idk if that is how you spell it
#help-33
still temple
jagged relic
conjunction?
jagged oracle
Conjecture?
jagged oracle
Conjecture
still temple
i mean to say conjecture
jagged oracle
Okok
knotty trellis
It's a statement that wasn't proved yet, but is thought to be true by some mathematicians
jagged oracle
i mean to say conjecture
U can say as a statement which is true or works out but has not been proven
knotty trellis
U can say as a statement which is true or works out but has not been proven
I would be careful with that
conjectures aren't always true
naive fox
it is like educated guess but not with proof
jagged oracle
Yes
jagged oracle
It's like giving a statement on some observations or a basis
And sayings it's true for every case
still temple
does this sentence make sense
jagged oracle
I cannot see it
still temple
it is sending weirdly
jagged oracle
I have dark mode on
still temple
1 moment
I learnt a lot about developing ideas, making conjectures and turning these thoughts into rigorous mathematical arguments.
sorry someone wrote this sentence im trying to understand what conjectures means
but i think its
forming ideas that then making a claim and then proving
right?
knotty trellis
looks like that
still temple
and this is a perfectly fine thing to say right?
jagged oracle
!original
marsh citrusBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
jagged oracle
Send the statement which u were sending earlier
still temple
this is the statement
naive fox
When I read conjecture, I think about the unsolvable problem.
jagged oracle
See conjecture is a statement
still temple
When I read conjecture, I think about the unsolvable problem.
ah ok
knotty trellis
When I read conjecture, I think about the unsolvable problem.
many conjectures were proved already
jagged oracle
Which is based on some mathematical observation or basis
naive fox
yes... but like that is what I feel
jagged oracle
And is assumed to be true or not true for every case but is not proven
knotty trellis
wdym for every case?
still temple
im confused
jagged oracle
Wait let me think how can I explain simply
knotty trellis
ah ok
Not all conjectures are "unsolvable", but the famous conjectures weren't solved for a really long time after a lot of attempts. That's why the word conjecture might evoke some extremely hard to solve problem
but in general, conjectures aren't necessarily unsolvable or extremely hard to solve
still temple
ah that makes sense
okay so
i could be looking at some new problem
see a pattern
think hm yes that sounds logical
make a claim
knotty trellis
and make a conjecture
still temple
and that claim is a conjecture
knotty trellis
yes
jagged oracle
Yes
still temple
oh wait
jagged oracle
Once it's proved it converts more likely into a theorem
still temple
so a conjecture is more of an assumption?
jagged oracle
Or a law like something
still temple
to continue going with maths
jagged oracle
see conjecture is making a claim
knotty trellis
and then i could prove that
if you can prove it quickly enough, then you would usually skip the conjecture part. The conjecture is usually made when you are not capable of proving the statement you made and so you publish it as a conjecture. Then other mathematicians may attempt to prove it
still temple
yeah and then i want to prove that claim
jagged oracle
When that claim gets proved to be correct or wrong it does not remain a conjecture
still temple
wait so
okay
new problem
see pattern
make conjecture
try to prove conjecture
does infact prove
jagged oracle
That's why when one says conjecture we get the idea of unsolved problems
still temple
i see
jagged oracle
Or which were not solved for long enough
jagged oracle
Oh ok
still temple
trying to understand this terminology
jagged oracle
See if u make a claim
still temple
so i can use it in the future
still temple
so this is more about time to solve?
jagged oracle
Conjecture is a claim that's goes unproven for a long enough time
knotty trellis
you dont really need to name the thing you make until you publish it
jagged oracle
Yes
knotty trellis
and if you prove it before publishing it, then you can just name it theorem straight away
jagged oracle
And even u can't consider it a conjecture straight away
knotty trellis
if you can't prove it, you can publish it as a conjecture and wait for others to prove it
jagged oracle
Because you don't know
knotty trellis
and it might be the case that after few years you will actually prove your own conjecture
jagged oracle
Maybe your knowledge level might fall infront of some other guy
Who may prove it fast enough
still temple
alright so im a student and if my teacher gave me a problem sheet to work through
naive fox
but one might need to differentiate the specific problem with conjecture.
jagged oracle
Its like saying
still temple
and theres a question in which i think i see a pattern and i suggest a reason for this
and then try to prove this
still temple
and theres a question in which i think i see a pattern and i suggest a reason fo...
this part is a conjecture
naive fox
I mean, you can say that "2(n^3+3n^2+2n) is divisible by 6". You can have a conjecture that n^3+3n^2+2n is indeed divisible by 6. Then prove it. But I will call this a problem rather than calling it conjecture.
still temple
as at that point i have no proof other than intuituion
jagged oracle
You are doing tough calculations by yourself
still temple
that is bed spelling
jagged oracle
And someone just uses a calculator
still temple
I mean, you can say that "2(n^3+3n^2+2n) is divisible by 6". You can have a conj...
