and this is what I've done:
#help-26
novel token
Do you know what separation of variables is in differential equations?
livid pelican
um I don't think so
novel token
Well basically just put all the r’s
On the left
And all the t’s on the right
Which is almost what you did
But..
That thing you called b which is dr/dt has a t!
livid pelican
yup
livid pelican
yes, that makes sense
novel token
Let’s go back to this
Cuz what you did became messy
From this equation try and separate r and t
Note: k and a can be wherever they don’t matter
livid pelican
novel token
Not quite
livid pelican
oh yeah xD
novel token
What’s the integral of x/(1-x^2)
livid pelican
-ln(x^2-a^2)/2 +C
novel token
-ln(a^2-x^2) +C
Yea you don’t need to divide by 2 cuz you already have 2r
And the denominator is a2-x2 not the other way around
livid pelican
-ln(a^2-x^2) +C
please can you explain this?
novel token
-ln(x^2-1)/2
Here you should divide by 2 cuz I said integral of x/… not 2x/…
novel token
please can you explain this?
Well can you tell me how you got -ln(x^2-1)/2
livid pelican
Here you should divide by 2 cuz I said integral of x/… not 2x/…
oh yeah but we I have x^2-a^2 rather than a2-x2
let u = a2-x2
for some u sub
livid pelican
we get dx = -1/2x du
novel token
good
livid pelican
so we have -1/2 \int 1/u du
novel token
ok
now before you finish
do the same steps for the integral we care about
integral of 2r/(a^2-r^2)
novel token
exactly
livid pelican
yet u = a^2 - x^2
novel token
yup
livid pelican
so we have -ln(a^2 - x^2)
novel token
+c
livid pelican
ah yes
novel token
so there you go
livid pelican
so kt = -ln(a^2 -r^2) + C
livid pelican
livid pelican
the radius
livid pelican
yup
novel token
indeed
novel token
perfect
livid pelican
so for these type of problems we should seperate variables, then integrate, then use conditions?
novel token
exactly
sturdy vigil
Who knows how to tackle this -1 into a logarithm?
topaz sinewBOT
Who knows how to tackle this -1 into a logarithm?
sweet shard
Who knows how to tackle this -1 into a logarithm?
is that a "minus 1" ?
sturdy vigil
Yes
sweet shard
Who knows how to tackle this -1 into a logarithm?
you don't need to. just add 1 to both sides
thorny flameBOT
sweet shard
and what equation are you working with and what variable are you solving for?
sweet shard
use $\log_2(2) = 1$
thorny flameBOT
riemann
sturdy vigil
What?
thorny flameBOT
sweet shard
Same as ^g log (a)?
yes
#help-4 message
sweet shard
Same as ^g log (a)?
it's also much more standard in the math resources as well.
than $^g \log(a)$
thorny flameBOT
riemann
sturdy vigil
I’m sorry I’ve just been taught differently hence the confusion
I just want to know how to get the -1 into the logarithmic
I have no formula’s
sweet shard
**riemann**
do you understand this now?
sturdy vigil
Yes
sweet shard
put it in here
sturdy vigil
I come to ^2log(x^3) -1
But -1 needs to be manipulated into the logarithm, that’s my question
thorny flameBOT
riemann
topaz sinewBOT
@sturdy vigil Has your question been resolved?
sturdy vigil
**riemann**
^2log(2) = 4 not 1?
topaz sinewBOT
^2log(2) = 4 not 1?
neon iron
62 students are picking two activities to do over the weekend.9 picked painting and sport.
11 did not pick painting or sport.
Twice as many students picked sport than painting as one of their activities.Find the amount that picked sport and not painting.
waxen storm
^2log(2) = 4 not 1?
Its 1
sturdy vigil
How is 2^2=1 and not 4?
waxen storm
^2log(2) = 4 not 1?
Let log (base 2) 2 = k
Then 2^k=2^1
so k=1
So log (base 2)2=1
sturdy vigil
I can only assume that ^g log(a) isn’t the same as the above mentioned
It’s also looking like Chinese to me
Perhaps I should go sleep 💤
waxen storm
62 students are picking two activities to do over the weekend.9 picked painting ...
