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#help-0
alpine sable
Something simple today, find a in
(0, 1, 1 / 0)
(1 a 1 /0)
(1 0 1/0)
rose sigil
what??
torn elk
If it's simple, where are you stucked?
ocean sealBOT
Toby
$\begin{bmatrix}0&1&1&0\\1&a&1&0\\1&0&1&0\end{bmatrix}$
alpine sable
is that the uh
amplified matrix?
0 isn't in the matrix itself
its a homogenous system
.close
formal shale
z=z(x,y), x=s+4t, y=2s-t , ∂^2z/∂t∂s=?
lone heartBOT
z=z(x,y), x=s+4t, y=2s-t , ∂^2z/∂t∂s=?
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
lavish drift
can someone help me by telling me what to put instead of "x"?
ancient saddle
z=z(x,y), x=s+4t, y=2s-t , ∂^2z/∂t∂s=?
What have you tried? 🤔
lavish drift
<#488120190538743810>
he aint even using real numbers
lavish drift
i sent 2 gifs.
tacit arch
i sent 2 gifs.
It's spam
lone heartBOT
@formal shale Has your question been resolved?
worn copper
Binomial expansion with fractions
lone heartBOT
Binomial expansion with fractions
alpine sable
expand the numerator using your formula
worn copper
what happens with the denominator then
serene isle
you can expand it and leave it on the top of the fraction, and then split it into multiple fractions
lone heartBOT
jolly meadow
how do I turn this into an infinite sum of square roots or fractions instead of one square root over everything?
lone heartBOT
Available help channel!
toxic elk
implicit differentiation
lone heartBOT
implicit differentiation
pulsar glen
its aigh
toxic elk
u get it? <@712321730940764171>
yes, thank you
lone heartBOT
lone heartBOT
Available help channel!
scenic wing
how do you graph a piecewise function how do you decide what to plug in ?
echo socket
If you know how to graph -3x + 4, then do it but for values before x = 1
wet nest
Just draw graph of -3x+4 for x<1 and graph of 2x-1 for x>=1
echo socket
And than graph 2x - 1 after that point
scenic wing
how do you graph -3x+4
quasi vector
And than graph 2x - 1 after that point
hey where'd the old pfp go :(
scenic wing
so i'd plug in 0 for x because thats less than 1
scenic wing
-1 ?
echo socket
hey where'd the old pfp go :(
It would be weird to keep a Christmas pfp up until and during summer
echo socket
It would be weird to keep a Christmas pfp up until and during summer
So I changed it
lone heartBOT
@scenic wing Has your question been resolved?
chrome merlin
the required data seems very vague... please help me with this
chrome merlin
the required data seems very vague... please help me with this
given data*
vale crag
well you have some numerical data about the derivatives (2nd equation)
sounds like a good idea to differentiate the top one tbh
@chrome merlin
chrome merlin
okay I will try that
@vale crag can you recommend a good video to learn about differentiation and integration?
vale crag
is it specific topics you want to revise, or you just straight up don't know differentiation and integration ?
chrome merlin
i know limits and functions.. basically uptill precalculus.. I don't know anything about calculus
vale crag
you could look at the videos of prof leonard I guess
the videos are pretty much whole classes so they're freaking long
but he takes good time to explain stuff
if you want more fast-paced stuff, I'd recommend organic chem tutor, or even khan academy if you want
lone heartBOT
@chrome merlin Has your question been resolved?
queen lion
Guys what am i supposed to do with pi here
lone heartBOT
Guys what am i supposed to do with pi here
tacit arch
,calc sin(pi-1)
ocean sealBOT
Result:
0.8414709848079
It's not
tacit arch
Guys what am i supposed to do with pi here
Do you know how to differentiate constants
errant falcon
Guys how can I find 2nd factorisation of 40
vale crag
Guys how can I find 2nd factorisation of 40
1 channel = 1 person here, you can go check #❓how-to-get-help for more explanation
but this could prolly go in #groups-rings-fields
queen lion
Should i just close this channel
vale crag
nah it's fine i'll help you
vale crag
so yeah what riemann was trying to say is that sin(pi-1) is irrelevant for the derivative
it's a constant (relative to x, the variable of your function)
it's like trying to find f'(x) if f(x)=2
it's just 0
queen lion
Wait so is pi -1 all a constant
queen lion
So i just derive sin
queen lion
Yea if thats also consant all of is p
vale crag
it doesn't count
queen lion
So just this is the answer
vale crag
assuming the rest is correct yes
vale crag
uh you forgot the chain rule for the e^ part
@queen lion
you have a composition e^(g(x))
the derivative of that is g'(x)*e^(g(x))
queen lion
Yea
queen lion
Yea im on wolf rn
vale crag
wtf idk how to write
ocean sealBOT
vale crag
wait why do you get 1/cos^2(cos(x)) ?