yeah
knotty trellis
this part is a conjecture
could be, but its kind of a big word for this
still temple
i agree
jagged oracle
You can see most of the conjectures were claims which were unproven for. A quite long time
naive fox
conjecture is more from general observation
still temple
yeah
from what i understand
conjecture is a term used for big things
like riemman
or fermats last theorem
jagged oracle
Conjecture is a statement given on a Mathematical basis
Like riemman
Saw that when re(s)=1/2
Zeta(z) becomes 0
On this mathematical basis he claimed
knotty trellis
Saw that when re(s)=1/2
thats not true
knotty trellis
the RH is that all non-trivial zeroes of the riemann zeta function lie on the critical line
jagged oracle
Yea it's not true cz its not proven right
I was just demonstrating the use of the terms conjecture
knotty trellis
but not that all points on the crtical line evaluate to 0
knotty trellis
yeah, but your statement is not the RH
still temple
my question has been answered can i close this?
knotty trellis
sure
jagged oracle
Sure
marsh citrusBOT
jagged oracle
Keep asking
knotty trellis
new .coose just dropped
marsh citrusBOT
Available help channel!
wary bluff
For this I would just apply green theorems right? with the bounds of the integral being
$\int_{1}^{2} \int_{1}^{4-y}$ right
marsh citrusBOT
For this I would just apply green theorems right? with the bounds of the integra...
elfin berryBOT
Calc III Victim
jagged oracle
Yea my buddy
jagged oracle
Feynmann?
wary bluff
nah u had the initial and terminal point given
jagged oracle
Yes
jagged oracle
What
wary bluff
bro mb I should have went through this weeks lec slides. they did a similiar question in class apparently
but I didnt attend the lec
wary bluff
wary bluff
nah fr
jagged oracle
Fr
wary bluff
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
sharp raptor
i need help
marsh citrusBOT
i need help
jagged oracle
Hlo
sharp raptor
hello
jagged oracle
!status
marsh citrusBOT
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
sharp raptor
im new to logarithm but i've done abit of log questions months ago
sharp raptor
Do u know antilog?
ill say no
jagged oracle
Ok
sharp raptor
Do u know antilog?
wait i do know abit about antilog
jagged oracle
Do u what does log a to the base b =c means
sharp raptor
wait i do know abit about antilog
its about exponents right?
sharp raptor
Do u what does log a to the base b =c means
i have no idea what ur saying
i could work with examples
and u try to explain through them
is this what ur referring to?
naive fox
Yeah. this basically tells us that 10^2 is 100. Now, if I don't know that it is 100 (maybe call it x), can you solve for it?
like, can you solve for x in 10^2 = x?
sharp raptor
like, can you solve for x in 10^2 = x?
It is equal
naive fox
and that should be similar to your question that you are trying to solve for x if the base is 9 and the exponent is -1
naive fox
It is equal
equal to?
sharp raptor
-1
naive fox
ok... 10^2 is what?
sharp raptor
100
naive fox
yeah. so in your case, your base is 9 and your exponent is -1
substitute that in
and you should get one expression to evaluate
what is that?
sharp raptor
0.1111
naive fox
I mean... sure. but maybe answer that in a fraction would help
sharp raptor
So thats the answer?
naive fox
yes
elfin berryBOT
evryone
naive fox
so $\log_2 8 = 3$ means $2^3 = 8$
elfin berryBOT
evryone
naive fox
in your case, $\log_9 x = -1$ means $9^{-1} = x$
elfin berryBOT
evryone
naive fox
it is just a different way of writing log
sharp raptor
Oh
How did -1 become an exponent is it because of transitioning of log into other side?
@naive fox
naive fox
There is a property for logarithm that $a^{\log_{a} b} = b$
elfin berryBOT
evryone
urban night
naive fox
using that, you can show that $\log_{9} x = -1$ means $9^{\log_{9} x} = 9^{-1}$
elfin berryBOT
evryone
naive fox
which leads to the conclusion that $x = 9^{-1}$
elfin berryBOT
evryone
naive fox
I can do that because exponential and logarithm are inverse of each other
sharp raptor
sharp raptor
I can do that because exponential and logarithm are inverse of each other
@naive fox correct?
sharp raptor
another question regarding logs 😭 and solve X
It's equal to and i need to find x again same like above
Log has base 3
could i cancel out the logbase3
and just continue on with my calculation
@naive fox
naive fox
using the same idea I have shown you that $a^{\log_a b} = b$ to simplify this. So, we raise the base (3) by the expression from left and right
$3^{\log_3(4x) - \log_3(2x-1)} = 3^1$
elfin berryBOT
evryone
naive fox
and we know that $a^{b-c} = \frac{a^b}{a^c}$
elfin berryBOT
evryone
naive fox
the rest should be relatively forward
sharp raptor
**evryone**
yes we do
sharp raptor
**evryone**
When i do this does it mean i can cancel out the logbase3 exponent u just made
naive fox
yes because you will have $\frac{3^{\log_3 (4x)}}{3^{\log_{3} (2x-1)}}$ which I have shown you that the log will disappear using the inverse identity
elfin berryBOT
evryone
sharp raptor
**evryone**
$\frac{3^{\log3 (4x)}}{3^{\log{3} (2x-1)}}$ = 1 right?