Is the answer 31
sweet shard
I can only assume that ^g log(a) isn’t the same as the above mentioned
do you have any calculators? this is a basic property of logarithms
sweet shard
It’s also looking like Chinese to me
like i said just get used to the notation that a majority of people who use math use. sorry if you're in the minority, but it's not that complicated to remember
topaz sinewBOT
@sturdy vigil Has your question been resolved?
neon iron
Is the answer 31
yeah but idk how
topaz sinewBOT
topaz sinewBOT
Available help channel!
misty basin
Could i have help
marble hawk
S(y2-y1)dx =576 then solve for c.
broken magnet
for p-series, why arent they convergent at p = 1
topaz sinewBOT
for p-series, why arent they convergent at p = 1
broken magnet
.close
faint fox
Hi I need help solving the scale factor
topaz sinewBOT
Hi I need help solving the scale factor
faint fox
When I solve it the way my teacher showed, I get an answer of 2
but when I do it in reverse, I get 0.5 which is what the textbook says
junior widget
AB and DE are corresponding, to get from m(AB) to m(DE) what do you have to scale AB by?
faint fox
2
junior widget
but when I do it in reverse, I get 0.5 which is what the textbook says
You got it correct
1/2 is the correct answer
faint fox
so then why does the textbook say 0.5
junior widget
DEF is the image of ABC
junior widget
so then why does the textbook say 0.5
Because the textbook is correct?
The answer is 1/2
thin oak
so then why does the textbook say 0.5
2/4 = 0.5
junior widget
AB * k = DE
8k = 4
k = 4/8 or 0.5
faint fox
so smaller triangle to larger triangle? basically instead of 8/4 I do 4/8
the way i solve it is:
n = AB/DE = number/number = number
but instead of AB/DE
do DE/AB?
nvm ur way actually makes a lot more sense
thanks man
much appreciated
.close
topaz sinewBOT
faint fox
.reopen
topaz sinewBOT
✅
faint fox
wait a minute @junior widget
can u explain how my teacher got this then
scale factor of 2
i just did it ur way and its also 0.5
is her method even corrrect
@junior widget
junior widget
Your teacher doesn't understand why they are using ABC and DEF
DEF is the image of ABC
At least, thats how the alphabet works
Either way, your answer and your teachers are both Correct in a way
faint fox
thats helpful but also not helpful cause idk wth shes gonna quiz me on when the time comes, gotta ask her tmrw
thanks for the help man
much appreciated
.close
digital vale
can u explain how my teacher got this then
use the sine rule.
topaz sinewBOT
use the sine rule.
faint fox
use the sine rule.
im grade 10 bro idek what that is
digital vale
nvm
digital vale
a you know trig?
faint fox
just started it today
digital vale
oh crap
you could google the cosine rule
it will help you solve it in a second lol
faint fox
we're prob gonna learn it cause my teacher made a bunch of sub folders
faint fox
it will help you solve it in a second lol
im guessing its the same with the quadratic functions cause our teacher made us go through hell before showing it to us
digital vale
im guessing its the same with the quadratic functions cause our teacher made us ...
factoring is not too bad
faint fox
factoring is easy
getting the roots without the quadratic equation in a trinomial is hard
especially if ur me
digital vale
use a computer lol
faint fox
i used to use some wolfram alpha widget
digital vale
it's much easier if you the computer and get the answer then factor it to get the answer
digital vale
can u explain how my teacher got this then
i think ur teacher got the y wrong
faint fox
cause of the scale factor?
empty sail
i think ur teacher got the y wrong
Why would it be wrong?
faint fox
the scale factor is questionable but everything else seems right
shes subbing it in from the other shape
empty sail
It's similar shapes, so $\frac{12}{6} = \frac{y}{4.5}$
thorny flameBOT
dldh06
empty sail
So y = 9
digital vale
Why would it be wrong?
i tried out the cosine rule and it give me 4 sqrt 7
oh yea similiar shape
faint fox
cant wait till i learn the cosine rule
:D
anyways thanks for all the help
u guys have a great night
😘
faint fox
cya
empty sail
good day <@338812629386657804>
FYI, your channel so you have to close it
topaz sinewBOT
@digital vale Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
neon iron
<@&286206848099549185>
topaz sinewBOT
@neon iron Has your question been resolved?
gleaming pasture
topaz sinewBOT
gleaming pasture
Can someone help me with this proof
topaz sinewBOT
@gleaming pasture Has your question been resolved?
wide berry
Can someone help me with this proof
what have u tried
frosty musk
void edge
anyone expert in algorithmic graph theory
topaz sinewBOT
anyone expert in algorithmic graph theory
void edge
please give a shout. need help
loud dawn
@void edge is it a very long/complicated question?
You might wanna ask in #numerical-analysis
neon iron
loud dawn
I’ve seen some questions that are very long
It would be easier to find someone who’s willing to read beforehand
Cause most people see big paragraph and nope out
neon iron
but i just needed an excuse to post that sticker
loud dawn
lol
topaz sinewBOT
@void edge Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
sterile ridge
Hey, what is the correct answer to the integral of 1/(3x) dx?
I got 1/3*ln|3x| when I used the formula 1/(ax+b) dx = 1/3*ln|ax+b| and my teacher got 1/3*ln|x| when he separated 1/3 from the original integral and integrated 1/x alone since constants survive.
