Its the same as the coefficients of each term of a polynomial
#help-0
junior blade
They came about when I was doing something involving prime numbers
"elementary symmetric polynomials" maybe?
fickle tinsel
Oh yeah thats perfect
junior blade
i remember seeing these come up for elasticity theory funny enough
totally unrelated to what you were talking about
fickle tinsel
Yeah
I'm trying to optimize a certain algorithm (if I can even write it out)
$S_n = \sum{d|n}{}{2^{\omega_n}}$
tall shuttle
Looks like vieta formulas for a Polynomial
ocean sealBOT
7aman
tall shuttle
Especifically P(x) = (x-a)(x-b)(x-c)(x-d)
ocean sealBOT
7aman
fickle tinsel
.close
wicked lynx
Help
wicked lynx
Ok so, many points fall on this scatter plot i'm doing, I don't know which one to pick
their's (4, 30) , (2.5,45) , (2, 50) and (0.5, 65)
ill screenshot as well
I was thinking the ones with the whole number (2, 50) and (4, 30)
bronze shadow
just estimate
wicked lynx
just estimate
really?
like I can choose whatever
one
ok I GOT IT THANKS
.close
hexed eagle
How do you go about finding all group homomorphisms from Z to Z when the group operation is addition?
golden canyon
I think you can consider what element 1 maps to
And 0 maps to 0, by properties of a homomorphism
lone heartBOT
@hexed eagle Has your question been resolved?
uneven sundial
Hey, could someone help me with this? I'm not sure how to approach it
lone heartBOT
Hey, could someone help me with this? I'm not sure how to approach it
@uneven sundial Has your question been resolved?
uneven sundial
<@&286206848099549185>
exotic belfry
it looks like that this is not the whole example. (g(x) is defined but not used, the second screen shot starts with d) - what is with a) - c) ?)
Help is not so easy when only part of the information is given.
you can calc the average rate r of f in the given intervall with the values of the table. then solve this for h'(x) = r.
uneven sundial
it looks like that this is not the whole example. (g(x) is defined but not used,...
Oh I'm sorry, I didn't realize I needed the other questions, that's my bad
one moment
here are a and b
and here is c
exotic belfry
you can calc the average rate r of f in the given intervall with the values of t...
this.
uneven sundial
you can calc the average rate r of f in the given intervall with the values of t...
ohhhh
oh i see it
4e^cosx = 3
e^cosx = 3/4
ln(e^cosx) = ln(3/4)
cosx = ln(3/4)
is this how you do this
oops
exotic belfry
and here is c
are you sure?
uneven sundial
are you sure?
I'm confused, is c just a replacement for x here or?
oh im supposed to plug it in, right
exotic belfry
c is x^2-x, so need to know if there is some x with f(x) = 5, where 0 < x^2-x < 3.
uneven sundial
x= 2? that would make c less than 3 and bigger than 0
i don't think there is any other value that satisfies that requirement
exotic belfry
assume x = 1.1, then x^2 -x = 0.11 which is between 0 and 3. do you know f(1.1)? You know f(0) is 4 and f'(0) is 2, which means f is increasing near 0. and you know f(3) = 1 and f'(3) < 0, so f is decreasing near 3. so you know there is an x between 0 and 3 where f(x) > 4 and it is a local maximum. Could this maximum >= 5 and could 3 > x^2-x > 0 for this x?
uneven sundial
I have to say I am not sure what you mean, I'm so sorry
maximum greater than or equal to 5, and c value greater than 0 and smaller than 3
exotic belfry
your function f looks like this:
uneven sundial
your function f looks like this:
yeah
exotic belfry
so you have a maximum:
uneven sundial
yes
exotic belfry
is this maximum greater 5 or lower 5?
uneven sundial
lower I think?
exotic belfry
in my sketch maybe, but in general? Can you definitly say that there is no such f with a maximum greater then 5?
uneven sundial
in my sketch maybe, but in general? Can you definitly say that there is no such ...
I mean based on my math skills, I don't think you can, no
exotic belfry
so think about your answer to c) where it is asked if a c exists with g(c)=5. Can you definitly say "No"?
uneven sundial
so think about your answer to c) where it is asked if a c exists with g(c)=5. Ca...
No, oh, so it's actually just that we cannot tell based on the provided information?
exotic belfry
I cant really say at the moment, I would have to spent some more time to think about it. I guess the answer isnt "so simple".
uneven sundial
I cant really say at the moment, I would have to spent some more time to think ...
Yeah I guess so, this is confusing
I don't think I have the mathematical skills to give a numerical answer to this question so I think I should write, we cannot say
exotic belfry
i guess someone can fit a polynom of degree 8 where the max is at x = 1.1 and f(x)> 5, so in this case such a c with g(c) =5 exists. And i guess someone could fit another polynom where the max is < 5. in this case such a c would not exist.