queen lion
queen lion
Lol
vale crag
i mean if wolfram says it's alright....
queen lion
We write tg insted of tan
queen lion
Idk why did it -sinx
alpine sable
Stupid question but can someone explain like from an intuitive point of view why the product of 2 negative numbers is positive
wanton nova
Adding a negative number is like subtracting the absolute value of that number
alpine sable
Adding a negative number is like subtracting the absolute value of that number
right
wanton nova
apply this to a multiplication
alpine sable
ah I see so -4 * -4 is adding -4 -4 times
wanton nova
which is repeated adding
placid zinc
If multiplying by negative is like "turning around",
Then multiplying two negatives is turning around twice.
wanton nova
ah I see so -4 * -4 is adding -4 -4 times
yeah
wanton nova
alpine sable
<:catThink:526983414226747393>
and how do they even exist in irl, can't get my head around that
wanton nova
technically they don't
alpine sable
technically they don't
how do they work in physics equations then
placid zinc
I mean real numbers don't "exist in real life" either. When's the last time you were walking down the street and saw a 1.54 hanging out
Numbers are an abstraction, and complex numbers are yet another.
vapid shuttle
How does $|x_n-x|<\frac{x-y}{2}$ tell us that $x-\frac{x-y}{2}<x_n$?
ocean sealBOT
AustinU
vapid shuttle
I guess I'm missing some skill with moving these absolute value signs around, I don't see how the second inequality follows from the first
vapid shuttle
also incase it matters we have y<x
vapid shuttle
there are only two cases to check
wdym?
worn fox
okay more generally: $|a| < b \implies -b < a < b$
ocean sealBOT
ΣΑC
ocean sealBOT
AustinU
vapid shuttle
though?
instead of a minus
ah
I see what you mean about the two cases
the other sides gives what we wanted
worn fox
**ΣΑC**
the whole two cases thing is what can let you prove this
but yeah its the -b side that gets you what you want
versed gulch
Pls help
versed gulch
What do you do if you get (a²-b²) the whole square??
tacit arch
What do you do if you get (a²-b²) the whole square??
if you're working on a problem, can you just show the original question
versed gulch
if you're working on a problem, can you just show the original question
Sure man, it's derivatives.
tacit arch
What do you do if you get (a²-b²) the whole square??
that's as simplified as it gets
versed gulch
that's as simplified as it gets
So the answer would be 2a²x/ (a²-b²)²?
Thank you man.
.close
scenic wing
why is it still a shift to the right when its 6-x instead of x-6
scenic wing
wait x-6 would be a shift to the left
so 6-x is a shift to the right ?
why doesn't it just say x+6 ?
so x+6 and 6-x are the same thing
<@&286206848099549185>
tardy stag
6-x is $+6 + (-x)$, does that help?
ocean sealBOT
kitten.in.a.teacup
scenic wing
**kitten.in.a.teacup**
what does the -x do
hollow ether
so x+6 and 6-x are the same thing
These two aren’t the same in absolutes
hollow ether
what does the -x do
If the product of 6-X is negative, the absolute will drop the negative
The -X doesn’t disappear though
scenic wing
graphically
hollow ether
Well you can already tell it won’t have any negative values on the y axis
So that eliminates B and C already
tardy stag
-x flips it horizontally but |x| is already symmetric so in this case it doesn't change anything
scenic wing
-x flips it horizontally but |x| is already symmetric so in this case it doesn't...