elfin berryBOT
saba
acoustic bramble
acoustic bramble
You multiply both sides by (2x-1)?
sharp raptor
OH wait
i got lost there
thanks
i need to put them in parenthesis yeah
i should be correct now
acoustic bramble
sharp raptor
woahhhhhhhh
u right again
😭
im so careless
ur not catching me wrong this time 😂
acoustic bramble
acoustic bramble
also, 6/2=3
sharp raptor
THIS IS THE EASIEST PART N IM FAILING 😭
acoustic bramble
don't worry, I once put the wrong thing into the calculator on a test
acoustic bramble
3×-1=-6?
acoustic bramble
x=3/2 is right
acoustic bramble
(you might need to simplify it to 1½)
acoustic bramble
it depends on your teacher
sharp raptor
oh yea theres no problem on giving 2 same answers right?
acoustic bramble
you could just put x=3/2=1½
sharp raptor
done
im still not done with my work i got a few more questions
4 questions about simultaneous equation method
i needa watch yt short covering it rq
its easy but i forgot the process
acoustic bramble
I don't know the term, but it might be something I know.
sharp raptor
idk if i should use substitution of elimination method
it didnt specify so im good tho
acoustic bramble
Ah that thing
sharp raptor
it has 3 marks so i need to show my work
its 4x + 3y = 17
3x + 5y = 21
i can use calculator
but i need those marks xd
acoustic bramble
A graphical calculator?
naive fox
I mean, you can write one equation in term of one variable and substitute that in another equation
acoustic bramble
Are you allowed to use a graphical calculator though?
sharp raptor
Are you allowed to use a graphical calculator though?
i dont even have a graphical calculator i didnt evn know it existed untill u mentioned it
😂
thats something new to learn..
acoustic bramble
(lazy me willing to use the equation solver)
naive fox
graphical calculator is just scientific calculator that can graph
you can solve these easily using graph
acoustic bramble
the cool calculator xd
acoustic bramble
It is required in my math class (VWO Wiskunde B, Netherlands)
naive fox
is logarithm considered basic math
I will say yes
sharp raptor
in my school its inside the addmath modules
naive fox
and yes, many places requires graphical calculator like in AP class
sharp raptor
additional mathematics
naive fox
I think that is foundational math, not additional or supplementary math from where I was
sharp raptor
I think that is foundational math, not additional or supplementary math from whe...
Oh i see
theres so much to learn and what i thought was the peak of math in my school which was called additional math was only the tip of the iceberg of the reality
i wouldnt even consider it a iceberg but something insignificant
acoustic bramble
theres so much to learn and what i thought was the peak of math in my school whi...
Ever heard of i, csc or coth?
sharp raptor
Ever heard of i, csc or coth?
no 💀
naive fox
Saying that those are insignificant might be overstatement as more advanced math use those to build more math
sharp raptor
Saying that those are insignificant might be overstatement as more advanced math...
it is a overstatement
😂
but yea true we need the foundation math that i called insignificant to continue on the math journey
naive fox
you need solid foundation to study more advanced math. sometimes math can be hard if your foundation is not strong
sharp raptor
you need solid foundation to study more advanced math. sometimes math can be har...
i agree
same goes to every subject
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
marsh citrusBOT
vital oracle
you can rely on a more general proof based on integrals to answer for this
how familiar are you with integrals
oh then its going to seem a bit contrived to use for this example
an integral in general can find the area between the function f(x) and the x-axis
however the area is considered to be negative in particular circumstances which happen to work well for your triangle proof
for one, if the function goes below the x-axis, the area is considered to be negative
also, if you swap the lower and upper bounds of an integral to be out of order, it will get a negative answer
these properties ensure that "triangle = integral from a to b + integral from b to c + integral from c to a"
converting the triangle's sides to three functions (lines) to take areas of
and it remains true without needing to consider whether y1, y2, or y3 are negative or not
vital oracle
oh then its going to seem a bit contrived to use for this example
an integral i...
it means this
with the two images below it being its exceptions
do you see the shaded area in the first image
the top of the shaded area is a function f(x)
the bottom of the shaded area is the x-axis
the area is between f(x) and the x-axis
where the integral "begins" and "ends" is given with the lower bound a and upper bound b
the integral can be limited to only be a portion of the line
you can see on the left it begins at a
and on the right it ends at b
these are the two x-values where it begins at ends
where the integral "begins" and "ends" is given with the lower bound a and upper bound b
can be any two x-values
a and b are not points
they are numbers
if a function goes below the x-axis, the integral still measures its area, but that area is considered to be negative
for example, if I drew a mirror image of this line below the x-axis, it has the same integral from a to b but negative
vital oracle
if a function goes below the x-axis, the integral still measures its area, but t...
