ but doqn
strong mulch
x with subscript 2 doesnt really mean anything here, the subscript is only used ...
oh
okay so i didnt remember
gleaming kelp
here are the steps again just to make it clear
strong mulch
hat difference does it make to be in front or after the x?
gleaming kelp
these are different notations
in fact, its not clear what x_2 even means in this context
x_2 might just be some other variable
strong mulch
these are different notations
okay
hat is the first one there?
gleaming kelp
okay
hat is the first one there?
2^x
gleaming kelp
oh you mean what its called?
strong mulch
yes
gleaming kelp
the x is in a superscript
gleaming kelp
anyway do u get what happens
gleaming kelp
im not sure what they taught you but this should be fine
strong mulch
i just started. i asnt really taught anything
hich is hy im having trouble
but
doesnt matter rn
gleaming kelp
this is qhat im trying to do
so which one is right
gleaming kelp
well ok we had to divide by 9 but that parts easy
gleaming kelp
y
y will be our inverse function
(remember that we already swapped the variables)
gleaming kelp
this is our work
gleaming kelp
these mean the same thing
teal drift
a eird funky number
It's a very normal fraction. If you are not comfortable with them, definitely go revise fractions...
You won't understand and be able to do any maths if you can't manage fractions with ease