wdym by symmetric
so -x is x beause absolute values
hollow ether
so -x is x beause absolute values
If the product of 6-x is negative(like if X is 7) then it would make the negative value a positive
|6-x| =/= |6+x|
left wharf
why is it still a shift to the right when its 6-x instead of x-6
If you shift horizontally to the left, you get |x+6|, which clearly will never get you anywhere. If, instead, you shift horizontally to the right, you get |x-6|, which is actually perfect, because that's equal to |6-x|. Why is that? Well, you get 6-x by multiplying x-6 by negative one, but multiplying by negative one only affects the sign, which the absolute value doesn't care about
To be a little more mathematical about it, it holds in general that |ab|=|a||b|. If b=-1, then we get that |-a|=|a|, i.e. we can negate the thing inside the absolute value and nothing will change. Now, the crucial insight, something that's honestly just good to remember (even though it's super easy to verify), is that if you swap the two things in a difference, then only the sign changes. That is, you can turn a-b into (-1) * (b-a). People always say subtraction isn't commutative, but it sort of is if you just add an additional minus sign (or multiply by -1)
lone heartBOT
@scenic wing Has your question been resolved?
loud igloo
From a lighthouse, a guard can see a cargo ship and a cruise ship at an angle of 64degrees. At a certain point in time, the cargo ship is 400m away from the lighthouse and it is 600m away from the cruise ship. Determine the distance between the lighthouse and the cruise ship.
loud igloo
I already know how to solve it
but i dont know why know that the 64degrees refers to the angle between the cargo and the cruise shi
p
can someone explain to me?
tardy stag
i guess it's a 64 degree angle of cargoship - guard - cruiseship
ie the guard is looking at the cargo ship, then turns their head by 64 degrees and is looking at the cruise ship
void solar
lone heartBOT
left wharf
a unit vector in that direction
lone heartBOT
lone heartBOT
Available help channel!
upbeat stream
I am reading page 308 of spivak's calculus. How sinx and cosx is defined by a two-step piecing together process here?
worn fox
it is telling you how to compute sinx and cosx for x between pi and 2pi, if you know the values of sinx and cosx for values between 0 and pi
upbeat stream
Yup. I just don't understand why the author says two-step piecing together process. Or maybe how to prove that it is true.
worn fox
uh honestly dont know what they mean by that
but you can prove these things graphically by just thinking about what those transformations do to the graph
or prove it algebraically if you know angle sum formulae
tough mulch
i don't understand how this beomes (1+tan²a)?
lone heartBOT
i don't understand how this beomes (1+tan²a)?
naive valley
just pull out the common factor of sin^2(alpha) from both terms
distributive property
crimson carbon
that or apply trig identities
to simplify it further
or well you factor that first
1+tan^2 alpha = sec^2 alpha (derived if dividing sin^2x from the pythagorean trigonometric identity)
tawdry urchin
let $z_1$ $z_2$ $z_3$ and $z_4$ be the four distinct complex solutions to the equation $z^4 - 6z^2 + 8z + 1 = -4(z^3 - z + 2)i$ Find the sum of the six pairwise distances between $z_1$, $z_2$, $z_3$, and $z_4$.
ocean sealBOT
Dork9399
tawdry urchin
idrk how to solve
somebody plz help me
i must solve this
or else my dog may die
naive valley
or else my dog may die
probably best to say your final goodbyes to fido 😁
naive valley
what's the significance of the sum of these distances? do you have any similar problems like this? what's the context, like what topic in complex analysis are you studying
tawdry urchin
this is just solving complex equations
naive valley
the brute force solution would be to find the four roots and then do the computation, but that seems like a rather stupid question if that's how to do it
wary stream
should i ping helper?
No
• After 15 minutes, feel free to ping
@Helpers.
tawdry urchin
how would you use vieta though
naive valley
you can see that there are no real roots, so two of the distances are just 2x the imaginary part of the roots with positive imaginary parts
not sure if that observation is helpful though
tawdry urchin
since it's asking for distance on the complex plane, its asking for diff not sum or product
tardy stag
yeah I'm not sure
tawdry urchin
pretty sure you would have to brute force the solutions
any ideas on how i can do that?
tardy stag
I mean there is a quartic formula
tawdry urchin
isnt that calc?