Bottom line my teacher thinks we’re both right but he wasnt able to prove that the results were the same by trying to get to 1/3*ln|x| from 1/3*ln|3x|.
If you derivate both integrals you do get back to 1/(3x) 
wide berry
Hey, what is the correct answer to the integral of 1/(3x) dx?
I got 1/3\*ln|3x|...
derivate both integrals
differentiate, not derivative
wasn't able to prove
But you differentiated both results and showed that they're the same?
The key is to realise that antiderivatives differ by a constant. 1/3 ln|x| - 1/3 ln|3x| = 1/3 ln|x/3x| = 1/3 ln(1/3) which is a constant
sterile ridge
> derivate both integrals
differentiate, not derivative
> wasn't able to prove
B...
Ah we use derivate also as a verb in Norwegian, we “derivate” to find the derivative
wide berry
Ah we use derivate also as a verb in Norwegian, we “derivate” to find the deriva...
Sure, in Norwegian, but not in English
sterile ridge
I didnt learn math in English 
sterile ridge
> derivate both integrals
differentiate, not derivative
> wasn't able to prove
B...
Yes, well, I differentiated both integrals in my head after class but he was trying to get to my result using his result and some logarithmic formulas… this was actually part of an answer to a longer integral, but this was the only difference in our answers
I’ll share both our answers when I get home
topaz sinewBOT
@sterile ridge Has your question been resolved?
topaz sinewBOT
@sterile ridge Has your question been resolved?
sterile ridge
Hey, so I'm back home, and the original math problem was; ∫(x² + 2x + 1/(3x)) dx where I got 1/3⋅x³ + x² + 1/3⋅ln|3x| + C and my teacher got 1/3⋅x³ + x² + 1/3⋅ln|x| + C
My teacher thinks we're both right, but struggled proving it. While we can see that these are two different solutions, how can these be the same? And if they're not the same, which is correct?
sterile ridge
> derivate both integrals
differentiate, not derivative
> wasn't able to prove
B...
So with this
The key is to realise that antiderivatives differ by a constant. 1/3 ln|x| - 1/3 ln|3x| = 1/3 ln|x/3x| = 1/3 ln(1/3) which is a constant
1/3ln(1/3) is part of the constant C?
Thing is though, if you inserted a value for x, wouldn't these two functions produce two different results?
So because of this, these can't both be correct solutions..?
wide berry
So because of this, these can't both be correct solutions..?
No.
For example, integrate 1/(3x) dx from 1 to 3.
Use 1/3 ln|x| as antiderivative to get 1/3 ln(3) - 1/3 ln 1 = 1/3 ln(3).
Use 1/3 ln|3x| as antiderivative to get 1/3 ln 9 - 1/3 ln 3 =1/3 ln(3).
Any constants cancel when doing the integration
sterile ridge
So, since C is an unknown constant, we can't for sure know what f(x) will be if we integrate f'(x), thus f(x) will differ by C which includes 1/3ln|3x|, making both integrations correct?
Is that what you mean?
sturdy oracle
Hey, so I'm back home, and the original math problem was; `∫(x² + 2x + 1/(3x)) d...
$\int \frac{1}{3x}{dx}= \frac{1}{3}\int \frac{1}{x}{dx}$
thorny flameBOT
Umbraleviathan
sturdy oracle
But then I'm getting (1/3)ln|x|
sterile ridge
But then I'm getting (1/3)ln|x|
Same as my teacher
sturdy oracle
It can't be ln|3x| because by chain rule, if you derive ln|3x| you get (1/x)
sterile ridge
However, if you use the formula ∫1/(ax+b)dx = 1/a⋅ln|ax+b| + C, then you get my result
sturdy oracle
where a = 3 and b = 0?
Uh lemme think
No that's not right
Lemme think
Oh you know what
That only works when b ≠ 0
That's because if b = 0, the "a" would cancel out
Leaving you, by chain rule, with (1/x)
sterile ridge
It can't be ln|3x| because by chain rule, if you derive ln|3x| you get (1/x)
Chain rule
(1/3 ⋅ ln|3x|)' = (1/3 ⋅ ln|u|)' = 1/3 ⋅ 1/u ⋅ u' = 1/3 ⋅ 1/(3x) ⋅ 3 = 1/(3x)
sterile ridge
No 🙃
If we differentiate both integrals, we get back to where we started
So both have to be correct, unless I'm missing something
sturdy oracle
Oh atcually
Hmm
Well m $\frac{1}{3}\ln{|3x|} = \frac{1}{3}ln{|x|} + \frac{1}{3}\ln{(3)}$
thorny flameBOT
Umbraleviathan
sturdy oracle
Which would get the same result if you derived it
sterile ridge
True, so, can one say that 1/3⋅ln3 is part of the unknown constant C?
sturdy oracle
You could, but it isn't the value of C
sterile ridge
No, but it's part of it, right?
sturdy oracle
Mmhm
topaz sinewBOT
sturdy oracle
Sweet, thanks!
