as 10 is being added to x so when it will go to the other side the sign of 10 becomes -ve from +ve so 5 -10 = -5
#help-27
hidden sparrow
restive river
could you give me another one
hidden sparrow
this is easy one-
x/10 = 20
restive river
without division
hidden sparrow
x + 5 = 10
restive river
x + 5 = 10
5 + 5 = 10
10=10
hidden sparrow
bro like why are u making the value of x = 5 I don't give you the value of x it should be solved as-
x + 5 = 10
x = 10 - 5
x = 5
you don't have to prove both sides are same you have to solve the equation
restive river
bro what
restive river
high school
hidden sparrow
like what grade 9th?
restive river
yes
hidden sparrow
Yo bro 😄 here are the basic rules for solving equations like x + 5 = 10:
✏️ How to Solve Equations:
Keep x on one side, move numbers to the other.
Do the opposite operation to move terms (if it's +5, do -5).
Simplify both sides step-by-step.
When x is alone, you’ve got your answer!
🔍 Example:
x + 5 = 10
Step 1: Subtract 5 from the other side
x = 10 - 5
x = 5 ✅
💡 You don’t need to guess x — just solve it step-by-step like a puzzle.
hidden sparrow
now try 2x - 1 = 2
hidden sparrow
2x - 1 = 2
step 1 move - 1 to the other side so -1 becomes +1
2x = 2 + 1
step 2 move 2 to the other side as two it multiplied by x so on the other side it will divide with 3 as 2+1 = 3
so x = 3/2
which is 1.5 if divided
restive river
ok do another equasion
hidden sparrow
x * 1 = 2
restive river
x - 1 = 2
3 - 1 = 2
2=2
hidden sparrow
x -1 = 2
x = 2+1
x =3
now I have to go (as I think ur quite weak in this u can watch a video of this topic on yt or other platform just search Linear equations in one variable explained)
bye!
devout snowBOT
@restive river Has your question been resolved?
fringe hedge
This function is at the heart of most elementary number theory. gcd(x,y) is defined as the largest g such that g∣x and g∣y
.
What does this function tell you?
If gcd(x,y)=1
, then in a sense you can tell that y does not help a number divide something by x because in a sense there is no part of g of x it can help divide. This is why its also referred to as x is coprime or relatively prime to y. Try formalizing this definition to see if you've understood it.
I need help on understanding this. I understand the first line but I am having difficulty understanding the last paragraph
devout snowBOT
> This function is at the heart of most elementary number theory. gcd(x,y) is de...
fringe hedge
what does it mean that y does not help a number divide something by x ?
stone stump
fringe hedge
fringe hedge
That if a number a does not divide x ay neither
what
fringe hedge
That if a number a does not divide x ay neither
what's the point of it ?
uncut imp
what
If you have a number a
And a does not divide x
Then a*y does not divide x either
fringe hedge
Then a*y does not divide x either
oh, I get this
fringe hedge
If you have a number a
here, are there any two numbers coprime ?
solar goblet
devout snowBOT
solar goblet
hello i'd like my work checked please
near trout
i don't immediately see anything wrong, skimming over it quickly
solar goblet
right yeah
devout snowBOT
@solar goblet Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
rain coral
devout snowBOT
pseudo basin
are you talking about the very last part
stark oxide
ig cause furthest isnt written anywhere else
pseudo basin
they're doing it via a complement
i.e. they're finding the probability that the furthest point ISN'T more than 10cm away (which means the same thing as saying all 3 are within 10cm of 0),
and then taking 1 minus that
devout snowBOT
@rain coral Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
frozen aurora
devout snowBOT
frozen aurora
can someone give a good intuitive explanation of this and why the two conditions don't contradict each other?
we are given a pair $p,q$ such that $p<q$.
ii-a says that there exists some $C>0$ such that for ALL $f\in C([a,b])$, we have
$$
\lVert f \rVert {p} \leq C \lVert f \rVert {q}
$$
ii-b says that exists some sequence $f{n} \in C([a,b])$ so that
$$
\lim{ n \to \infty } \frac{\lVert f_{n} \rVert {q}}{\lVert f{n} \rVert _{p}} = 0
$$
but from (ii-a) we get that
$$
\frac{\lVert f \rVert _{q}}{\lVert f \rVert _{p}} \geq \frac{1}{C}
$$
and this holds for ALL $f$ with ONE $C$. then how can the limit go to zero, even for that special sequance in (ii-b)?
woven radishBOT
artemetra
frozen aurora
ping when replying
olive snow
you can't have both at the same time
frozen aurora
both ii-a and ii-b?
olive snow
yeah
frozen aurora
but that's in the book and the exercise right after is to prove them
maybe i am misreading the theorem
frozen aurora
yeah i get that but the book says both are true
frozen aurora
7.5: (a) Use Hölder in combination with the trick |f(x)|^p = 1 \cdot |f(x)|^p.