So my answer would be "For some f such an c exists, for some others f such an c does not exist" (and i would name an example for f for each case)
uneven sundial
i guess someone can fit a polynom of degree 8 where the max is at x = 1.1 and f(...
But how would I give an example
How do I compute such an answer
exotic belfry
write a polynom of degree 8 (or maybe higher?), so you have some ax^8+bx^7+.... then you have 4 values given, take the first derivative, here you have again 4 values given, assule f(1.1)=10 (for example) so you have a linear system of equations in the unknowns a, b, ... which you can solve.
so you get an f where a c with g(c)=5 exists. and then do the same thing where the max < 5, again solve a linear system of equations ...
but: thats the way I would do it. not sure if you are expected it to do this way.
uneven sundial
I don't think ap calculus ab for highschoolers expects you to know this I will be honest
I'm not even following what you are saying, im so sorry
I think its best if I leave it at cannot be determined
And I hate to bother you more with this but could you also help me with problem d? if you have time of course
exotic belfry
i thought d) is already solved.
uneven sundial
i thought d) is already solved.
OH
wait
4e^cosx = 3
e^cosx = 3/4
ln(e^cosx) = ln(3/4)
cosx = ln(3/4)
I wanted to ask if there's anything else I can do here
because supposedly I have to find the x value, but I'm not sure how I even do that, since the x is in the cosine
or is this all I can do?
exotic belfry
arccos is the inverse of cos.
uneven sundial
Thank you so much, I forgot you can cancel out the cosines, thank you so much again, sorry for bothering you with all of this, thank you again
.close
cold trench
How to prove formula, (P ∧ Q) → (P ∧ (P → Q)), using natural deduction rules. I am trying to prove the validity of the following formula using natural deduction rules.
(P ∧ Q) → (P ∧ (P → Q))
This is my attempt but I'm unsure if its right, would anyone be able to help know if this is wrong and how to fix it. Assume (P ∧ Q)
P ∧-elimination 1
Q ∧-elimination 1
Assume P
Assume (P → Q)
Therefore, (P → Q)
Therefore, (P ∧ (P → Q)) ∧-introduction 4,6
Therefore, (P ∧ Q) → (P ∧ (P → Q)) →-introduction 1-7
prime badge
is incredible.pm natural deduction?
cold trench
what is incredible.pm
prime badge
http://incredible.pm/
a site where i learned to not be afraid of logic notation kinda
it has weird rules which could be natural deduction
cold trench
some rules i need to use are implication introduction, implication elimination, conjunction introduction, conjunction emilimataion, assumption, etc. Is my answer correct?
cold trench
so what would the full answer be, including the steps usede
prime badge
idk, i think you did everything right
the implication part looks weird tbh
why is it "assume P → Q" if you;re in the process of proving that
cold trench
im not sure, i struggle alot with natural deduction
prime badge
dm it
lone heartBOT
@cold trench Has your question been resolved?
lone heartBOT
@cold trench Has your question been resolved?
lone heartBOT
Available help channel!
bold elk
Help
bold elk
wind cloak
lone heartBOT
@bold elk Has your question been resolved?
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@bold elk Has your question been resolved?
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@bold elk Has your question been resolved?
worn pawn
someone help please
proven heart
someone help please
f(something) is the height of the orange curve at that x value.
First you need to pick which two statements you want to make true and the one remaining statement that needs to be a lie.
proven heart
f(something) is the height of the orange curve at that x value.
By f(x1)=g(x2), they mean that the height of the orange graph at x1 and the height of the graph(you are about to draw) at x2 be the same.
lone heartBOT
@worn pawn Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
onyx quail
lone heartBOT
wide marlin
wide marlin
is the answer b
empty moth
https://cdn.discordapp.com/attachments/486841085210132490/1174553299299618866/ch...
,w d/dx(\frac{x}{cot(x)}) where x = \frac{\pi}{3}
ocean sealBOT
wide marlin
,w d/dx(\frac{x}{cot(x)}) where x = \frac{\pi}{3}
so is that a yes
empty moth
so is that a yes
yep
lone heartBOT
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.