<@&286206848099549185>
somebody
please
my dog
i dont think he'll make it
how would i go about solving this
my first step would be assuming z = a + bi, where a and b are real
but i would get a quartic in a and b
so how would i deal with that
everyone say goodbye to my dog ig
<@&286206848099549185> someone help
bro frick complex numbers
ima go to bed now
.close
static valve
Help I forgot what it's called when you expand something like x^2 - 4x + 6 and rewrite as (x - 1) (x - 3)
static valve
Please it's on the tip of my tongue and I wanna put it in my notes it's driving me insane I've been pondering for an hour now
naive valley
finding the linear factors?
lone heartBOT
lone heartBOT
Available help channel!
grim cave
Hi there I’m here to learn algebra
lone heartBOT
Hi there I’m here to learn algebra
grim cave
When I mean I wanna learn I want to learn everything about it
grim cave
But does it teach everything tho?
When I mean everything I mean the whole subject
I wanna be a math god
wary stream
I'm pretty sure that not on site compiles an entire subject, completely, into one site, so you can compile your own resources
As suggested, Khan academy is a good start
You can look up other resources on it too
karmic pulsar
from math import *
grim cave
I wanna learn math so I can get a good financial job
And have skills in the business world
wary stream
And as I suggested, Khan academy
For the skills, you can learn those during the job
When you get a job, you never stop learning
wary stream
I wanna learn math so I can get a good financial job
You can only go so far with the resources you find online, you still need the experience with that field and in that field, you'll learn even more
Not one person will know everything, which is why companies have teams with multiple people within them. Because as mentioned, individually, not one person will know everything but combined, is how a person will shine
woven plaza
When I mean I wanna learn I want to learn everything about it
Start from lamar edu website they have everything
tardy stag
pauls notes taught me the entirety of calc bc, big fan
steep harbor
I need help
lone heartBOT
I need help
cerulean garnet
Post question
steep harbor
Wait
I tried to do it
With the cosine rule and some other ways
But got the wrong answers
steep harbor
Oh then I read the question wrong
I thought MN was a straight line
Bruh
Ok
I have more questions 🙂
wary stream
minor arc MN
surreal meadow
!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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
3
surreal meadow
please give us the answer and show your working
steep harbor
Ok
The correct answer for question 17 is 5.14 and the question for 18 is 68c
I don't even know what I was doing
surreal meadow
how did you get d/2 = r
that’s a thing when d is a diameter
d is not the diameter of the circles here
steep harbor
Then what do I do?
steep harbor
How do I find that?
surreal meadow
find what
steep harbor
Pink
surreal meadow
do you know how to find the area of a sector of a circle?
surreal meadow
then subtract the area of the black triangle
steep harbor
Yeah I know
surreal meadow
this is geometric intuition that you should be building by trying the questions out on your own
surreal meadow
do you see how the pink area is half of the red area (what you want to find)
.
again i suggest you try looking for the relationship
steep harbor
Yes but how do I find it?
surreal meadow
find what
steep harbor
In the question
surreal meadow
find what
steep harbor
Shaded area or the pink thing
surreal meadow
what do you mean by "find" and please be exact with what you want to "find"
surreal meadow
i feel like we just talked about how to find that
reread my messages if you didn't understand how
steep harbor
Oh ok I try
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.
quaint vigil
Ok
quaint vigil
Can I explain it
steep harbor
?
surreal meadow
what are you trying to ask
quaint vigil
See geometrically find the area of non shaded part upper part first .
surreal meadow
ask it in a different way
steep harbor
So in the question's diagram, is there an area like the shaded on in the diagram u sent?
quaint vigil
Find this one
steep harbor
How?
quaint vigil
Won't explain the second one. See the geometry
surreal meadow
try to think of how
think about what you were given
even refer to my diagram if it helps
steep harbor
I can draw a diagonal and use Pythagoras theorem with it
quaint vigil
Oh bro I sent the shaded area. It is very easy to find that one.
steep harbor
I don't know how
quaint vigil
See the quarter circle and square
What is the difference in their area see that one.
steep harbor
See the quarter circle and square
Where?
quaint vigil
See there are two quarter circles and a square. Pick one quarter circle and compare with the square area.
surreal meadow
@steep harbor do you know what "the square has sides of length 3cm and arcs have centers at the corners" means?
quaint vigil
It is one fourth of a circle
surreal meadow
it seems as if you either didn't read the question or didn't understand it
steep harbor
Not really the arcs bit
surreal meadow
ok
they are parts of a circle
whose centers are at the corners
that's where my drawings came from
that's what the "quarter circle" is refering to
steep harbor
Corners of the square?
surreal meadow
it would be beneficial to everybody if you shared your confusions at the start
surreal meadow
Corners of the square?
what other corners would they be
steep harbor
Ok
quaint vigil
steep harbor
But still why is it a quarter?