(b) Use the example f_n(x) = x^n on [0,1].
this is the hints for proofs of the two statements
olive snow
like from what i understand is that ii-a means that there is no extreme difference between norms and ii-b says this extreme difference happen
frozen aurora
i thought of this as being able to bound it from above and unable to bound it from below
cuz they use this fact to show that p-norms aren't equivalent on C([a,b]) but in fact one half of the inequality holds there
by equivalence of norms i mean this
so only the rightmost inequality holds but not the leftmost
at least i think this is what they are trying to communicate
but it makes no sense why what i am doing is invalid somehow
olive snow
7.5: (a) Use Hölder in combination with the trick |f(x)|^p = 1 \cdot |f(x)|^p.
...
Holder inequality ?
frozen aurora
hmmm
olive snow
lets call them differently since you already have p and q
if you have like, n = q/(q-p) and m = q/p you can achieve to have 1/n+1/m = 1
but since f(x) = 1
you will have that :
int |f(x)|^p <= norm(1)_n * norm(f(x)^p)_m
frozen aurora
if you have like, n = q/(q-p) and m = q/p you can achieve to have 1/n+1/m = 1
okay great
that makes a lot of sense
olive snow
and yeah with integrals notation
you can end it
ending with norm(f)^p_p <= norm(f)^p_q
taking p-th root
frozen aurora
yep got that
frozen aurora
7.5: (a) Use Hölder in combination with the trick |f(x)|^p = 1 \cdot |f(x)|^p.
...
now for b
frozen aurora
7.5: (a) Use Hölder in combination with the trick |f(x)|^p = 1 \cdot |f(x)|^p.
...
it doesn't seem to go to 0 tho?
let me type it out
olive snow
Ig its try to make no sense of the reverse inequality for the given counterexample
frozen aurora
i get:
$$
\displaystyle
\frac{\lVert x^{n} \rVert_{q}}{\lVert x^{n} \rVert_{p}} = \frac{ \int_{0}^{1} x^{nq} dx}{\int_{0}^{1}x^{np}dx} = \frac{\left( \frac{x^{nq+1}}{nq+1} \right) \Big|{0}^{1}}{\left( \frac{x^{np+1}}{np+1} \right) \Big|{0}^{1}} = \frac{np+1}{nq+1}
$$
woven radishBOT
artemetra
olive snow
Thats why it doesn't hold
frozen aurora
frozen aurora
Thats why it doesn't hold
i have an exam tomorrow where something like this will most likely be there
i am soooo cooked
supple knot
functional analysis is pain
olive snow
I don't like it personnaly
frozen aurora
this isn't even proper functional analysis, i'll be taking that next semester
supple knot
just read all the examples on this blog https://www.mathcounterexamples.net/tag/analysis-2/
devout snowBOT
@frozen aurora Has your question been resolved?
frozen aurora
yeah no i think this is some typo
signal ice
Hi! I don't study in English so I don't know if all my terms are correct, but I'm going to try explain my problem. I'm stuck on the general idea of a function composition. I can't wrap my head around how to actually use the formula \int f'(x)g'(f(x))dx=g(f(x))+C, especially without differentiating g(x) first. I get stuck on every single composed function when I try to integrate it, but right now specifically I'm trying to solve 4x/x^2+4
devout snowBOT
Hi! I don't study in English so I don't know if all my terms are correct, but I'...
vital sedge
Do you want to keep it rigorous? Because I think this is just a u-substitution.
north roost
…Which is reverse of chain rule
signal ice
Do you want to keep it rigorous? Because I think this is just a u-substitution.
Yeah I would like to keep it rigorous.
pseudo basin
you mean 4x/(x^2+4) first of all?
you need brackets when you write fractions like that and the numerator and/or denominator are held together by + or -
so you're calculating $\int \frac{4x}{x^2 + 4} \dd{x}$ right
woven radishBOT
Ann
signal ice
yes!
pseudo basin
right ok
so here is the idea
i'm going to adjust your formula a bit and write it like $$\int f'(x) g(f(x)) \dd{x} = G(f(x)) + C$$ where $G$ is an antiderivative of $g$
woven radishBOT
Ann
pseudo basin
(just g and G instead of g' and g, no other change)
the way it's written and executed in practice looks a bit different than a direct application of this formula
in english the process is called substitution, or as you'll commonly hear it u-substitution or u-sub because the new letter is very commonly chosen as u
and the way it looks is: $$\int f'(x) g(f(x)) \dd{x} = \int g(u) \dd{u} = G(u) + C = G(f(x)) + C$$
woven radishBOT
Ann
pseudo basin
so what you end up with is that you introduce $u := f(x)$ and then take the derivative of that to get $\dv{u}{x} = f'(x)$, but for the purposes of integration it is written $\dd{u} = f'(x) \dd{x}$
woven radishBOT
Ann
pseudo basin
this is really also the whole reason why we write the differential symbol (dx, du, dt etc) in integral notation -- it is a formal device to keep things in order when doing substitutions like that
signal ice
so what exactly was the u here? i think i missed it
signal ice
is f(x)=x^2+4 and g(x)=4x in my problem?