the area thats under the x-axis is considered negative, and the area thats over the x-axis is considered positive
@still temple do you think you have enough information to figure out all of the necessary cases using this new way of finding areas
its more ideal if you try this down on paper
by itself this would be too much to attempt to prove mentally
for reference, you can consider this for when all the points are above the x-axis
I think you should start with an easier case
wait
are you just looking for confirmation so that you just want to find the area of that triangle
(integral from a to b of the lower-left line) + (integral from b to c of the lower-right line) will create these two areas
and the integral from a to c of the upper line creates this area
so the integral from c to a would be the negative of this area, like this
oh wait I showed the wrong formula, I had the bounds wrong
lets continue anyways
so when you add together (integral from a to b) + (integral from b to c) + (integral from c to a),
it all overlaps like this
this leaves you with only the area inside the triangle, but negative (because I got the bounds wrong when I typed them)
the integral is the sum of the blue positive area and the orange negative area
we're doing something very different here so thats ok
vital oracle
the integral is the sum of the blue positive area and the orange negative area
this is the integral from a to b of the lower-left line which adds the blue area then subtracts the orange area
this is the integral from b to c of the lower-right line which also adds the blue and subtracts the orange area
do you understand those parts so far
vital oracle
so the integral from c to a would be the negative of this area, like this
this integral from c to a of the top line is considered to be negative since the bounds are swapped
does that make sense at least with the integral properties I showed you
the resulting image is what I got from overlapping these areas together, representing that I added them
you can see there the red color is really blue in an orange tint
when completely overlapped, the red area shows the positive and negative area which canceled out
the result is a negative area that represents the area of the triangle
even though its negative, it still represents the correct shape, so erasing the - sign of the ultimate area you calculate will work
does that make sense
so far, is it proven to you that these 3 integrals always add together to the triangle area (positive or negative)?
now we can figure out the formula for this integral of a line
theres an easy formula that ends up doing this, which is:
as a trapezium, the formula is $(b-a)\frac{h_1+h_2}{2}$
elfin berryBOT
mtt
vital oracle
now if you use this formula for the integral, youll notice it already fits all the criteria for the integrals we've been doing so far
if you make a and b out of order, then a - b = -(b - a) shows that it negates the resulting area
as for (h1 + h2) / 2 its not as clear that it calculates the heights correctly
yea we're only talking about the formula for an integral
we're not doing the triangle part yet
also (h1 + h2) / 2 represents the height here too
-(h1 + h2) / 2
(-h1 - h2) / 2
so if you have (-h1 - h2) / 2 you can pull out the - to get that it also just flips the area
Im talking about the height but yea you would
vital oracle
also (h1 + h2) / 2 represents the height here too
so (b - a) * (h1 + h2) / 2 still works if both h1 and h2 are negative
when its like this though its harder to prove, but you can eventually show that this setup will also give you (b - a) * (h1 + h2) / 2
mark a point at d
the "trapezium" here is two right triangles
the two angles near point d are vertical angles and so are equal, so these are two similar right triangles
the left triangle's height is |h1| and the right triangle's height is |h2|
left base is d - a, right base is b - d
so using similar triangles,
(d - a) / |h1| = (b - d) / |h2|
solve for d to get
(|h2| d - |h2| a) = (|h1| b - |h1| d)
|h2| d + |h1| d = |h2| a + |h1| b
( |h2| + |h1| ) d = |h2| a + |h1| b
d = (|h2| a + |h1| b) / ( |h2| + |h1| )
thats a typo
heres the two right triangles
the marked angles near the intersection are equal because of vertical angles
with two of the same angles, the third angle must also be the same since both triangles add to 180
with all 3 angles equal, the triangles are similar
usually you just prove that two of the angles are equal so then you can go with "the triangles are similar due to the AA postulate"
AA stands for angle-angle for two angles being equal
right back to this
wait thats the wrong picture
yea when two lines cross, they form equal angles like that called vertical angles
you can think of it as "if they werent equal, the lines would be crooked"
yes the lines cant bend
it should form an X
so using this example, the two areas can be subtracted as:
1/2 (d - a) |h1| - 1/2 (b - d) |h2|
1/2 d |h1| - 1/2 a |h1| - 1/2 b |h2| + 1/2 d |h2|
1/2 d |h1| + 1/2 d |h2| - 1/2 b |h2| - 1/2 a |h1|
1/2 d ( |h1| + |h2| ) - 1/2 (b |h2| + a |h1| )
1/2 (|h2| a + |h1| b) / ( |h1| + |h2| ) * ( |h1| + |h2| ) - 1/2 (b |h2| + a |h1| )
1/2 (a |h2| + b |h1| ) - 1/2 (b |h2| + a |h1| )
1/2 (a |h2| + b |h1| - (b |h2| + a |h1| ))
1/2 (a |h2| + b |h1| - b |h2| - a |h1| )
1/2 (b |h1| - b |h2| - a |h1| + a |h2| )
1/2 (b( |h1| - |h2| ) - a( |h1| - |h2| ))
1/2 (b - a) ( |h1| - |h2| )
this works for any of these "trapeziums" if h1 is the positive height and h2 is the negative height
now since h1 is positive, its h1
and since h2 is negative, its written as -h2 to make it positive
so the final formula you get is
1/2 (b - a)(h1 - -h2)
1/2 (b - a)(h1 + h2)
no worries Ive just kept going
wdym
marsh citrusBOT
@still temple Has your question been resolved?