alpine sable
,w derivative of sin²x/cosx
ocean sealBOT
alpine sable
@wide marlin you can use bots for verification
wide marlin
.close
vagrant sage
vagrant sage
<@&286206848099549185>
carmine reef
Well you can do surface area before and surface area after
whole otter
Ok do
So
Let’s have a square of 1x1x1
Start simple
So we can split it
And we have cubes of 1/2 x 1/2 x 1/2
Each side is 1/4
Each cube surface area is 3/2
Since we have 8,
We can conclude the surface area is 12
The increase is 11
So now we can say a cube surface area is m
m * m * m
Split it,
1/2m * 1/2m * 1/2m for every cube
One side area is m^2/4
Surface area for one cube is 3m^2/2
For eight, you get 12m^2
So initially the surface area was 6m^2
But now it is doubled
So
You have your formula
vagrant sage
k thnx
lone heartBOT
@vagrant sage Has your question been resolved?
tulip oasis
lone heartBOT
lone heartBOT
@tulip oasis Has your question been resolved?
lone heartBOT
@tulip oasis Has your question been resolved?
celest ridge
@tulip oasis
noble rover
How do you integrate f'(x)?
lone heartBOT
How do you integrate f'(x)?
native cloud
$\int \frac{\cot \left(2x\right)}{\sin ^2\left(2x\right)}dx$
ocean sealBOT
LE SSERAFIM
native cloud
Rewriting it like this might help
foggy pecan
note that (sin2x)' = 2cos2x, thus, you can play with substitution
native cloud
$\int \frac{\cot \left(2x\right)}{\sin ^2\left(2x\right)}dx=\int \csc ^2\left(2x\right)\cot \left(2x\right)dx$
ocean sealBOT
LE SSERAFIM
native cloud
I would u-sub from here on
lone heartBOT
lone heartBOT
Available help channel!
stuck fractal
I'
stuck fractal
i'm confused on what i need to do and how to solve it
Every week, our school Cafeteria sells approximately 2000 chick wraps for $1.50 each'. Through mark research, the cafeteria managerr determiness that for every $0.10 increase in price, she will sell 100 fewer wraps. a) What is the maximum revenue?
this is a quadratic word problem
swift shore
Okay let’s start by giving names to things
w(p) = number of wraps sold for price p
Do you realize that if you graph w(p), it will look like a line
@stuck fractal
lone heartBOT
@stuck fractal Has your question been resolved?
stuck fractal
Do you realize that if you graph w(p), it will look like a line
huh oh
what would i do next?
swift shore
Well wait
lone heartBOT
@stuck fractal Has your question been resolved?
indigo solar
lone heartBOT
hearty quartz
So why have you not applied gaussian elimination
indigo solar
So why have you not applied gaussian elimination
Not learnt that
hearty quartz
Not learnt that
So for your calculations you seem to be taking the cross product for some reason when calculating the determinant. The determinant is calculated using the leibniz definition of determinant.
indigo solar
I was finding the cross product because I was trying to find the intersection of those 2 planes
hearty quartz
Not learnt that
For this question I recommend you apply Gaussian elimination even if you have not learned it. Just to clear consistency and unique solution are different. It could be there could an infinite number of solutions.
lone heartBOT
@indigo solar Has your question been resolved?
wheat isle
lone heartBOT
wheat isle
for part B can I just sub in 20 for t?
zealous lichen
yes
zealous lichen
plug in h(t)=50
wheat isle
plug in h(t)=50
so 50 = -cos(pi*t/30)+31 and solve the trig equation?
but whats my domain restriction
zealous lichen
first, t represent time here
second, the question asked for the first time reaching 50m
wheat isle
first time means first solution?
the first possible trig solution?
i guess so
@zealous lichen is this working out correct
t=19.2...
oh
i calculated 50 - 31 wrong
thats L moment
i got it
.close
lone heartBOT
lone heartBOT
Available help channel!
trim coral
lone heartBOT
alpine sable
?
trim coral
If i had a logistic function in this form, how would I find the k value, (the growth rate if I had the percentage percentage value that my population increased by)?
pale kestrel
@alpine sable if ur not going to help, dont post in someones channel
feral hawk
Yo
trim coral
hello
lone heartBOT
@trim coral Has your question been resolved?
eternal blaze
If i had a logistic function in this form, how would I find the k value, (the gr...
Offer more informatuion, is $p(t)$ the percentage, and what's the meaning of $p(t), M, c ; \text{and} ; k$
ocean sealBOT
零下三度极寒
trim coral
Offer more informatuion, is $p(t)$ the percentage, and what's the meaning of $p(...
Its a logistic function, but im not sure hoe to derive the k value
I have a percentage growth
And i wanna convert it to a k value
But i cant just use it there
I have a percentage growth of 13% would i just do ln(1.13)?
To be used as a k value?