Oh
Oh
Are the two non shaded areas equal?
I think yes right?
quaint vigil
See the geometry what it looks to your eyes
quaint vigil
Yes
steep harbor
Because their centre is in the corner right?
steep harbor
Yes I got the answer
I just want to know if it's equal because the centers are in the corners
quaint vigil
Man, make your basics strong, 💪 also never stop quitting.
steep harbor
By doing what?
quaint vigil
Through eyes they are.
surreal meadow
I just want to know if it's equal because the centers are in the corners
that's not "why"
steep harbor
I have another question that involves using eyes
surreal meadow
but the shape is symmetric
steep harbor
Yeah
surreal meadow
so the unshaded areas are equal yes
quaint vigil
Find it. I believe you will .
You should explore the maths.
Maths is creativity and freedom.
I am going . I think I should go now. Only you will know it. By doing yourself.
surreal meadow
what's the question
steep harbor
Given :- A long time ago Dulani found an island shaped like a triangle with three straight shores of length 3 km, 4 km and 5 km. He said nobody could come within 1 km of his shore. What was the area of his exclusion zone ?
Solution :-
we know that, 3,4,5 forms a right angled ∆ .
it has been said that, nobody could comewithin 1 km of his shore.
we can say that, The exclusion zone can be made up of 6 pieces.
Three are rectangular pieces, each 1 km wide and with lengths 3km, 4km, and 5 km.
The other three pieces are sectors of circles of radius 1 km.
we know that,
Area of rectangle = Length * Breadth.
Area of circle = π * (radius)² .
then,
→ Area of exclusion zone = Area of three rectangular pieces + Area of circle = 3 * 1 + 4 * 1 + 5 * 1 + π(1)² = 3 + 4 + 5 + π = 12 + 3.14 = (15.14) km² .
quaint vigil
No, it is seen there.
steep harbor
That is working
It's just that they are assuming the circular areas as making up a full circle
Which doesn't really make sense
quaint vigil
Which question ❓ you are referring to.
steep harbor
The given
A long time ago Dulani found an island shaped like a triangle with three straight shores of length 3 km, 4 km and 5 km. He said nobody could come within 1 km of his shore. What was the area of his exclusion zone ?
Look
Do I have to assume the sectors add up to a full circle?
quaint vigil
Is it triangle within triangle 📐
steep harbor
?
surreal meadow
Do I have to assume the sectors add up to a full circle?
what else would they add up to
steep harbor
They could be anything, why exactly one full circle?
surreal meadow
split it into cases. could it be more than 1 circle?
quaint vigil
I think it must be equidistant
surreal meadow
maybe we can reason it more easily
the idea is that the sides of each of those sectors are parallel to the ones on the other ends
steep harbor
So assuming that it adds up to a full circle?
steep harbor
Oh
surreal meadow
we would most certainly get a circle, since each side matches up
lone heartBOT
quaint vigil
He is correct 💯
lone heartBOT
Available help channel!
static valve
HELP
static valve
How do I solve this
I'm working on the top problem, I canceled out the x and now I have 5 + 15/3, but I'm stuck.
vale wigeon
no, you cannot cancel out addends like you did.
static valve
oh no
vale wigeon
you would agree that $\frac{1}{2} \neq \frac{10+1}{10+2}$, right?
ocean sealBOT
Ann (glomed)
static valve
yes thats true
ocean sealBOT
Ann (glomed)
vale wigeon
what can be done here is that you can factor out 5 from the numerator (but DON'T cancel anything yet!)
what do you get?
static valve
Wait- factor out how?
vale wigeon
do you know what "factor out" means
static valve
I thought I did but to be fair I've been studying all day and I'm tired
vale wigeon
are you under a due-yesterday deadline?
static valve
Kind of, I have an exam on wed that will determine if I get an A or god forbid a C
I really really want to do well on this test
So, I have 5x + 15 / x + 3, can I factor out the 5x doing something with the x?