lavish sigil
Well first
woven radishBOT
jewels!
lavish sigil
If you were to write the integral like that
f(x) = x^2 and g(x) = 1/(x + 4)
Or f(x) = x^2 + 4 and g(x) = 1/x
It's not really concrete
signal ice
**jewels!**
how would we get to this? I'm trying to understand the step by step logic to be able to do it with other functions as well
lavish sigil
Admittedly this is a weird example
The formula gives you the illusion of having the functions in a line neatly multiplied together
jaunty mantle
$\int \frac{f’(x)}{f(x)},dx$
woven radishBOT
frosst
lavish sigil
Also I do not like the way this formula is presented to you, have you not learnt substitutions before?
jaunty mantle
Can you see that your problem looks like this?
signal ice
Also I do not like the way this formula is presented to you, have you not learnt...
I'm not entirely sure I understand what you mean by substitutions but I think we have done it before. I took the formula straight out of the formula book that my school allows us to use during the exam.
signal ice
Can you see that your problem looks like this?
4x is differentiated? Is that what you're getting at?
signal ice
x^2+4, no?
signal ice
2x
jaunty mantle
Okay
And 4x is just 2 * 2x
Which is 2 * the derivative on the denominator
Do you agree?
signal ice
yeah
jaunty mantle
So your problem if I let f(x) = x² + 4
$\int \frac{2f’(x)}{f(x)},dx = 2\int \frac{f’(x)}{f(x)},dx$
woven radishBOT
frosst
jaunty mantle
Do you agree?
signal ice
yea
signal ice
Oh, yeah
jaunty mantle
At this point we know this has the anti derivative of 2ln|f(x)| + C
And we are done
So 2 ln(x² + 4) + C
Does this make sense?
signal ice
At this point we know this has the anti derivative of 2ln|f(x)| + C
can you explain this?
jaunty mantle
$\dv{x} \ln(f(x)) =$?
woven radishBOT
frosst
signal ice
1/x? I think?
signal ice
I'm lost, the chain rule?
jaunty mantle
Yes do you know what the chain rule is?
signal ice
not off the top of my head atleast
signal ice
oh I missed that class, that's why I don't remember it
jaunty mantle
$\dv{x} g(f(x)) = f’(x)g’(f(x))$
woven radishBOT
frosst
jaunty mantle
Swapped it around so it’s the same as what you had at the top
Now, $\dv{x} \ln(x) = \frac{1}{x}$
woven radishBOT
frosst
jaunty mantle
Yeah?
signal ice
I think I get it
jaunty mantle
All of it?
signal ice
Maybe. i'll try to complete the question on paper
jaunty mantle
That will help yeah
signal ice
How exactly do I use the chain rule on 2 \int 2x/(x^2+4)? I think I understand the rule itself, just not how to use it
jaunty mantle
You aren’t using the chain rule
Chain rule is for derivatives
We’re doing integration
signal ice
oh okay sorry
jaunty mantle
We’re using reverse chain rule
signal ice
ohh wait that's the formula
jaunty mantle
We start with something that looks like chain rule spits out, then we know the integral must be the composition of functions
signal ice
It's this rule?
jaunty mantle
Yes
jaunty mantle
**frosst**
Because, what is this
signal ice
f'(x)ln(f(x) with the chain rule? or did I use it wrong
okay I got the right answer from my original question atleast
jaunty mantle
f'(x)ln(f(x) with the chain rule? or did I use it wrong
You didn’t derive the ln function
jaunty mantle
Yes
jaunty mantle
It's this rule?
That’s where this comes from
devout snowBOT
devout snowBOT
Available help channel!
restive river
in the above graph, can we deduce that it is a planar graph just by looking at it? according to me I think it is planar just by seeing it, but my teacher used the concept of edge subdivision to prove that it is a planar graph so I am a bit confused rn
devout snowBOT
in the above graph, can we deduce that it is a planar graph just by looking at i...
strange nimbus
in the above graph, can we deduce that it is a planar graph just by looking at i...
Yes, it's planar because none of the edges cross over each other, but you probably should practice harder methods on simple examples like this.
slate peak
How do I find $\sum_{n=1}^{\infty} \frac {an+X}{b^{n}}$
devout snowBOT
How do I find $\sum_{n=1}^{\infty} \frac {an+X}{b^{n}}$
woven radishBOT
laestia
slate peak
I was trying something like separating the top and bottom but that doesn't work
is there a way to calculate it without brute force
pseudo basin
you need to know how to calculate $\sum n\cdot r^n$ and also geometric series
woven radishBOT
Ann
pseudo basin
an/b^n and X/b^n yes
slate peak
Like $\sum_{n=1}^{\infty} \frac {an}{b^{n}}+\sum_{n=1}^{\infty} \frac {X}{b^{n}}$
woven radishBOT
laestia
pseudo basin
yes that is what i meant
slate peak
I can do the latter half for X part but not an/b^n
pseudo basin
yes
devout snowBOT
heavy current
hello 
this channel is closed, so you should open your own channel if you need math help
how old are you? 