M is carrying capacity
C is derived at p(0) or initial population
eternal blaze
Oh, I see
Give me a little time to know how people use it to fit population growth on wikipedia
trim coral
.close
lone heartBOT
lone heartBOT
Available help channel!
strange fractal
Hello
pseudo ice
strange fractal
What does this mean
pseudo ice
question 16
Both 15 and 16 are sus 
pseudo ice
What does this mean
You forgot to work out cos(C) (in 15) and sin(C) (in 16)
pseudo ice
strange fractal
c=?
pseudo ice
Please don’t do this (the top of the circled is c^2, the bottom should be c, they aren’t equal)
pseudo ice
c=?
Yeah for the bottom it’s a better idea to write c = sqrt{…}
Don’t want you to lose small marks now 
ocean sealBOT
The current time for chartbit is 01:47 PM (GMT) on Thu, 16/11/2023.
ocean sealBOT
You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.
strange fractal
,ti --set
ocean sealBOT
Your timezone has been set to Australia/Perth!
Your current time is 09:47 PM (AWST) on Thu, 16/11/2023.
strange fractal
,ti
ocean sealBOT
The current time for nutgun. is 09:47 PM (AWST) on Thu, 16/11/2023.
strange fractal
ohh
pseudo ice
cool 
strange fractal
pseudo ice
,ti @strange fractal
ocean sealBOT
The current time for nutgun. is 09:48 PM (AWST) on Thu, 16/11/2023.
chartbit is 8 hours behind, at 01:48 PM (GMT) on Thu, 16/11/2023.
pseudo ice
do they look right now?
Yep looking better
pseudo ice
looolll im in the future
Well ahead of me 💁♀️
pseudo ice
In fact perfect 
very happy now
swift thorn
lone heartBOT
lone heartBOT
@swift thorn Has your question been resolved?
swift thorn
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native ferry
Can someone explain how to get the derivative of f(x) = x ln(x^2)
native ferry
I think it has something to do with the chain rule
But I don’t fully understand the chain rule
old heath
You can do it with just product rule
native ferry
So
bronze nebula
use the product rule
native ferry
would I have to do the product rule twice
old heath
No
bronze nebula
No
native ferry
2 ln x
bronze nebula
yes , then use product rule
silver gazelle
Can someone help? Im@not sure what to do
lone heartBOT
Can someone help? Im@not sure what to do
ionic jewel
Can someone help? Im@not sure what to do
use (x,y) points to solve for a and b
lone heartBOT
@silver gazelle Has your question been resolved?
silver gazelle
Ok I did that but like what does it mean by when does the input value equal each other is it asking for the range or the Intersection when I graph it?
Like I got this
<@&286206848099549185> ?
tacit arch
,rotate
ocean sealBOT
tacit arch
Ok I did that but like what does it mean by when does the input value equal each...
https://www.cuemath.com/calculus/exponential-functions/
Scroll down to "Domain and Range..."
lone heartBOT
@silver gazelle Has your question been resolved?
blissful flame
hello I have a doubt
lone heartBOT
hello I have a doubt
quasi scarab
this doesnt require that knowledge i think
blissful flame
I moved the x-1/x to the left part
quasi scarab
left: the denom is smaller, right: the nominator is smaller, what does it tell you?
wild umbra
I moved the x-1/x to the left part
right now simplify it a bit
i think u did a typing mistake
blissful flame
yes
wild umbra
edit it instead of deleting the whole msg lol
blissful flame
x/x-1 -(x-1)/x<0
that
now when i do x/x-1 -(x-1)/x i get x square
in diffrent parts
im confused
wild umbra
take the LCM
blissful flame
what is an LCM?
wild umbra
$\frac{x}{x-1}-\frac{x-1}{x}$\
$\frac{x(x)-(x-1(x))}{(x)(x-1)}<0$
blissful flame
when i tried to do it i got (x.x) (x-1)(x-1)/(x-1)(x)
I multiplied the denominators the same as you
quasi scarab
$\frac{x}{x-1}-\frac{x-1}{x}$\\
$\frac{x(x)-(x-1(x))}{(x)(x-1)}<0$
this doesnt seem correct
blissful flame
but i multipied cross
tall topaz
$\frac{x}{x-1}-\frac{x-1}{x} < 0 \iff
\frac{x(x)-(x-1)(x-1)}{(x)(x-1)}<0$
blissful flame
a/b-(a/b) is (a.b)-(a.b)/(b.b)
tall topaz
oh wait
ocean sealBOT
$Pure$
wild umbra
yea
blissful flame
**$Pure$**
that is what i got
blissful flame
i don´t how to continue
wild umbra
just simplify both numerator and denominator and then its a normal inequality
ocean sealBOT
$Pure$
blissful flame
isn´t it an exponential inequality if you have an x square?
tall topaz
and since that thing is negative you can decude that the numerator and denominator must have different signs (+ and -) then you can split into 2 cases and solve that way.
tall topaz
isn´t it an exponential inequality if you have an x square?