My brain is just a little fried
vapid shuttle
you shouldn't factor out the "5x" but, the 5 you definitely should
5x is 5 times x, and 15 is 5 times 3 (they share a common factor of 5)
static valve
Right right I forgot
vapid shuttle
does this give you an idea of how to?
ocean sealBOT
AustinU
vapid shuttle
the two terms on the right share a common factor of a
the left side we could say is the version where a is factored out
ocean sealBOT
AustinU
vapid shuttle
**Ann (glomed)**
assuming up until this part was correct
which I didn't check
but yeah
static valve
yeah it is the factoring was just really messing with me
vapid shuttle
you got it
static valve
This is hour 8 of my study sesh, I've taken breaks but it's broken me
vapid shuttle
it's just reversing distributing
a(b+c) = ab + ac
that is easy for you
now when you start with the other side
ab+ac
reversing should be just as easy now
a(b+c)
static valve
Youre so right, I'm gonna put this into my notes so I don't forget
Thank you very much
vapid shuttle
no problem
static valve
.close
lone heartBOT
lone heartBOT
Available help channel!
brisk orbit
lone heartBOT
https://i.imgur.com/l3UQ9NO.png
brisk orbit
sin(-180-t)??
khan academy must have made a mistake surely unless there's a trig identity sin(-180-t)?
vale wigeon
sin(-180° - t) = sin(360° - 180° - t) = sin(180° - t) = sin(t)
lone heartBOT
@brisk orbit Has your question been resolved?
brisk orbit
sin(-180° - t) = sin(360° - 180° - t) = sin(180° - t) = sin(t)
how is sin(-180-t) = sin(360-180-t)
tardy stag
because sin(360+x) = sin(x)
vale wigeon
^
brisk orbit
so sin([t+360) - [180-t]) xd
can't be tho it would need to be 180 + t
hmm...
well -180 + t
I don't get it
tacit arch
so sin([t+360) - [180-t]) xd
what are you trying to do
brisk orbit
what are you trying to do
understand how the identity sin(-180-t) came about
tardy stag
,,\begin{align*}
\sin(t) &= \sin(180^\circ - t) \
&= \sin(180^\circ - t - 360^\circ) \
&= \sin(-180^\circ - t) \end{align*}
ocean sealBOT
kitten.in.a.teacup
tardy stag
does that make sense? Or if not, which step doesn't make sense to you?
lone heartBOT
@brisk orbit Has your question been resolved?
dull lance
lone heartBOT
dull lance
How do I derive 167.
What do I do with the power of -2
Power of 0.5*
Just realized
brisk orbit
does that make sense? Or if not, which step doesn't make sense to you?
thanks
tardy stag
Power of 0.5*
yeah it's power of 0.5 and you do just like any other power
dull lance
yeah it's power of 0.5 and you do just like any other power
First time seeing power 😅
Just started this topic
tardy stag
you haven't done like y = x^2?
dull lance
I was doing a physics exam when they taught this so trying to catch up
I got -3cos(x^(-0.5)) if thats correct
barren shuttle
Chain rule
tardy stag
yeah chain rule, do the derivative of sin() first then multiply it by the derivative of sqrt(x)
dull lance
Hmm alr
tardy stag
like you did with the previous two
tardy stag
no it'll be $6\cos(\sqrt{x})\cdot\frac{1}{2}x^{-1/2}$
ocean sealBOT
kitten.in.a.teacup
tardy stag
yeah and x^(-1/2) is usually written as 1/sqrt(x)
fathom harness
I was trying something else lol
dull lance
XD
tardy stag
almost, where'd that negative sign come from?
dull lance
almost, where'd that negative sign come from?
Negative cos
Oh wait
Nvm, got sin and cos mixed up
oifaoisdfbioa
T_T
tardy stag
happens
tardy stag
you're picking this up very quickly
dull lance
AAAAAA
Going to be a rough one
T_T
What happens when I have natural log multiplied by cos x
mossy nova
so ur starting differentiation?
dull lance
Do I do product rule
dull lance
so ur starting differentiation?