The only way I think you would've gotten your answer is by u-subbing then
3x = u
This is how you get (1/3)ln|3x|
topaz sinewBOT
Available help channel!
icy pilot
topaz sinewBOT
icy pilot
Is there a way to find the range just from the equation? or do you have to draw the graph and points
the 3 in the equation represents the y value so I get the 3, but how do you know whether it's going to go to positive or negative infinity from just the equation?
junior widget
Is there a way to find the range just from the equation? or do you have to draw ...
There is a way to find the asymptote
Then you know it keeps going to to infinity
The asymptote is just 3 because the +3
icy pilot
How do you know it keeps going to infinity?
junior widget
How do you know it keeps going to infinity?
Because it's an exponent
All real values work
So you can just keep making x larger
,w graph 2^x + 3
thorny flameBOT
icy pilot
what's the latex of
topaz sinewBOT
what's the latex of
floral rampart
$$f(x) = a\log_b(x-h)+k$$ do you want those arrows too?
thorny flameBOT
ohNoiAmHere
icy pilot
$$f(x) = a\log_b(x-h)+k$$ do you want those arrows too?
No, thanks
Btw, the b of the logarithmic graph doesn't represent growth / decay like how the exponentials does right?
floral rampart
hmm, it's simply the base of the logarithm, something with a larger base will be smaller. its not really growth though
there are models with log though
topaz sinewBOT
@icy pilot Has your question been resolved?
old flicker
do you guys know if these two equations represent the same plane?
-x+3y-z=0
-5x+15y-5z=0
topaz sinewBOT
do you guys know if these two equations represent the same plane?
-x+3y-z=0
-5x+...
old flicker
I guess it does since u can multiply the top equation with 5
oak sequoia
hearty wraith
topaz sinewBOT
hearty wraith
can someone help me please
keen venture
First you'll want to find x in terms of θ
Then the calculus is the easy part. Differentiate in terms of t, keeping in mind that dθ/dt = π
topaz sinewBOT
Available help channel!
mossy sapphire
what is half of 10 powered to 500? And what number gets the same result if you multiply it by 0,2 or subtract 0,2 from it?
topaz sinewBOT
what is half of 10 powered to 500? And what number gets the same result if you m...
@mossy sapphire Has your question been resolved?
mossy sapphire
<@&286206848099549185>
topaz sinewBOT
@mossy sapphire Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
terse finch
hi
terse finch
i'm curently tring to do the 1 (a) for this i need to modifiate the 3 expretion to get the 1 ou the 2
for the moment i try partial integration but i don't fin an end to the cycle, i have been thinking of using change of variable but can't find one usefull so if you have any lead please
<@&286206848099549185>
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
livid field
topaz sinewBOT
livid field
Also see the given figure of thos above question
livid field
I don't understand that whether they are talking about area of whole triangle or right angled triangle .
topaz sinewBOT
@livid field Has your question been resolved?
trail timber
help
trail timber
im stuck
topaz sinewBOT
@trail timber Has your question been resolved?
topaz sinewBOT
@trail timber Has your question been resolved?
sweet shard
timber jungle
topaz sinewBOT
timber jungle
i need help with a decent amount of questions if anyone can help pls do i have a big exam tmrw
hallow depot
its to late
neon iron
do you know about vector addition?
timber jungle
do you know about vector addition?
yes
timber jungle
90?
neon iron
i already solved for the hypo
no need for that
neon iron
i did tan-1(theta) to get angle
what did you take as base?
timber jungle
not tan-1(theta) i mean tan-1(15/5)
neon iron
You did a common mistake
neon iron
nope
you've taken 5 as the base
so the angle you got is wrt east direction
got what you did wrong?
neon iron
this is how i drew it
draw the theata; there are two angles here and you're getting confused b/w em,
neon iron
you're getting confused b/w these two angles
neon iron
perfect, so the angle is 71.6° right?
timber jungle
yes
neon iron
now look at the options
neon iron
perfect
neon iron
is that it?
did you know why you did that?
neon iron
because in the options you're trying to find the angle wrt south which is y axis, whereas the angle you calculated is wrt x axis
neon iron
yes
neon iron
so i found theta 1
because you've taken 5 as the base and tan theata = perpendicular/base
perfect
so if you've calculated tan-1(5/15) you'll get the angle from y axis
@timber jungle got it?
timber jungle
i got the first part but i dont rlly get why i would do tan-1(5/15) can u show me a triangle with the xy plane pls
timber jungle
this may be a dumb question but how do i know which is the perpendicular and which is the base ,-,
neon iron
this may be a dumb question but how do i know which is the perpendicular and whi...