<@&268886789983436800> uhh 
you're not allowed to be on discord at nine, I'm afraid
slate peak
mods, smite this child
devout snowBOT
Available help channel!
formal venture
devout snowBOT
formal venture
Should it not be 1/3?
Because the only time it can be red again is if its the left most box
potent zodiac
Yea but there are 2 red balls in that box
acoustic leaf
you can select any of the following:
- left red ball, left box
- right red ball, left box
- red ball, right box
the other ball is also red in the first two scenarios
pseudo basin
@formal venture would you like an equivalent rephrasing of this problem
it might make it a bit clearer
pseudo basin
let's say there's a group of 6 people forming 3 unrelated pairs of siblings:
- two brothers, Andrew A. and Bob A.
- two sisters, Liz B. and Mary B.
- a brother and a sister, Carl C. and Diana C.
formal venture
mhm
pseudo basin
we pick a person at random from these 6 and it turns out to be a guy
what's the probability he has a brother
formal venture
Well the only box that could have another brother is andrew/bob
pseudo basin
assume nobody has any siblings other than the ones listed
yes
out of the 3 guys we could have picked, 2 have brothers
formal venture
Okay so when I do that, am I considered the box as one of the 1/3, or the choices
pseudo basin
... neither of that makes sense to me so im gonna say no to both
pseudo basin
you do not really consider the boxes (or in this case families) at all directly
pseudo basin
yeah thus 2/3
formal venture
ahh
Im following
thank you
whered the middle one come from though?
or is it just weirdly greyed out
and the right red ball is supposed to be crossed out
this makes sense now though, thank you
acoustic leaf
it's hard to tell but there are check marks over the selected ball in each
that's the difference between the left two boxes, the first one has the left ball selected and the second one has the right ball selected
pseudo basin
whered the middle one come from though?
wdym
the middle case is where we pick bob
the left one is where we pick andrew
devout snowBOT
devout snowBOT
Available help channel!
livid stream
integrate 1/(sqrt(4x + 1)) dx from 1 to 2
devout snowBOT
integrate 1/(sqrt(4x + 1)) dx from 1 to 2
pale bolt
,r
livid stream
Why
lavish nimbus
U-substitute $$\int_1^2 \frac{dx}{\sqrt{4x+1}}$$
livid stream
Hey
woven radishBOT
Good
burnt lance
**Good**
easy bro
u have to do the derivate but inverse
add 1 more to the xponent instead of 1 less
but do the f' x g - g' x f/ g^2 but with 1 more
livid stream
Bro i mean the answer is 1 or (3*√5)/2 as there is two different answer in my sir answer and my answer and my book answer
lavish sigil
,w integrate 1/sqrt(4x + 1) from 1 to 2
burnt lance
use symbolab
lavish sigil
smh
pale bolt
it's just 4x
lavish sigil
Oh
woven radishBOT
livid stream
Is it √3+√5/2
burnt lance
i think yes it is
pale bolt
kinda hard to read but I think you didn't change the bounds wrt t
livid stream
So what's the answe mine 1 with support of book or sir's in honis 3+√5/2
I rewrite it ok
pale bolt
the answer is $\frac{3-\sqrt5}2$
woven radishBOT
pale bolt
not the best notation but work seems right
livid stream
It's +1
pale bolt
should be indicating the bounds are in terms of x, and you need the dt after the integrals
livid stream
What u mean? I directly do it as i solved it 5 times
pale bolt
wait I think I don't understand your work actually
livid stream
doesn't seem to be
This are my two work which one is correct
pale bolt
this is wrong because the sqrt shouldn't go across when you sub in the bounds
livid stream
Ok i got it btw so we take 4x+1 as whole term
pale bolt
$\sqrt x |_1^2 = \sqrt2 - \sqrt 1 \neq \sqrt {2-1}$
woven radishBOT
devout snowBOT
devout snowBOT
Available help channel!
waxen steeple
i got far enough to get that u(x, t) = 1/root(2pi) integral from -inf to inf of B(k)e^(cike^(-t)) e^(ikx) dk but i got a bit stuck from here
devout snowBOT
i got far enough to get that u(x, t) = 1/root(2pi) integral from -inf to inf of ...
waxen steeple
$u(x, t) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty B(k) e^{c i k e^{-t}} e^{i k x} , dk$
woven radishBOT
ashyboi
waxen steeple
$\text{With the initial conditions, I found that } B(k) = \mathcal{F}\big(f(x - c)\big)$
woven radishBOT
ashyboi
devout snowBOT
@waxen steeple Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
humble helm
hello, how do I plot a mixture of betas in R?
devout snowBOT
hello, how do I plot a mixture of betas in R?
@humble helm Has your question been resolved?
devout snowBOT
@humble helm Has your question been resolved?
barren abyss
devout snowBOT
devout snowBOT
Available help channel!
digital willow
can someone teach me to do z table?
devout snowBOT
can someone teach me to do z table?