I dont really know what that means
blissful flame
I don´t know either 😦
quasi scarab
then lets say its not exponential xd
quasi scarab
it looks like it, but i didnt check it, but yeah: 0, 1/2 and 1 are the critical (?) points, so u need to check the intervals that those give with 1-1 example and see if its neg or not, and you are done
buoyant hornet
lone heartBOT
@blissful flame Has your question been resolved?
young parrot
got a discrete math problem:
The answer, according to the textbook, is that D is Reflexive, Symmetric and Transitive
young parrot
I do not understand why it would be reflexive
isnt (8,8) a counterexample?
or am i misunderstanding the concept?
prime badge
no, it makes sense that you're confused
they mean like 8 = 8
and also −13, and also 50
they are all congruent at the same time
young parrot
sorry im still not getting it
8 mod 7 is 1, which isnt equal to 8 so (8,8) isnt in the relation right?
young parrot
how would i know that they mean that?
prime badge
i don't know
young parrot
so are you saying that the answer is wrong? like a typo?
prime badge
i mean there was supposed to be an exercise where you learn that they could mean that
you wouldn't know otherwise
young parrot
oh i see
its a whole different notation
i thought it was the "equivalent to" symbol
guess my highschool did not properly prepare me for this
thanks
.close
wild cedar
lone heartBOT
junior vigil
!status
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
!showwork
lone heartBOT
Show your work, and if possible, explain where you are stuck.
wild cedar
can someone explain to me how i can solve it
charred summit
can someone explain to me how i can solve it
First at what step are you here
!status
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
charred summit
So you didn't try to like substitute values at x and check what you will get
Like when x was 1 in the graph f(x) was 8
This would eliminate 2 options
wild cedar
is it d?
charred summit
But the one that would really eliminate 3 options and give you the correct choice is substitute x = 2 as f(x) here will be 16
f(x) here is meant to be y
So that would help you solve the problem
@wild cedar
Got it?
Hmm I don't think this problem requires all that writing but keep on
wild cedar
yeah i got thanks for the help i just need to substitute the value of x and solve the equation if y = to the value in the graph respect to x it is tthe correct answer right?
charred summit
yeah i got thanks for the help i just need to substitute the value of x and solv...
Yeah so what did you get from the choices
charred summit
Correct
wild cedar
thanks for the help
queen salmon
What would be a simple way of solving this?
lone heartBOT
What would be a simple way of solving this?
queen salmon
$2\abs{z} < \abs{z^2 + 1}$ where z is a complex number
ocean sealBOT
LesbianLemon
celest stump
Divide both sides by 2
Or actually
You could divide just the lhs by 2
@queen salmon
Then you could get rid of the absolute signs and work from there
celest stump
If you want graph on Desmos 2(absx) and (abs(x) you can see 2(abs(x)) is always larger
celest stump
Why?
celest stump
Then neither is true in the original case
near apex
I think you are forgetting that z is a complex number.
celest stump
Z is not any complex number
fickle heath
You're supposed to find solutions, not say whether it's true for all numbers
celest stump
^
fickle heath
That was meant for you @celest stump
near apex
Z is not any complex number
We know but so far domain is not restricted at all.
celest stump
That was meant for you <@869395681683587133>
Why doesn’t this hold true?
queen salmon
Yeah with complex numbers absolute value is the distance from the origin
queen salmon
Well you can probably solve any equation by just saying z = x + yi
But it gets ugly very fast often
near apex
Usually, there are methods to solve without having to go for that.
queen salmon
Yes
near apex
We are just unable to see probably.
celest stump
It’s acc quite straightforward if I did it right
queen salmon
And that is how?
celest stump
Oh nvm
queen salmon
Yeah my intuition is telling me its something to do with |z^2 + 1| = |z - i||z + i|
Because those two are distances from i and -i and on the left you have distance from 0
But i dont see how exactly to use that
fickle heath
Neat
near apex
Okay, i have tried to visualise it geometrically and seemingly it should not have any solutions above lines Im(z) = 2i and below Im(z) = -2i. I dunno if that helps.
Hmm. Did i visualise it wrong? Lol
fickle heath
Guess so
queen salmon
Might have flipped the inequality
queen salmon
Two circles with radius sqrt 2
near apex
Ignore that.
queen salmon
Hmm
near apex
I have a useless suggestion but i'll mention, in case, if it can be used somehow. If we make the RHS 1, on LHS we get sth which comes exactly in form of tan(2x) expansion except with the modulus. No use probably, right?
Oh wait.
near apex
$\frac{|2z|}{|z-i||z+i|} = \bigg| \frac{1}{z-i} + \frac{1}{z+i}\bigg| < 1$
This helps?