Yessir
tardy stag
uh do you mean $\ln x \cdot \cos x$ or $\ln(\cos x)$?
ocean sealBOT
kitten.in.a.teacup
tardy stag
second one isn't multiplied, it would be read as "log of cosine of x"
anyway it's still the chain rule
dull lance
second one isn't multiplied, it would be read as "log of cosine of x"
Oh
AAAAAAAAAAAAA
T_T
tardy stag
and yeah $\frac{d}{dz} \ln z = \frac{1}{z}$
ocean sealBOT
kitten.in.a.teacup
tardy stag
remember, it's take the derivative of the outer thing first (while leavingn the inner thing alone), then multiply by the derivative of the inner thing
tardy stag
mossy nova
woo
dull lance
WOOOOOOOOOOOOO
tardy stag
mossy nova
cuz u gotta rembember other things as well
tardy stag
164 doesn't seem right to me; you start with $2\csc^2x$ so it should be $4\csc x \cdot \frac{d}{dx}(\csc x)$
ocean sealBOT
kitten.in.a.teacup
dull lance
have u done limits by any chance?
Not yet
tardy stag
i'm a little confused by this line; that's not f(x)
mossy nova
oh, tbh i started with limits first, then differentiation
dull lance
Oh, supposed to be dash?
tardy stag
remember $\csc^2 x$ is the way we write $(\csc x)^2$
ocean sealBOT
kitten.in.a.teacup
tardy stag
you can't just... do that lol
dull lance
T_T
tardy stag
like x^3 is not the same as 3x 
tardy stag
power rule does work! but like you meant to write $f'(x) = 2\times2(\csc x)$ (note the prime)
ocean sealBOT
kitten.in.a.teacup
tardy stag
(and you still need the chain rule tacked on the end)
mossy nova
bruh, idk, ill try to write in latex someday
tardy stag
latex has the amazing property that anything you write in it is so beautiful it must be true
dull lance
mossy nova
still, considering i havent wrote anything in latex, it might be a difficult job for me
tardy stag
164 should be times csc cot, not minus
dull lance
Times -cosec(x)
tardy stag
oh there's an x in there I didn't even see it
tardy stag
i'd recommend using dot for multiplication most of the time since you've got x's as variable names, i know it's hard to adjust
tardy stag
yeah that's right then! now simplify it a bit
tardy stag
tardy stag
Any time!
tardy stag
ugh
yeah so the thing about math is that practicing helps and eventually you get really fast at it
but it's kinda tedious in the process lol
dull lance
ugh
yeah so the thing about math is that practicing helps and eventually you get...
XD
Lmfao
Yeah def practiseee
Just came back from shower
Gonna do more practise
lone heartBOT
@dull lance Has your question been resolved?
lone heartBOT
Available help channel!
harsh copper
lone heartBOT
harsh copper
what do u do for part ii
vale crag
you plug in the value k=a
harsh copper
at the start or after u derivative it
harsh copper
is it 2ak - 2ak
harsh copper
for ii) is it 2ak - 2ak then replace k with a
vale crag
is it 2ak - 2ak
nah doesn't work
derivative of a^2k is not 2ak
a^2 is a constant number (in regards to k)
harsh copper
do u have to use product or smth
vale crag
no
it's like differentiating 2x wrt x
the 2 is the constant
same for a^2 here
derivative of a^2*k wrt k is a^2
vale crag
yeah
vale crag
then replace k with a
exactly
vale crag
dQ/dk is the derivative of Q with respect to k
if you know leibniz notation for the derivative (the dQ/dk thing)
harsh copper
dy/dx
harsh copper
so u want ur final answer in terms of x
vale crag
it's more a matter of which variable you "move around" in order to compute the derivative
if you only have a function with one variable, there's not really a choice to make
if you have multiple variables, you have to specify with which one you take the derivative
harsh copper
so if y = x^2 differentiating y wrt x is 2x
vale crag
yes
harsh copper
buit what if questions says differentiate x wrt y
vale crag
you could inverse your function
ie get some expression of the from x=... (if it's possible)
which depends on y
harsh copper
x = +- y^1/2
vale crag
yeah well the inverse doesn't exist for all real numbers
harsh copper
but if x = +- y^1/2 differentiating x with repct with y be 1/2y^-1/2
and -1/2y^-1/2
vale crag
the red thing would be the "inverse" of y=x^2
as you see it's not a function
it fails the vertical line test
harsh copper