@digital willow Has your question been resolved?
fossil locust
can someone teach me to do z table?
probably just post your specific question
then it's easier for others to help you
devout snowBOT
@digital willow Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
somber citrus
devout snowBOT
somber citrus
how do you know you that you need to integrate
deep vortex
how do you know you that you need to integrate
They took $\frac{\dd y}{\dd t} = -ky$ and multiplied by $\dd t$ and divided by $y$ to get [\frac 1y \dd y = -k \dd t]
Now you might as well write an integral sign in front of both sides
somber citrus
i see
somber citrus
Now you might as well write an integral sign in front of both sides
true
do you know where y0 comes from?
deep vortex
do you know where y0 comes from?
We get ln(|y|) = -kt + C, so |y| = e^(-kt + C) = e^Ce^(-kt)
Then you call e^C from now on y0
deep vortex
And leave off the || because you know y is positive as amount of birds
somber citrus
.close
devout snowBOT
devout snowBOT
Available help channel!
bitter herald
devout snowBOT
bitter herald
r/n==t
1/ndn=dt
pseudo basin
,rccw
woven radishBOT
misty crest
$\sum_{\gamma = 1}^n \frac{1}{n} \ell y\left(1 + \frac{\xi^2}{n^2}\right)$
woven radishBOT
knief
dire spear
Hello
wind mason
lol
wind mason
$\sum_{r=1}^n\frac1n\ln\qty(1+\frac{r^2}{n^2})$
woven radishBOT
;(
wind mason
That's my best bet
bitter herald
Yes that's it
misty crest
looks like \xi to me
faint hearth
hi, what is your question?
faint hearth
r/n==t
1/ndn=dt
are you trying to compute the limit of this sum as n -> inf?
then yes, you can make it into an integral
wind mason
r/n==t
1/ndn=dt
Why are we getting calculus involved in a finite summation
wind mason
are you trying to compute the limit of this sum as n -> inf?
This?
bitter herald
are you trying to compute the limit of this sum as n -> inf?
Yeah
wind mason
And my best thought is to use riemann integration
Ok, then it works fine
And please clarify that next time
bitter herald
My next step is 0 to 1 integration log(1+x^2)dx
faint hearth
if you want a hint on integrating this, try ||integration by parts||
wind mason
?
wind mason
,rccw
woven radishBOT
peak needle
this looks good to me! 😄
wind mason
Good start, now you can just split it
bitter herald
this looks good to me! 😄
What happened?
wind mason
i.e., what c can you add to the numerator to make 2x^2+c divisible by x^2+1?
bitter herald
I need help with Integration
peak needle
add and subtract 2 from the numerator to continue your integration
bitter herald
Right side
wind mason
i solve it for you
!nosols
devout snowBOT
i solve it for you
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.
peak needle
add and subtract 2 from the numerator to continue your integration
alternatively, you can long divide the numerator by the denominator
both will give you the same result 😄
craggy rampart
What happened
craggy rampart
Ohhh sorry sorry
rare kernel
i solve it for you
best helper ever
craggy rampart
I think this Chanel is for helping people
rare kernel
I think this Chanel is for helping people
oh are u sure
craggy rampart
not like this
wind mason
I think this Chanel is for helping people
Okay brother, we're cluttering this post
!redir
devout snowBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
woven radishBOT
fastrack_and_backtrack
peak needle
add and subtract 2 from the numerator to continue your integration
if you could not go anywhere with the hints, you can refer to the image above. for now i have made it a spoiler 😄
peak needle
**fastrack\_and\_backtrack**
sorry the integration will be ||arctan||, not ||ln||, mistake on my part 😄
peak needle
because integral of 1/1+x^2 is arctan x
bitter herald
But i am asking why log answer is wrong
faint hearth
which one do you mean by "log answer"?
faint hearth
how did you get that?
bitter herald
peak needle
thats wrong
bitter herald
I'm asking why
peak needle
integration of 1/1+x^2 is arctan (x)
peak needle
Why log thing is wrong
you made a mistake here
peak needle
differentiate it, you will not get 1/(1+x^2) 😄
pseudo basin
<@183668144404037632>
!noping
devout snowBOT
<@183668144404037632>
Please do not ping individual helpers unprompted.
bitter herald
Ok
peak needle
I don't want trigonometry
you must use it here, because the correct answer is arctan x
bitter herald
,w d/dx log(1+x^2)/2
woven radishBOT
ebon path
devout snowBOT
runic grove
sup
ebon path
i dont understand why it was divided into -9a and not into 4a
i just wanted to know how it got -9a
jaunty mantle
In the second second step 3
runic grove
what
jaunty mantle
You see how the remainder was -9a²?
ebon path
You see how the remainder was -9a²?
yep i see
jaunty mantle
At the top of the division you’re asking
What times a-3 gives me -9a²
The answer is -9a
ebon path
oh wait i seem to realize something
jaunty mantle
It’ll give you also +27a but that’s a¹ not a² and you’re trying to “take care” of the a² at the moment
You’ll fix the a¹ term later
ebon path
that none of it was divided by 3 and only was divided by a
so i dived by only a and multiply it by a - 3
is that how it works?
jaunty mantle
What??