I got the same question when I started trg.
1 min I'll explain
@timber jungle read it few times and try to visualise what I'm saying you'll get it ;)
the last lines are enough to get it
timber jungle
alr i get it i think
timber jungle
7?
neon iron
fuck this isn't a right angle
timber jungle
ye was gonna ask that xD
neon iron
assume the angle to be 90°
neon iron
7?
"the line opposite to theata is the perpendicular" you need some visualisation
check some yt videos it'll help
timber jungle
isnt 7 the line opp to the angle?
neon iron
isnt 7 the line opp to the angle?
so 7 is the perpendicular
neon iron
hence 9 is the base
neon iron
u wanted base <_<
so you got it right?
timber jungle
ye ye i get it
neon iron
nice
look at the problem, now you'll be able to solve it
tan theata = (perpendicular/base)
timber jungle
np!
neon iron
have my physics work pending
timber jungle
<@&286206848099549185>
sweet shard
<@&286206848099549185>
plug in the polar to cartesian transformations to the polar equation
r^2 = x^2 + y^2 etc
timber jungle
i dont get it i tried multiplying the whole thing by r
sweet shard
first step is $r (1 + \cos(\theta)) = 2$ then use $x = r\cos(\theta)$ and/or $y=r\sin(\theta)$
thorny flameBOT
riemann
sweet shard
if i multiply by r i get
x^2+y^2+r^2cos(theta)=2
you want to substitute all r and theta for x and y
topaz sinewBOT
Available help channel!
unkempt stratus
@sweet shard
rapid inlet
topaz sinewBOT
mellow venture
rapid inlet
Yeah I don't know exactly what it means
sturdy oracle
You don't know what the chain rule is?
rapid inlet
I know what the chain rule is
rapid inlet
-_-
sturdy oracle
A composite within a composite
derivOuter • derivInner • derivInnerInner • derivInnerInnerInner ...
So let's start with the sine
Take the derivative with respect to the outer
What would that look like
sturdy oracle
Yeah so that's a beginning
So now you gotta multiply that by the derivative of sin(6x^7)
Doing this step-by-step
tulip light
$$\frac{d}{dx} f(g(h(x))) = f'(g(h(x))) \cdot \frac{d}{dx} g(h(x))$$
just as a note, you can think of g(h(x)) as a single function and use chain rule as if you had f(g(x)) then for the derivative of g(h(x)) you apply chain rule again
thorny flameBOT
Doggo
rapid inlet
So now you gotta multiply that by the derivative of sin(6x^7)
why is that
atomic swift
I did a similar problem
rapid inlet
i'm not trying to be difficult i'm just trying to figure it out so i can do it myself later
sturdy oracle
Yeah you can use J42's as an example
You gotta like
Well you have the first step done
rapid inlet
I would think that would only apply if sin^2(x) = sin(sin(x))
brb gotta grab something from the oven
thorny flameBOT
Umbraleviathan
atomic swift
First let u=6x^7 and find du/dx
sturdy oracle
It's easier to just use chain rule for this
atomic swift
Then let v=sin(u) and find dv/du
Finally differentiate your term with respect to v
Then multiply by du/dx and dv/du
atomic swift
Its the same thing but more working
Just watch black pen red pen on YouTube and you will be brilliant at differentiation it really helped me this year in maths
rapid inlet
so uhh then you get
cos(6x^7) right?
or no
I forget how to take a derivative of sin with something other than just x in it
rapid inlet
But now you gotta do the inner, which is the sine
is that what you mean
oh wait am I supposed to use chain rule here
like
$\frac{d}{dx}(sin(6x^7)) = cos(6x^7)*(42x^6)$
thorny flameBOT
Eyesonjune
sturdy oracle
Yeah
rapid inlet
now what do I do
neon iron
$\1+1
thorny flameBOT
Eyesonjune
rapid inlet
.close
jovial mason
I'm very stuck at b)
topaz sinewBOT
I'm very stuck at b)
jovial mason
can you help me understand the hint? I'm not sure what it means by applying T n-1 times
for (b)
sweet shard
$T^{n-1}(v) =T(T(....(T(v))))$
thorny flameBOT
riemann
sweet shard
for n = 3: $T^2(v) = T(Tv)$
thorny flameBOT
riemann
sweet shard
If $v$ is an eigenvector, then $Tv = \lambda v$
thorny flameBOT
riemann
sweet shard
Since $T$ is a linear operator, factor out lambda
thorny flameBOT
riemann
jovial mason
I'm not sure how this proves linear independence, do I have to factor out lambda n times for every v_n?