does it matter if it is a function
vale crag
I mean yeah
if i'm computing the derivative for some y
am I talking about the top one or the bottom one
the slopes are different
harsh copper
so u cant find the derivative of many to one and many to many functions
vale crag
yeah
harsh copper
so like a parabola
vale crag
yeah if you take a parabola which is not "parallel" to the x-axis (ie not like y=x^2), you're kinda screwed
harsh copper
wdym
vale crag
cause there would be multiple points possible
harsh copper
arent all parabolas parallel to x axis
vale crag
what about this one
harsh copper
does that count as a parabola
vale crag
it's a parabola geometrically at least
harsh copper
isnt that y^2 graph
vale crag
ofc if you say a parabola is something of the form y=x^2 it's not
but anyway you have 2 outputs for this input (the vertical line)
harsh copper
but parabolas doesnt have an inverse function and still differentiable
vale crag
but parabolas doesnt have an inverse function and still differentiable
the derivative won't be a function then
like for x=7 I have two possible outputs
so two possible tangents
two possible slopes
harsh copper
y=x^2 y=2x 1 to 1 function
harsh copper
so y^2 = x
vale crag
yes
vale crag
so that's why we don't talk of derivatives of multi-valued functions
cause you end up with weird shit like this
harsh copper
.close
river owl
how do i rotate a 3d vector on the x axis by an angle n?
lone heartBOT
how do i rotate a 3d vector on the x axis by an angle `n`?
river owl
use a rotation matrix
what is that
river owl
https://en.wikipedia.org/wiki/Rotation_matrix?oldformat=true#In_three_dimensions
ok thanks
.close
idle lynx
Hi how do I find the domain of the hyperbola y = -2/2x+3 + 1?
jolly widget
Hi how do I find the domain of the hyperbola y = -2/2x+3 + 1?
firstly ask yourself where the function is defined. Do you know how to find that?
idle lynx
Uh sorry nooo
tawny condor
$\frac{-2}{2x+3} + 1$
ocean sealBOT
redstoneplayz09
tawny condor
A function is something that let's you plug in x values, and get back y values
What x values would be problematic if plugged into the equation?
jolly widget
I mean, I suppose it still makes sense to talk abt a hyperbola's range and domain
even if it is not a function
tawny condor
It's a rational function, idk what you call it in English
jolly widget
I'
idle lynx
Ohhhh wait seriously?
jolly widget
Ohhhh wait seriously?
you see
raven haven
what happens if x = -3/2
idle lynx
That’s where the asymptote is
jolly widget
oh wait it is
ok so
usually it's helpful to express the hyperbola in terms of
lemme pull out a khan academy Screenshot RQ
ok wait now that I look at it, this is a specific case, lemme generalise it rq
so basically idea is to convert the eqn to the form $\frac{(x-a)^2}{c^2} - \frac{(y-b)}{d^2} = 1$ where a, b, c d are just constants
ocean sealBOT
Kiameimon | Welt Rene (glomed)
jolly widget
reason being
it makes the hyperbola a lot easier to interpret (why?) Lemme do my best to explain.
but first let's just *take what I say for granted and use your eqn as an example so that it hopefully becomes more clear
$y = \frac{-2}{2x+3} + 1$
ocean sealBOT
Kiameimon | Welt Rene (glomed)
jolly widget
..........
so my intuition didn't screw me up.
💀
nevertheless this question is still solvable if we ignore the "hyperbola" part...
idle lynx
Oh okay, it might just be a mistake in my practice test then
jolly widget
but I can still go through what I was talking abt earlier or link u to khan academy to learn more abt what I was talking abt with hyperbolas
idle lynx
Oh yes, can I have the khan academy link pls?
jolly widget
nevertheless... yes. ALl you have to do is show that i'ts undefined at that point for this qn
jolly widget
Oh yes, can I have the khan academy link pls?
sure gimme a sec
idle lynx
nevertheless... yes. ALl you have to do is show that i'ts undefined at that poin...
Okk 👍
calm willow
Hi
night wing
!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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
mmm seeing it it occurs to me that the problem should give you some extra info about the direction of the force