Look at the very top
Why does it say a²
It’s because a-3 * a² gives you a³
ebon path
cause it was divided by only a
jaunty mantle
You’re trying to get rid of the a³ term
So you’re trying to construct the a³ from (a-3)
So you do okay (a-3)*a² = a³ + some stuff
Okay, the a³ term is correct
Now let’s deal with the a² term
In multiplying (a-3) by a² to “fix” the a³ term, you inadvertently add -3a² to your result
But what you really want is -12a²
So you’re now missing -9a²
Does this make sense?
ebon path
yep but i was just wondering if i still divided -9a^2 by -3 aswell or is the only use of -3 is a multiplier
jaunty mantle
What the fuck
There is no division going on in long division
There is only multiplication and subtraction
Not once have I used the word division because there is no division
Don’t think of it as division in that sense
You’re trying to fix the solution one term at a time
ebon path
oh
jaunty mantle
So at first you go (a-3)(a²) = a³ - 3a²
But what you really want is a³ - 12a² + 32a - 15
So then you try okay, what if I do (a-3)(a² - 9a)
You get a³ -3a² - 9a² + 27a = a³ - 12a² + 27a
ebon path
but i watch a youtube video stating that how to divide is like 14a^4 divided by 7a^2 is 2a^2
jaunty mantle
Okay, the first 2 terms are now fixed
ebon path
so i just inputted that thought on this long division
jaunty mantle
That division tells you what to actually put up at the top
But then you expand and do multiplication on the bottom
Then subtract
jaunty mantle
So at first you go (a-3)(a²) = a³ - 3a²
So like, how do I know to choose a²? Because a³/a = a², and here I only care about dividing the largest power so ignore the -3
ebon path
wait so uhm i just divde the first number? for example 3a^2 - 2
i only use this to divide 3a^2?
and the rest i use only for multiplication?
jaunty mantle
The -3 doesn’t contribute to “fixing” the a³ term so it doesn’t matter, you’ll “fix” its contribution in the later steps
jaunty mantle
wait so uhm i just divde the first number? for example 3a^2 - 2
i only use this ...
I don’t know what the heck you’re saying
Divide what by what for the first number
Division occurs between 2 things and you’re just saying 1 of them
jaunty mantle
To figure out what to write up top yea
But after that you need to multiply up top (the thing you just wrote down) with the full (a-3) and write that on the bottom
Then do the subtraction
It’s very very much like normal long division
Each aⁿ is a different “digit”
And there’s no carry
ebon path
i see i think im starting to get it, ill just watch a youtube video first to make more sense
jaunty mantle
If you try to divide 10 by 7 then you just write 1/7 in the tens slot because 1 goes into 7 “1/7”th times
Then 0 goes into 7 0 times so you get 1/7 in the 10s slot and 0 in the ones slot
Which is 1/7 * 10 + 0 * 1
Which is 10/7 which is what you expect when you divide 10 by 7
ebon path
mhm, but i dont understand what is this for, or which part in the long division this is
jaunty mantle
Normally in long division you’re limited to writing down integers on the top but if you allow yourself to write any fraction or decimal in each digit it becomes just like polynomial long division
ebon path
oh i seee
devout snowBOT
devout snowBOT
Available help channel!
high imp
devout snowBOT
high imp
For part c to find the range do you solve the inequality focusing on just the numerator, and then the denominator???
Or why do u split the fraction
junior flax
I don’t understand your question
junior flax
Both the numerator and denominator are important
high imp
Like ofc u set the function greater to 0 but I don't get the rest of it
junior flax
Numerator has to not equal zero, and numerator and denominator have to be the same sign
junior flax
Like why not bring the denominator to the other side
You’d lose information
wind mason
Like why not bring the denominator to the other side
You don't know the sign of the denominator.
high imp
What are the steps to solving it
wind mason
You'd have to create extra cases, at that.
wind mason
What are the steps to solving it
Determine when the numerator and denominator are the same sign.
high imp
And how do u do that
high imp
But the method here I assume they didn't use a sign chart
wind mason
And how do u do that
Solving the respective inequalities.
high imp
What's that
wind mason
Or, actually.
high imp
Wait what else can u do
wind mason
Wait what else can u do
Notice what properties your function has since f'(x)>0 for all x in the domain of f.
high imp
Yes
wind mason
Not that.
wind mason
Since f'>0, f is strictly increasing, and hence there would only be one root for f.
high imp
So because there's only one root ??
wind mason
This simplifies our focus to just finding the root of f and determining at what point (before or after), it is greater than 0.
high imp
U said there's only 1 root
woven radishBOT
;(
high imp
Is the method I have correct??
wind mason
Is the method I have correct??