sweet shard
do the hint first
blazing crescent
what does a discriminant show?
topaz sinewBOT
what does a discriminant show?
blazing crescent
$b^2-4ac$
thorny flameBOT
yomiko
neon venture
it's one of the best way to determine the number of roots of a quadratic
blazing crescent
it's one of the best way to determine the number of roots of a quadratic
does it only work on x^2 function?
faint coral
does it only work on x^2 function?
yes
neon venture
does it only work on x^2 function?
i mentionned "quadratic" so yes
blazing crescent
what about if i want to know how many roots on other functions
blazing crescent
i mentionned "quadratic" so yes
like x^3 or x^4
blazing crescent
what about if i want to know how many roots on other functions
^
neon venture
A polynomial of degree n has at least n roots
subtle flame
Hello I’m very stuck at this question I don’t get it
topaz sinewBOT
Hello I’m very stuck at this question I don’t get it
subtle flame
This is basically my work
But it still feels wrong 🫤
Not sure if I’m doing it correctly but I cant grasp what the videos are saying either
bitter hemlock
hello, the key thing to notice is that triangles BAC and DBC are similar (they share angle C, they both have a 90 degree angle, therefore all their angles are congruent)
Using ratios of corresponding sides of similar triangles you can see there is this relation:
4/x = x/3; solving for x yields x = 2√ 3
here are the corresponding sides of these similar triangles if that makes it easier to visualize
subtle flame
hello, the key thing to notice is that triangles BAC and DBC are similar (they s...
Thank u so sm ❤️❤️❤️❤️❤️ this made it so much clearer
topaz sinewBOT
Available help channel!
buoyant path
I'm trying to get the primitive function of:
topaz sinewBOT
I'm trying to get the primitive function of:
buoyant path
The answer is supposed to be
But I have no idea how that could be the answer
what I tried was just
visual rose
primitive function is the antiderivative?
buoyant path
Yeah
visual rose
ok
visual rose
do you recall the rules for derivation when $f=e^{ux}$ ?
thorny flameBOT
madlor
visual rose
ok, whats $f'$?
thorny flameBOT
madlor
visual rose
that is correct
okay
now do you agree that the antiderivative would be the excact opposite?
buoyant path
I tried doing that but in reverse
visual rose
yeah, what did that look like?
visual rose
go for it 👍
buoyant path
yep I was just overthinking things
All I had to do was take 150/-0.3
ty for the help
buoyant path
.close
neon iron
"A solution contains 1% salt. The solution is set outside and aftersome time, water loss has occured. The solution has lost x% of it's mass and the new salt content is 10%. What is the value of x?"
I setup two equations, $\frac{S}{m} = 0.01$ which describes its intitial state. After the loss, $\frac{S}{mx} = 0.1$ We can subsitute S from the first equation to the second one: $\frac{0.01m}{mx} = 0.1 \Rightarrow x =\frac{0.01}{0.1} = 0.1$
thorny flameBOT
Duck Observer
neon iron
The answer sas "x has to be greater than 80%"
Which means mine is wrong
Could anyone guide me?
tulip light
**Duck Observer**
losing x% mass means you multiply by $1 - x$ assuming $0 \leq x \leq 1$
thorny flameBOT
Doggo
tulip light
@neon iron
neon iron
$x_f = 1-x = 1-0.1 = 0.9?$
thorny flameBOT
Duck Observer
neon iron
Ah
neon iron
I will try and solve it with (1-x)
Oh 😦
Solving it with (1-x) in the second equation gives: $\frac{0.01}{(1-x)} = 0.1 \Rightarrow x = \frac{0.1-0.01}{0.1} = 0.9$
thorny flameBOT
Duck Observer
tulip light
mhm seems right
neon iron
mhm seems right
Thank you, may the Duck Bless you, Doggo
topaz sinewBOT
@neon iron Has your question been resolved?
final wren
Hey, can someone help me find the derivative of equations of type x^2 + y^2 = 1?
sullen depot
how does induction work with the special E that means the sum of all?
sullen depot
llike for example this one
when i get to the step of replacing N with K do I just leave the I's alone? or do othey get replaced with k's too?
I don't need to solve it fully I only need to get it to the form of what the left and right side would be at k+1
topaz sinewBOT
@sullen depot Has your question been resolved?
sullen depot
<@&286206848099549185>
Im a bit confused about the K+1 step as well Like I understand your just putting K+1 instead of K but theres another thing you have to do to it that I'm not seeing and I don't quite get what I'm missing about it.
topaz sinewBOT
@sullen depot Has your question been resolved?
topaz sinewBOT
@sullen depot Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
ripe ridge
can someone explain how those two sets are equal
topaz sinewBOT
can someone explain how those two sets are equal
ripe ridge
so C is the subsets of A
which is S with one more element
how do they have the same number of elements when C has one more element
hollow bone
so C is the subsets of A
C is not all the subsets of A
ripe ridge
i meant B is
hollow bone
its the set of subsets that contain element d
ripe ridge
my bad
ripe ridge
its the set of subesets that doesnt contain element d
it is the set of subsets of A
A without d
isnt it?