earnest siren
https://www.youtube.com/watch?v=9n1GXe1gAKo&list=PLpkegBCPWkWOuyg_JWtkANQi8cy9Q-GoO&index=2
I don't get this 😭
If you have a gas cloud with a free fall time, then won't it always contract, unless the cloud itself has some thing to counter-act that which is at the speed of sound???
marsh citrusBOT
https://www.youtube.com/watch?v=9n1GXe1gAKo&list=PLpkegBCPWkWOuyg_JWtkANQi8cy9Q-...
earnest siren
I just don't get where the whole if t_s > L/c_s then unstable
marsh citrusBOT
@earnest siren Has your question been resolved?
marsh citrusBOT
@earnest siren Has your question been resolved?
marsh citrusBOT
@earnest siren Has your question been resolved?
earnest siren
I know this is a physics questions
but the physics server also ignored it 😭
wondering if it is a bad question now
😭
muted narwhal
wondering if it is a bad question now
no it's more like you asked how to make bread to people who mine iron
quiet anvil
Nah, there's a reasonably large overlap
earnest siren
no it's more like you asked how to make bread to people who mine iron
lol
earnest siren
Nah, there's a reasonably large overlap
sure, but there isn't anything math related in this question
Trying to get a conceptual understanding ig
quiet anvil
I haven't watched the video, nor really read the background, but perhaps an example of a gas cloud not collapsing under its own gravity might help: an explosion. Such as a nebula from a supernova
earnest siren
In the video he said a cloud going unstable
could mean it diffuses outwards
and it isn't made clear if an unstable cloud could also contract
quiet anvil
Like one with too much angular momentum?
earnest siren
Like one with too much angular momentum?
no, like some jeans mass thing
But it seems like if you don't have the jeans mass, the cloud will become unstable
But the video presents it like you need to have more mass or something IDK
marsh citrusBOT
@earnest siren Has your question been resolved?
marsh citrusBOT
@earnest siren Has your question been resolved?
brave spire
https://www.youtube.com/watch?v=9n1GXe1gAKo&list=PLpkegBCPWkWOuyg_JWtkANQi8cy9Q-...
Yo
marsh citrusBOT
marsh citrusBOT
Available help channel!
hybrid charm
Hello, I need help understanding a step in solving a problem here. Why is it that when they sub t-2 in for f, it doesn't become like t^2 to the original t or the other t in the t-2 seems to be gone. What is the reasoning behind this step.
This is for self study
marsh citrusBOT
Hello, I need help understanding a step in solving a problem here. Why is it tha...
shadow thorn
(f o g)(t) = f(g(t))
hybrid charm
yeah
shadow thorn
g(t) = t^2+5
so
perform f(t) on g(t)
what does f(t) do?
f(t) = t - 2
it just subtracts 2
so subtract 2 from t^2 + 5
hybrid charm
yeah right, but what happens to the t? Don't you add that in somewhere
shadow thorn
which t sorry
hybrid charm
it just subtracts 2
I'm wondering why it is just subtract 2 versus also add in another t somewhere
shadow thorn
I'm wondering why it is just subtract 2 versus also add in another t somewhere
think of it like this
shadow thorn
is g(t)
i replace t with g(t)
because
we are performing f on g(t)
think of it like this
f(t) = t - 2
f(u) = u -2
f(1) = 1 - 2
so
hybrid charm
Oh I see, you are substituting it in, so there wouldn't be another t variable. Is this right?
shadow thorn
f(g(t)) = g(t) - 2
shadow thorn
Oh I see, you are substituting it in, so there wouldn't be another t variable. I...
i mean g(t) has a t variable
hybrid charm
I see, so then where did you find out that t or u was 1 in this case?
shadow thorn
i didnt
f( something ) = something - 2
this is what im trying to say
t can be anything
all t is
is just an input
f ( input ) = output = input - 2
hybrid charm
all t is
I see, what is tripping me up is that since you add f(t)
Why wouldn't f(g(t) look something like this
t(g(t)-2
Instead of what you got which was
g(t)-2
shadow thorn
you should realize that t isnt special
t is just an input
f(g(t)) is g(t) - 2
whatever you put inside f
you will get that thing - 2
this is how you should look at functions
hybrid charm
this is how you should look at functions
I see, this makes sense. Thank you for your help
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fickle shell
marsh citrusBOT
fickle shell
Hmm
I got the 3 points A B and C
A is (ln(8), 2), B is (ln(8), -2) and C is (0, ln(4))
What do I do with this tho?