The one in blue pen, yes.
wind mason
Or actually, no, there's still a screw-up.
high imp
Yh i think so
wind mason
Since there's an asymptote you still need to consider signage.
(before and after the asymptote.)
devout snowBOT
devout snowBOT
Available help channel!
worthy herald
i cant figure why the answer is wrong
devout snowBOT
i cant figure why the answer is wrong
drifting sinew
i cant figure why the answer is wrong
!show
devout snowBOT
i cant figure why the answer is wrong
Show your work, and if possible, explain where you are stuck.
@worthy herald Has your question been resolved?
worthy herald
devout snowBOT
Available help channel!
lament schooner
doesnt this short circuit? what can i do for a
devout snowBOT
doesnt this short circuit? what can i do for a
valid iron
maybe we could play arround with kirchofs junction law
oh wait
is it jus asking for the current in the circuit?
lament schooner
yea
topaz beacon
for a just imagine the capacitor isnt there
topaz beacon
yes
lament schooner
can you find the current in the circuit
i need to know why it doesnt short circuit
topaz beacon
and you imagine the capacitor isnt there
valid iron
so it will act like a wire no?
lament schooner
i need to know why it doesnt short circuit
.
valid iron
and you imagine the capacitor isnt there
if we imagine that wouldnt that mean no current passesthrough cd
valid iron
i need to know why it doesnt short circuit
potential between c d is same
topaz beacon
if we imagine that wouldnt that mean no current passesthrough cd
i think we mean the same thing
valid iron
so just consider it as a wire
topaz beacon
the wire still exists, but no capacitor
valid iron
i think we mean the same thing
yeah just caught that..
yep mb
join the cd points and redraw the circuit
topaz beacon
eventually the capacitor will build up enough electrons thus creating a potential difference syrex
lament schooner
ah i see what you mean
valid iron
yep the charge opposing the ef formed by the emf in steady state
topaz beacon
also it would short circuit without a capacitor (with or without the wire) because you have a voltage source
lament schooner
and for the part b uh
topaz beacon
if you have a current source, the buildup might continue until the electrons have enough potential to jump the gap
valid iron
also it would short circuit without a capacitor (with or without the wire) becau...
oh wait i never thought of it that way , thanks yeah
topaz beacon
ok im just bad at talking electricity
valid iron
i think we are going off topic
valid iron
and for the part b uh
what will the capacitor behave as
after a sufficient ammount of time
topaz beacon
also known as?
topaz beacon
i was looking for open circuit
topaz beacon
well q=cv, so lets find the voltage across the capacitor
lament schooner
well q=cv, so lets find the voltage across the capacitor
yea but at the point where its fully charged
how can i find delta V
unless i just do pointdV-pointcV
devout snowBOT
devout snowBOT
Available help channel!
tall trellis
i need help with this
<@&286206848099549185>
a problem my friend sent me i need help
craggy dagger
i need help with this
Seems to be quite vague. Best bet is just ask your friend to draw diagrams to clarify
tall trellis
Seems to be quite vague. Best bet is just ask your friend to draw diagrams to cl...
no the problem is just like this
craggy dagger
Do shared energy combinations add or multiply? What is this "multiversal complexity"
tall trellis
do you know this
craggy dagger
tbh looks like ai slop
tall trellis
It depends on how the universes interact
tall trellis
tbh looks like ai slop
no my friend sent me it
tall trellis
bruh my friend sent me this so like no point
craggy dagger
forgot command but whatever
If they intended something, then ask them. If they didn't then theres really no point
tall trellis
If they intended something, then ask them. If they didn't then theres really no ...
no like how to slove this
i need some help
on like 4 and 5 mostly
@ dido can someone please help me
craggy dagger
no like how to slove this
Are you assuming every question must have an answer
tall trellis
Are you assuming every question must have an answer
it will
craggy dagger
Why do you think it has an answer
tall trellis
Why do you think it has an answer
becuase my firend said this has an asnwer
devout snowBOT
Available help channel!
craggy dagger
becuase my firend said this has an asnwer
Why trust your friend on that?
devout snowBOT
Why trust your friend on that?
tall trellis
Why trust your friend on that?
becuase he got it from the book and it had an asnwer
craggy dagger
"the book"? Which book?
tall trellis
he sloved it adn this is an challange
i got most of it except for 4-5
so close this if you dont want to help i will find someone else to help
.close
@craggy dagger
craggy dagger
.close
devout snowBOT
devout snowBOT
Available help channel!
muted sapphire
Help
misty crest
muted sapphire
Yeyyep bro
misty crest
🤔
muted sapphire
My mind is baffling
misty crest
what’s the formula for the volume of a right circular cylinder
muted sapphire
misty crest
word
muted sapphire
what’s the formula for the volume of a right circular cylinder
Pi r^2h+2/3pir^3
misty crest
🤔
muted sapphire
Pi r^2h+2/3pir^3
That is the total volume
misty crest
that’s not what i asked
misty crest
did you draw a picture
muted sapphire
Yeah
misty crest
send it bruh
muted sapphire
Not very accurate
muted sapphire
send it bruh
misty crest
i think it’s supposed to be a silo
like this
but what you drew is ok
just sideways
muted sapphire
I see
misty crest
but yes volume is correct
now what is the amount of metal
in terms of geometry terms
what quantity
muted sapphire
The surface area?