This is less than 1.
near apex
tan 2x has a minus on the bottom tho?
Ah yes. That doesn't help then.
ocean sealBOT
Enemagneto
queen salmon
Yeah still not sure where the circles come from
I guess if you write it as $\abs{\frac{z}{z^2+1}} + \abs{\frac{z}{z^2+1}} < 1$
ocean sealBOT
LesbianLemon
junior vigil
$|z-c|=r$ is a circle in the complex plane with center $c$ and radius $r$
ocean sealBOT
Moosey
near apex
We can do that?
near apex
**LesbianLemon**
This.
near apex
Yeah. We can't.
fickle heath
Why not?
near apex
I am going crazy.
queen salmon
Not quite the same
near apex
Yeah. They are same numbers here.
queen salmon
**LesbianLemon**
And this is a definition of an ellipse
But in this case its a circle since they are the same
Just a circle when looking at z/(z^2+1)
Now would need to translate this to just z
near apex
Could you possibly ping me if you find a solution?
fickle heath
<@&286206848099549185>
junior vigil
fickle heath
You forgot a factor of 2
junior vigil
ye
added :)
i'm fairly certain you need to convert to Re(z) and Im(z) at some point
fickle heath
junior vigil
it's also more helpful to just square both sides at beginning so you don't have to deal with that icky sqrt()
queen salmon
If you know how to solve after substituting then please enlighten me
When i did that i got something annoying
queen salmon
Problem is the right hand side is already a square inside the absolute value
fickle heath
Perhaps this can help
https://www.desmos.com/calculator/uk8awk2ipv
queen salmon
Maybe i have an idea
Ok i got the solution now but its probably not how youre supposed to solve this
@near apex
near apex
Tell me, regardless.
queen salmon
I put in $z = x + yi$ and forced it into something along the lines of $(x^2 + (y + 1)^2 - 2)(x^2 + (y - 1)^2 - 2) > 0$
ocean sealBOT
LesbianLemon
queen salmon
This came from me seeing the solution
So how i was supposed to solve this without knowing that beforehand i have no idea
If you want i can write it up a bit more
queen salmon
.close
young fossil
hello
wild umbra
!status
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
minor needle
Try to factor the denominators and the numerators
young fossil
ok
minor needle
Then see what cancels out
alpine sable
find the solution set of each of the following equations, where U=R
(2+x^2)=(x^2+6) . 2
pls help
🥺
pls help
lone heartBOT
@young fossil Has your question been resolved?
alpine sable
find the solution set of each of the following equations, where U=R
@minor needle
lone heartBOT
lone heartBOT
Available help channel!
inland ocean
The points (0, −1), (1, 1), and (a, b) are distinct collinear points on the graph of y^2 = x^2 − x + 1. Find a + b.
How on earth do you find out the line passing through the two points equation?
blissful breach
lone heartBOT
blissful breach
Solving for the variable
There is a better picture
I know this is wrong lmao but idk why
blissful breach
Getting the variable one in one side and the number on the other to divide
sleek night
2x=4 not 6 me thinks
blissful breach
I’m so slow ahah. I have 20 of these questions to do 💀 I missed class yesterday when they started so now I’m so behind
How does this look?
ionic jewel
-5x
sleek night
Idk why it seems like it should be x²-5x+2
sleek night
You should add more steps to the final count if u get confused easily it helps usually
blissful breach
yeah and +2
Why +2?
sleek night
Bcs -2=-4 so -2+4=2
ionic jewel
yeah we are all dumb 👍
sleek night
Oh shit
ionic jewel
i saw your -4 underneath and read that instead
blissful breach
To make the side 0
sleek night
IT LOOKED LIKE A -
blissful breach
Sorry my arranging is trash 😂
ionic jewel
okay sure, the x term is still wrong though, but otherwise good
sleek night
yeah its good
lone heartBOT
@blissful breach Has your question been resolved?
proven flare
lone heartBOT
frail trail
of this using the epsilon delta defintion
What is epsilon delta definition?
lone heartBOT
@proven flare Has your question been resolved?
covert cobalt
X^2+1=0
pure jasper
whats the question? are you trying to solve for x in C or R.
x in C
restive forge
x=-0.5, 0.5^2+1=0
pure jasper
wtf
lone heartBOT
@covert cobalt Has your question been resolved?
lone heartBOT
Available help channel!
@idle spear Has your question been resolved?