fickle shell
Ok whats the best way to do that
north bison
Well choose two points
fickle shell
Im gonna have logs inside square roots 
north bison
Have you drawn a diagram
You can || split it into 2 right angled triangles since it's isosceles, note that the x co-ordinate is the same for A and B and the ||
fickle shell
Have you drawn a diagram
I mean I can but in my exam I dont have time to draw any
fickle shell
idk where ln(4) and ln(8) are quickly in my head
rain magnet
U just need to take the first and second derivatives
fickle shell
U just need to take the first and second derivatives
Yeah I did that to get the points
Its the triangle bit that im stuck on
Well I guess I kinda know how to do that bit too but its so fucking awful im just wondering what the best way is
fickle shell
But you can see it's isoceles
True I see
rain magnet
Well I guess I kinda know how to do that bit too but its so fucking awful im jus...
there shud be something symmetrical here cuz both the function and the area has a natural log
U do get the base is 4 right, that's immediately observable
The base of the triangle
fickle shell
So this helps us get a right angle triangle right?
north bison
I didn't calculate ln(4) or ln(8), but drawing a rough diagram helped me notice that (you can sort of notice this since the x co-ordinates of A and B are the same and the y co-ordinate is symmetric, 2 and -2)
fickle shell
To find the area easily
rain magnet
If u have the pts the area is easy
north bison
So this helps us get a right angle triangle right?
Yes
rain magnet
But theyre awful
Tell me what they r
fickle shell
Tell me what they r
A is (ln(8), 2), B is (ln(8), -2) and C is (0, ln(4))
north bison
So if you look at the diagram you can work out GE from Pythagoras and then just multiply the area you work out by 2
fickle shell
So if you look at the diagram you can work out GE from Pythagoras and then just ...
Whats GE?
north bison
I'll make a better diagram hold on
rain magnet
They r (-2, ln(4)+ln(2)) (2,ln(4)+ln(2)) and (0,ln4)
rain magnet
A is (ln(8), 2), B is (ln(8), -2) and C is (0, ln(4))
This is untrue
Inflection pt is where the second derivative = 0
north bison
Work out CD and you know AD is 2
Then use pythagoras and work out AC
Use 1/2 a b and multiply by 2
You should get ln(4)
rain magnet
A is (ln(8), 2), B is (ln(8), -2) and C is (0, ln(4))
Uve just got the x and the y coordinates interchanged
north bison
Because it's the y coordinate
fickle shell
Oh nvm
north bison
Distance above the axis
fickle shell
yeye
fickle shell
Uve just got the x and the y coordinates interchanged
Yes youre right sry
Ok I think I can solve this now
Thank you so much everyone!!
❤️
.close
marsh citrusBOT
marsh citrusBOT
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bitter ferry
heya, I had this one question
Let C be the curve in R2 with parameterisation
r(t)=[e^t/4⋅cos(t),e^t/4⋅sin(t)] for t∈[−10⋅π,10⋅π]
Give an equation of the form y=h(x) for the tangent line to C at the point
r(π)=[−e^π/4,0]
bitter ferry
differentiating r(t) i get, r'(t) = [cos(t) * 1/4 * e^t/4 - sin(t) * e^t/4 , sin(t) * 1/4 * e^t/4 + cos(t) + e^t/4]
r't(π) = [-1/4 * e^π/4 , -e^π/4]
still temple
ye
bitter ferry
so how do i form an equation of the form y=h(x) with this
bitter ferry
yeah
still temple
u got dy/dt n dx/dt
do (dy/dt)/(dx/dt) to make it as dy/dx
u get the slope at t = pi
bitter ferry
so -e^π/4 / -1/4 * e^π/4, which is 1 / 1/4 -> 4
still temple
nice
marsh citrusBOT
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lucid bridge
How do we do square roots sorry
tired ore
How do we do square roots sorry
what do you mean exactly
marsh citrusBOT
@lucid bridge Has your question been resolved?
lucid bridge
https://youtu.be/I7TFYa1v9xI?si=jnHZ6JFlxSh0tXFk
tysm this helped me a lot
calm harbor
!done
marsh citrusBOT
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@lucid bridge Has your question been resolved?
calm harbor
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marsh citrusBOT
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boreal heath
let p(x) = 2x^2 + 7x + c where c =/ 0. If a and b are the roots of p(x) then find the value of 1/a + 1/b in terms of c
marsh citrusBOT
let p(x) = 2x^2 + 7x + c where c =/ 0. If a and b are the roots of p(x) then fin...
boreal heath
?
i started by finding the sum and the product
of the two
which are -7/2 = a+b
and c/2 = a*b
since we dont really know what c is
im confused tho and idk if i really did the right thing lowkey
ok thats awkward
<@&286206848099549185>
🙏
oh dear
velvet cedar
since we dont really know what c is
"In terms of c" so your question will be an expression containing c. You don't need a value of c
velvet cedar
Have you simplified 1/a + 1/b?
spark otter
what is/are the link(s) between a,b and coefficients from p(x)?
boreal heath
which are -7/2 = a+b
.
spark otter
ok
wary kite
maybe simplify 1/a + 1/b
boreal heath
ok
spark otter
so you have -7/2 = a+b
and c/2 = a*b
wary kite
🤷🏼♂️
spark otter
so
boreal heath
right
boreal heath
i think you want me to like figure out how to make it have a+b in it or smth?
idk how to simplify it though tbh
livid swan
i think you want me to like figure out how to make it have a+b in it or smth?