misty crest
yes sir
muted sapphire
Oh
misty crest
now what is the surface area
fossil locust
3Pi r^2+2pirh
yep, from 2 pi r h + pi r^2 + 1/2 * (4 pi r^2)
misty crest
where did you get 3pir^2?
muted sapphire
True
misty crest
hmm
is the pi r^2 supposed to be from the bottom of the hemisphere?
i don’t think it will have a bottom
misty crest
https://tenor.com/view/silofall-deal-with-it-silo-destruction-falling-gif-100823...
^
🗣️
3pir^2 comes from the bottom of the hemisphere but here i don’t think it’s supposed to be closed
muted sapphire
misty crest
lmao
muted sapphire
So it is just 2pi r ^2?
fossil locust
3pir^2 comes from the bottom of the hemisphere but here i don’t think it’s suppo...
no it's from the bottom of the cylinder
the cylinder has a base and that's the pi r^2
fossil locust
cause the hemisphere is on top of the cylinder
if the cylinder has no base then all the liquid would just flow out the bottom
yeah....
misty crest
who said it had to have liquid
muted sapphire
lol
misty crest
lol
misty crest
farming and shit
muted sapphire
True
drifting sinew
What's going on here? 👀
muted sapphire
So what should u do next
misty crest
agricultural engineering
muted sapphire
Despite the bottom
muted sapphire
Nope.
misty crest
and just check which one
muted sapphire
Because I made the question
muted sapphire
Probably yes
misty crest
3Pi r^2+2pirh
alright so you’re here
muted sapphire
Yeah
muted sapphire
Contact a professional constructor to calculate for me
misty crest
usually how it goes
muted sapphire
They are not very good at maths
misty crest
maths
misty crest
aren’t you canadian
misty crest
sorry
misty crest
so far we have
V = pi r^2 h + 2/3 pi r^3
A = 2pi r h + 3pi r^2
muted sapphire
Yep
misty crest
we want A to be a minimum
muted sapphire
Yep
misty crest
with any of these optimization problems you need to differentiate A and set dA/dt = 0
but we have two variables, h and r so we need to express one in terms of the other
definitely easier to express h in terms of r
so solve for h in terms of r and V
muted sapphire
H=v/pi2r^2 -2/3r
muted sapphire
with any of these optimization problems you need to differentiate A and set dA/d...
Looks similar to change in rates stuffs
misty crest
$h = \frac{V}{\pi r^2} - \frac{2}{3}r$
woven radishBOT
knief
misty crest
did you mean this?
muted sapphire
Yep
misty crest
ok now substitution that into A
muted sapphire
Okay
misty crest
$A = 2\pi r\left(\frac{V}{\pi r^2} - \frac{2}{3}r\right) + 3\pi r^2$
woven radishBOT
knief
muted sapphire
And then find A’?
misty crest
$A = \frac{2V}{r} + \frac{5\pi}{3}r^2$
woven radishBOT
knief
misty crest
yea?
and then find dA/dt
and set it equal to zero
find r
find h
or no need
we want to find A
muted sapphire
Why this question associate with change in rates
muted sapphire
https://tenor.com/view/philosophy-academy-athens-art-raphael-gif-17399902
Why I got negative for r lol
misty crest
$\frac{-2V}{r^2} + \frac{10\pi}{3}r = 0$
woven radishBOT
knief
misty crest
,w \frac{-2V}{r^2} + \frac{10\pi}{3}r = 0
woven radishBOT
woven radishBOT
knief
misty crest
$r = \sqrt[3]{\frac{3V}{5\pi}}$
woven radishBOT
knief
misty crest
nah
muted sapphire
V is constant and arbitrary rn
Oh
misty crest
what?
muted sapphire
So we are done?
muted sapphire
But there aren’t any numbers
misty crest
muted sapphire
Yeah
muted sapphire
socrates is a myth fr
What
muted sapphire
Existence is to be perceived
misty crest
🤣
misty crest
deep bro
misty crest
true philosopher
muted sapphire
Or actually 0x0x0
misty crest
you could be the next diogenes bro
muted sapphire
As long as it in my head
misty crest
why be aristotle
muted sapphire
Because he is balling
misty crest
word
muted sapphire
damn you’re young
Bruh I don’t understand any American slangs lol
muted sapphire
misty crest
🦅
misty crest
ever heard what an eagle sounds like?
muted sapphire
misty crest
🤣
muted sapphire
ever heard what an eagle sounds like?
Ik
misty crest
https://tenor.com/view/donald-trump-trump-america-pm-america-usa-gif-94457947833...
genius
art of the deal
muted sapphire
misty crest
what was the word