Available help channel!
rotund shoal
lone heartBOT
rotund shoal
Looking at some working out. What was the point of making two graphs instead of just the one?
by solving the original equation, you can already determine when its le to 0 right?
lone heartBOT
@rotund shoal Has your question been resolved?
rotund shoal
<@&286206848099549185>
lone heartBOT
@rotund shoal Has your question been resolved?
pseudo ice
The intention of them asking you to plot both is that in part (c), you’re supposed to use the sketch you just made (the intersection point x coordinates you know from part a) to solve the inequality
You could e.g. check signs in between each interval if you wished, were it not a “hence” question
lone heartBOT
@rotund shoal Has your question been resolved?
foggy pecan
first at all, you have to correctly set the relation between blue and red area
blue area is bounded by two functions, upper one is a constant y = f(a) and lower is y = f(x),
I told you , how to express blue area
\int_{0}^{a}\left( f(a) - f(x) \right)dx
foggy pecan
$\int_{0}^{a}\left( f(a) - f(x) \right)dx$
ocean sealBOT
Joanna Angel
foggy pecan
and read area: $\int_{0}^{a}\left( f(a) - \sqrt{x} \right)dx$
ocean sealBOT
Joanna Angel
vivid minnow
unless a is a variable?
foggy pecan
this: $\int_{0}^{a}\left( f(x) - \sqrt{x} \right)dx$
ocean sealBOT
Joanna Angel
foggy pecan
and relaiton between areas is $\int_{0}^{a}\left( f(a) - f(x) \right)dx = \int_{0}^{a}\left( f(x) - \sqrt{x} \right)dx$
ocean sealBOT
Joanna Angel
foggy pecan
and now, you need to thikn how to transform into diff euqation
ocean sealBOT
QuasiStar 超新星
foggy pecan
Quasi, inverse function is useless here, i do not udnerstand why you shud take inverse function, inverse to square root, wud be a parabola
if you wud like to use inverse function for f, you wud need to integrate dy, on other interval like [0, f(a)]
yes but what about red area ?
my relation i wrote, doe snot containt inverse function, hence i tihnk it is better
what i got more is:
$\int_{0}^{a}\left( f(a) - f(x) \right)dx = \int_{0}^{a}\left( f(x) - \sqrt{x} \right)dx <=>
2\int_{0}^{a}\left( f(x) \right)dx = af(a)+\frac{2}{3}a\sqrt{a}$
ocean sealBOT
Joanna Angel
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
foggy pecan
plz analyse it if you understand it
few things i calcualted in my mind, since writng latex is not fast haah
and when you analyse it then you can try to differentiate the euqation i got , then i can see, you wil get a derivative f' and f
you only need to remind how to differentitate the integral
hasty creek
this makes it clearer
foggy pecan
next line i got this: $2f(x)=f(x)+xf'(x)+\sqrt{x}$
ocean sealBOT
Joanna Angel
foggy pecan
that i got after diferetiation
i naturally change variables from a to x, to make it look as typicaldiff equation
so we receibe the classical linear diff eqaution of the first order
$f'(x)-\frac{1}{x}f(x)+\frac{1}{\sqrt{x}}=0$
ocean sealBOT
Joanna Angel
foggy pecan
so lok at my equaiton
is the same )
i received the same equation
to make you remind the formula for linear diff equaitons of the first order you can use this:
foggy pecan
yes
ocean sealBOT
QuasiStar 超新星
foggy pecan
yes replace a with x
before
differentiaiton
then you get: $y'-\frac{1}{t}y=-\frac{1}{\sqrt{t}} <=> y(t)=\left( \int_{}^{}-\frac{1}{\sqrt{t}}exp\int_{}^{}-\frac{1}{t}dt+C \right)exp\int_{}^{}\frac{1}{t}dt$
but these integrals are very simple, only how it looks can be scaring lol
ocean sealBOT
Joanna Angel
foggy pecan
$Finally: y(t)=\left( \frac{2}{\sqrt{t}}+C \right)t=Ct+2\sqrt{t}$
ocean sealBOT
Joanna Angel
foggy pecan
you may return to x instead fo t
ofc
plz notice that my answer is perfectly mathcing the point (b) too from yoru task from yoru instructor
what is the name of your subject at school? Calculus 1 ?
ocean sealBOT
QuasiStar 超新星
foggy pecan
ok)
for me it is typical calculus 1 or precaculus, depends on university
have you ever solved linear diff equation of the first order ?