Helloo
It's simple
wary kite
really? what’s 3/4 + 2/3?
boreal heath
uhm
oh
oh i c
so you want me to make both denominators the same or something?
b/ab + a/ab?
b+a/ab
livid swan
Just make common dominator
1/a+1/b=(a+b)/a*b
spark otter
uh huh
wary kite
Just make common dominator
1/a+1/b=(a+b)/a*b
way to be
boreal heath
or am i wrong about that
wary kite
or am i wrong about that
you’re not
boreal heath
oh ok
oh so then its just
-7
i mean
srry
-7/2/c/2?
pretend i put the parenthesis in
😄
livid swan
Right
velvet cedar
Wait
boreal heath
c/2 rip
velvet cedar
Yh
marsh citrusBOT
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odd sparrow
marsh citrusBOT
odd sparrow
Need some help with understanding how to calculate Var(X)
Why is only the outside "x" squared when calculating E(X^2)?
spark otter
Why is only the outside "x" squared when calculating E(X^2)?
transfer theorem, $E[g(X)] = \int_\bR g(x)f_X(x)dx$
elfin berryBOT
rafilou2003
spark otter
apply to g(x) = x^2
marsh citrusBOT
void elm
jagged oracle
Yes
No bro found his mistake himself
And must have thought that there is no need
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nova sleet
how can I derive triple angle, its not working
marsh citrusBOT
how can I derive triple angle, its not working
thorny bison
how can I derive triple angle, its not working
Group three angles into two use double angle and then use double angle again on the grouped angles
Sin(a+b+c) = sin((a+b) +c) = double angle first on a+b and c then on a+b
thorny bison
or 3sin cos^2 - 3sin^3
Can you show your working?
nova sleet
sin(2x + x)
sin(2x) cos + cos(2x) sin
sin(x+x) cos + cos(x+x) sin
2sin cos cos + (cos^2-sin^2)sin
2sin cos cos + (1-2sin^2) sin
2sin cos cos + sin - 3sin^3
2sin cos^2 - 3sin^3
thorny bison
sin(2x + x)
sin(2x) cos + cos(2x) sin
sin(x+x) cos + cos(x+x) sin
2sin cos cos +...
Convert cos²x to 1- sin²x
nova sleet
i tried but I got a wrong answer
2sin(1-sin^2)-3sin^3
2sin - 2sin^3 - 3sin^3
2sin - 5sin^3
thorny bison
sin(2x + x)
sin(2x) cos + cos(2x) sin
sin(x+x) cos + cos(x+x) sin
2sin cos cos +...
Wait how did 3sin³x come here your fifth step is wrong
nova sleet
oh it should be 2sin^3
thorny bison
oh it should be 2sin^3
Yes and you missed a sinx above
nova sleet
sin(2x + x)
sin(2x) cos + cos(2x) sin
sin(x+x) cos + cos(x+x) sin
2sin cos cos + (cos^2-sin^2)sin
2sin cos cos + (1-2sin^2) sin
2sin cos cos + sin - 2sin^3
3sin cos^2 - 2sin^3
3sin(1-sin^2)-2sin^3
3sin - 2sin^3 - 2sin^3
3sin - 4sin^3
still wrong
thorny bison
sin(2x + x)
sin(2x) cos + cos(2x) sin
sin(x+x) cos + cos(x+x) sin
2sin cos cos +...
Look at 6th and 7th step you missed a sinx
nova sleet
oh true
thorny bison
So it should be 3sinx - 4 sin³x which is the correct answer
marsh citrusBOT
Available help channel!
last cedar
marsh citrusBOT
last cedar
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iron ocean
how to get lcd
marsh citrusBOT
how to get lcd
latent coral
how to get lcd
do you have a specific example in mind?
latent coral
in fraction form?
marsh citrusBOT
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Available help channel!
boreal relic
Assignment: Write the rational exponents in radical form. Simplify if possible.
- 2^1/5
- 10^-1/2
- 18^1/4
- (-3)^1/3
- 9^1/8
- 2^2/5
- 27^5/3
- 10^4/5
marsh citrusBOT
Assignment: Write the rational exponents in radical form. Simplify if possible.
...
low ruin
Assignment: Write the rational exponents in radical form. Simplify if possible.
...