I mean it even says that
hollow bone
yeah its the set of subsets of A\ {d}
ripe ridge
then how is | B | = | C |
hollow bone
for each set in B you can match a set in C, (one to one correspondance)
forall X in B it corresponds to XU{d} in C
and forall X in C, since d is in X
X = {d} U Y where Y is a subset of A\ {d}
so Y is in B
so there is indeed a one to one correspondance between elements of B and C
ripe ridge
ripe ridge
forall X in B it corresponds to XU{d} in C
so the subsets of B are the subsets of C
but with d
ripe ridge
hmm i think i got it, thanks
im gonna wait to see if anyone else has anything to add
if not ill close it
hollow bone
topaz sinewBOT
@ripe ridge Has your question been resolved?
fluid lark
for legendre's formula what if the number inside the brackets doesn't have a factorial?
topaz sinewBOT
for legendre's formula what if the number inside the brackets doesn't have a fac...
@fluid lark Has your question been resolved?
topaz sinewBOT
@fluid lark Has your question been resolved?
fluid lark
<@&286206848099549185>
knotty ledge
You should show the formula and exactly what you mean
fluid lark
.close
queen forum
Just doing some graphing functions revision, not sure how to go about rewriting this function\
topaz sinewBOT
Just doing some graphing functions revision, not sure how to go about rewriting ...
@queen forum Has your question been resolved?
thorny flameBOT
Rœmer
mental skiff
We can find $\frac{x^2 +x}{x-1} = \frac{x^2-1+x+1}{x-1} = \frac{x^2 -1}{x-1} + \frac{x+1}{x-1}$
and then rewriting should be fairly easy
thorny flameBOT
Rœmer
queen forum
I can see where you're going with it 
mental skiff
have you solved it ?
wraith marsh
Can anyone help me with some homework problems
mental skiff
Can anyone help me with some homework problems
ask in one of the openhelp channels
mental skiff
nice !
queen forum
.close
topaz sinewBOT
mental skiff
np
topaz sinewBOT
Available help channel!
jade cobalt
Umm I just asked a question but uhh I’m weak sry ;-;
topaz sinewBOT
Umm I just asked a question but uhh I’m weak sry ;-;
jade cobalt
This equals this ?? I’m not sure about it but got nothing in my mind I could do to solve it xd
knotty ledge
,rccw
thorny flameBOT
thorny flameBOT
iCaird
knotty ledge
,rccw
thorny flameBOT
knotty ledge
take a screenshot of it on the computer/phone
jade cobalt
knotty ledge
alright
and do they want every solution? just integer ones?
because with the way you've wrote it, finding all solutions is very very tricky and I don't think you'd be expected to find those
but if its meant to be what I wrote earlier than its a lot easier
hollow hedge
so the problem just asks for roots in that interval?
jade cobalt
Dunno how to say it in English xd
Like when the function come across x and y xd
Uhh
hollow hedge
right, that wouldnt be touching
touching here would imply the curve is tangent to these axis
a better word would be "intercepting" or simply "crossing"
anyway, since you are restricted to an interval, it's easier to solve
what have you tried?
jade cobalt
I tried doing this but not even sure if it works
Since they don’t have same angle
First 1 got cos x second got cos x^3
hollow hedge
you work is wrong
hollow hedge
cos(x) if not a factor of cos(x^3)
jade cobalt
Wt u suggest xd
hollow hedge
ok so we are finding the x-intercepts first, lets agree on this first ok?
jade cobalt
I’ve been studying for programming exam for weeks so I’ve forgot a lot of math 😅
hollow hedge
so we dont get confused and think about the y-intercept
hollow hedge
anyway, notice that since cos(x)-cos(x^3)=0, that implied cos(x)=cos(x^3)
can you see how we can advance?
hollow hedge
yes, but that's not what i meant
hollow hedge
if cos(x)=cos(x^3), would it imply that x=x^3?
jade cobalt
Not sure tbh xd
hollow hedge
yes it would (kind of), because cosine here is a function, and a function (assuming that it is injective) can only be equal to itself if their input are equal to each other
or well another way of saying it is if f(x_1)=f(x_2) then x_1=x_2 considering that f(x) is injective
though, that's the easy part
the hard part here is cosine is not injective
jade cobalt
What injective mean xd
hollow hedge
one-to-one, one input going in and only one output going out
i dont want to go into this too much
jade cobalt
or well another way of saying it is if f(x_1)=f(x_2) then x_1=x_2 considering th...