you can write this way:
$f'\left(x\right)-\frac{1}{x}f\left(x\right)=-\frac{1}{\sqrt{x}}$
ocean sealBOT
Joanna Angel
foggy pecan
but due to my work with my students, i put y = f(t). and y'=f'(t)
$y'-\frac{1}{t}y=-\frac{1}{\sqrt{t}}$
ocean sealBOT
Joanna Angel
foggy pecan
The general form of such an equation is: $y'+p(t)y=q(t)$
ocean sealBOT
Joanna Angel
foggy pecan
and the general form of the solution loosk in the following way:
$y(t)=\left[ \int_{}^{}q(t)exp\int_{}^{}p(t)dt + C\right]exp\left( -\int_{}^{}p(t)dt \right)$
ocean sealBOT
Joanna Angel
foggy pecan
where: $p(t)=-\frac{1}{t}$ and $q(t)=-\frac{1}{\sqrt{t}}$
ocean sealBOT
Joanna Angel
ocean sealBOT
Joanna Angel
foggy pecan
happens
we may additionally, consider the initial condition: y(a) = f(a)
and then it is easy to evaluate C
though, it is rather for bok style than fo rshcool haha
your instructor also have set k, and did not want to comotue it further ) was lazy lil bit
yw)
not -e
you get exp(lnx)
since minus and minus makes it plus
and exp(lnx) = x
i shwo you
ocean sealBOT
QuasiStar 超新星
foggy pecan
it is wrong
return to what i wrote last
$y(t)=\left[ \int{}^{}[q(t)exp\int{}^{}p(t)dt]dt + C\right]exp\left( -\int_{}^{}p(t)dt \right)$
where: $p(t)=-\frac{1}{t}$ and $q(t)=-\frac{1}{\sqrt{t}}$
ocean sealBOT
Joanna Angel
foggy pecan
you need to put given functions and caerfully write
ocean sealBOT
Joanna Angel
foggy pecan
great)
lone heartBOT
foggy pecan
yw)
lone heartBOT
Available help channel!
copper kite
This is the question
lone heartBOT
This is the question
copper kite
This is the Worked solution but i am struggling to understand what the first paragraph means
can someone explain why the angle subtended is pi/N
dusty dagger
hi
lone heartBOT
@copper kite Has your question been resolved?
rocky atlas
N is the number of sides of N-gon
copper kite
N is the number of sides of N-gon
yes
rocky atlas
And the angle in question would be the angle between centre to vertex and centre to half of adjacent edge to that vertex
So if we find the angle between centre to vertex and centre to adjacent vertex to be 2pi/N, we can say that half of which would be pi/N
rocky atlas
Np
copper kite
.close
last aurora
does anyone know how the first line becomes the second line?
rocky atlas
Seems like they used product rule
last aurora
Seems like they used product rule
wouldnt that leave only 2* dz/dx though?
rocky atlas
Used uv rule to differentiate wrt r later
rocky atlas
sry im like completely lost here
No worry. I wasn't scolding or anything
last aurora
wait lemme clarify
rocky atlas
Ok
rocky atlas
Yes
last aurora
a would be d/dr
rocky atlas
Or ab rule
rocky atlas
We use product rule within derivative
last aurora
i think i am lost.
rocky atlas
What happened
last aurora
is it ok if u write out the steps for me ;-;
rocky atlas
actually I'm eating and typing from 1 hand
last aurora
o ok
rocky atlas
So my eat is finished now
last aurora
;^;
rocky atlas
Product rule is used to differentiate a product between 2 terms
So if we want to use product rule on uv, it's actually, d/dx(uv)
You can't use product rule thinking d/dx is a and uv is b
last aurora
assuming u and v are all functions of x right?
rocky atlas
Can be or can not be
last aurora
okay
rocky atlas
The result is satosfactory
Like if I want to differentiate a constant, suppose 5 with respect to x, I can write 5 as a product of 2.5 and 2 and use product rule
It will give d/dx(2.5)*2 + d/dx(2)*2.5, and we see it's 0
last aurora
yeh i see that
rocky atlas
So u get the idea
rocky atlas
It can be anything, not necessarily the function of what we are differentiating wrt
rocky atlas
im just confused as how product rule works in partial derivs
Well if variable is y, and you're differentiating wrt x, it just dy/dx, nothing serious
rocky atlas
the textbook went into an example with product rule without teaching it first
I see, that's must be tough
So back to original question then, shall we
last aurora
yah
rocky atlas
We are focusing on the left side of equation
the expression is d/dr(2r(dz/dz) + 2s(dz/dy))
I just wrote it here since it's what next which you're suffering from
rocky atlas
Yes
rocky atlas
If you're given a(b+c) you can expand bracket right?
last aurora
ab+ac
rocky atlas
Not really
last aurora
so i cannot really treat d/dr as a constant and distribute it out
rocky atlas
Yes
last aurora
alright
rocky atlas
From what I see, z, r and s are variables
last aurora
yes
rocky atlas
Anything related to them can't be treated as constant
rocky atlas
So after expanding we get something else
last aurora
yes that is what i have been guessing for the past half an hour
rocky atlas
this is full question and sol btw
That won't be needed thou since we are only focusing on the next sentence ur confused over haha
last aurora
got it
last aurora
i can see that