A lot exponents just knowing the relevant theorems. So this question you want to use a^1/n = nth root a
boreal relic
A lot exponents just knowing the relevant theorems. So this question you want to...
yeah
but how do you do 2 and 4 specifically?
low ruin
So we have 10^(-1/2). This is little but confusing because negative sign. So you can make use of the theorem a^(bc) = (a^b)^c
=>(10^-1)^1/2
Use the theorem a^-1 = 1/a
=> (1/10)^1/2
=> sqrt(1/10)
You can make use of the theorem sqrt(ab) = sqrt(a)sqrt(b). note that a and b cannot both be negative
doing that we get 1/sqrt(10)
And if you want can rationalise the denominator
marsh citrusBOT
Available help channel!
dull imp
marsh citrusBOT
dull imp
Find the equation of curve satisfying this and passing through (1,-1)
lucid zenith
this is a homogeneous differential equation
dull imp
,rotate
elfin berryBOT
dull imp
How should I do after this
dull imp
It's becoming a cubic that I am unable to integrate
elfin berryBOT
lucid zenith
seems like it's not too bad to integrate
dull imp
Wait a sec bto
lucid zenith
you have $x\dv{v}{x}=-\frac{(v+1)(v^2+1)}{v^2+2v-1}$
elfin berryBOT
kheerii
lucid zenith
you missed a - sign but yeah
dull imp
Oops
lucid zenith
notice that you can factorise the denominator
dull imp
So how To integrate lhs?
lucid zenith
partial fractions
dull imp
I have to factorise denominatir right?
lucid zenith
yes
dull imp
,rotate
elfin berryBOT
lucid zenith
yes
dull imp
Now partial fractions?
lucid zenith
yes
dull imp
,rotate
elfin berryBOT
dull imp
This
elfin berryBOT
lucid zenith
yep
dull imp
👍
Thanks
But is there a faster process?
Than splitting the cubic in factors then partial fractions
@lucid zenith I am stuck here at this step
My denominatot is becoming 0
still temple
marsh citrusBOT
still temple
For what condition between a b c f g h?
Will Discriminant always be a perfect square?
So that this equation can be factorised into two linears
cloud field
,rccw
elfin berryBOT
cloud field
,rccw
elfin berryBOT
cloud field
hi
cloud field
what about it
still temple
What is the condition.between coefficient abc fgh
So that it can be factorised into two linear
Lemme give u an example
See this question
It can elaborate
still temple
what about it
.
cloud field
i see
still temple
Can you assist?
I even know the relation
I do not know how it came
The relation is that abc+2fgh-af²-bg²-ch²=0
cloud field
The relation is that abc+2fgh-af²-bg²-ch²=0
so you want to show this?
still temple
Yes
Derive this
From the general form of 2 degree equation
that is
ax²+2hxy+by²+2gx+2fy+c=0
If this expression can be factorised into two linear equations i.e maximum degree one
still temple
The relation is that abc+2fgh-af²-bg²-ch²=0
Then this equation is true
still temple
so you want to show this?
.
still temple
Then this equation is true
Always and vice versa
cloud field
right i got it
still temple
So what it is
cloud field
The relation is that abc+2fgh-af²-bg²-ch²=0
what you said here
still temple
How do we derive it
open hamlet
is deriving defrinciating ?
cloud field
is deriving defrinciating ?
no
cloud field
Can you tell in chat?
you need to set d = 0
cloud field
wait no its not d that is 0
cloud field
See this example
ok its like this:
you find the discriminant for x, you get a quadratic equation in y
then you set the discriminant of y equal to 0
marsh citrusBOT
@still temple Has your question been resolved?
carmine sandal
I don't understand how it goes from the first line to the second one
carmine sandal
I can get from the first one to the last one
But im not sure what the intermediate steps are between the first and second
devout mauve
thorny bison
I don't understand how it goes from the first line to the second one
Subtract 2
marsh citrusBOT
still temple
ok its like this:
you find the discriminant for x, you get a quadratic equation...
Hello what how?
.reopen
still temple
.reopen
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Available help channel!
still temple
marsh citrusBOT
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
toxic hazel
I don't understand the reasoning in the underlined text.
marsh citrusBOT
I don't understand the reasoning in the underlined text.
@toxic hazel Has your question been resolved?
marsh citrusBOT
toxic hazel
.reopen
marsh citrusBOT
@toxic hazel Has your question been resolved?
marsh citrusBOT
@toxic hazel Has your question been resolved?
zenith sable
Hi! Can someone help me w my hw😭 I understand the lesson but I dont get how to solve this.
marsh citrusBOT
Hi! Can someone help me w my hw😭 I understand the lesson but I dont get how to ...
zenith sable
still temple
In one part
red phoenix
what grade math is it
red phoenix
what did you try?
still temple
240/h and 270/h
zenith sable
what grade math is it
Im in 9th grade
still temple
Dude no matter which grade. Dude just wants to understand rather than know
still temple
240/h and 270/h
Take h as anything that would be easier to draw
Area of bottom rectangle is 270/h and 240/h
Take h as something that would be easier to draw
red phoenix
I was makeing sure i llearned it