But I understand this part
hollow hedge
but basically just remember this, since cos(x) is an even function and periodic, hence if we have cos(x)=cos(y) then x=y+2kpi or x=-y+2kpi where k is an integer
hollow hedge
But I understand this part
im just saying those hoping that you would understand, what i want you to know is the message above
jade cobalt
Isn’t it 2pi * k ?
hollow hedge
(basically, i cant just throw you some random knowledge without explaining)
hollow hedge
Isn’t it 2pi * k ?
that....is the same thing
hollow hedge
but anyway, now that you have this knowledge, could you solve cos(x)=cos(x^3)?
jade cobalt
but basically just remember this, since cos(x) is an even function and periodic,...
According to wt u write here xd
hollow hedge
(note that since we are restricted to [-90,90], there is no need for the 2kpi)
the 2kpi here just represents the periodicity of the function, basically saying that there would be infinite solutions in general
jade cobalt
Mhm
hollow hedge
so anyway, it simplifies down to x=x^3 and x=-x^3
can you solve for x in these equations?
jade cobalt
All I can think of is x = 0 xd or x = 1
jade cobalt
Nope
hollow hedge
ok, but one thing to notice here, x=1 is actually not in degrees
it is in radians
so you have to convert to degrees here for the answer to be correct
hollow hedge
you are in radians, so you need to divide by radians, when you divide by radians you get the ratio between 1 and what you divided by, so you have to multiply by the same amount of what you divided by in degrees
hence 1*180/pi
jade cobalt
Aha
Ok listen
This is the drawing
The 1 and -1 is the 180 in radians ?
Umm
Wait
Hold up xd
No Brian working atm
Those r the 1 we found
I feel like I lost my math knowledge…
Or our math teacher send question not normal
Cuz if I have to do all that in exam I’m finished /:
jade cobalt
This is the drawing
But how here they cross x= 0 too ?
jade cobalt
Hello I’ll translate xd
topaz sinewBOT
Hello I’ll translate xd
topaz sinewBOT
@jade cobalt Has your question been resolved?
jade cobalt
Should I just close it ?
hollow hedge
But how here they cross x= 0 too ?
that's because there is a removable discontinuity there at x=0
and sorry, had to do something
the graph cross the x axis at (0,0) because the limit as x approaches to 0 of the function approaches the value 0
you probably dont need this knowledge now
and also yes, x=-1 is a root too, i forgot to mention that
x=x^3 gives 3 solutions
hollow hedge
Hello I’ll translate xd
and what have you tried?
topaz sinewBOT
@jade cobalt Has your question been resolved?
jade cobalt
and what have you tried?
I find out thx xd
swift condor
topaz sinewBOT
swift condor
Hi, not sure how to find this
This is what I came up for the first part
Since now p_0 is constant and the derivative should be constant too
Does that mean I can just do it like this?
Seems like it’s not actually correct
I just made a simple linear demand curve and it does hold up, not sure if it works for a non-linear one, but this might be due to that assumption which I forgot the name of
Something like this but not exactly
Seems to hold up for non linear too
So turns out that is correct but would be really helpful if someone could guide me on why it’s like this?
topaz sinewBOT
@swift condor Has your question been resolved?
floral rampart
Find all functions that satisfy $$F(x) = \frac{x}{2} + xF(x+1).$$
thorny flameBOT
ohNoiAmHere
floral rampart
i have no clue how to start this
i tried a substitution but got some ugly recurence
topaz sinewBOT
@floral rampart Has your question been resolved?
floral rampart
<@&286206848099549185>
topaz sinewBOT
@floral rampart Has your question been resolved?
long trellis
In line AB there are 4 segments ABCD A(1,2) D(4,8) AB=BC=CD find B and C by using midpoint formula
topaz sinewBOT
In line AB there are 4 segments ABCD A(1,2) D(4,8) AB=BC=CD find B and C by usin...
@long trellis Has your question been resolved?
long trellis
<@&286206848099549185>
safe lichen
Midpoint formula
Just an average
Thing of it as an avaerage
Very simple formula
restive inlet
the midpoint formula isn't quite what you want to use here
safe lichen
But the questions asks you to use it
start by reading the question first @restive inlet
restive inlet
i am aware of what they wrote
sometimes questions are ill formed and/or it might be something they assumed they were supposed to use
long trellis
This is what I mean sorry for my bad English
safe lichen
You don't have to spam sorry for my bad englihs all the time
Can u send the photo not sideways pleas
restive inlet
,rcw
thorny flameBOT
long trellis
Find the middle
Midpoint of ab?