#help-39
cloud sky
pearl pondBOT
cloud sky
Can u help me guys?
prime bramble
well, it’s gonna depend on what you mean by ^2
$f^2(x)$ could mean: $(f(x))^2, f’’(x)$, or $f(f(x))$, depending on the context
cloud sky
And that's the problem, depending on where the 2 is, I don't know if we're actually taking Y squared or if it's going to be a composite function.
jolly parrotBOT
higher!
Compile Error! Click the 
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prime bramble
And that's the problem, depending on where the 2 is, I don't know if we're actua...
what is the context?
this is going to depend all on the context
prime bramble
**higher!**
Compile Error! Click the <:errors:504266556054962196> reaction for m...
any of these are valid interpretations depending on the situation
cloud sky
f function has 2 on it and I wanted to take the derivative of this expression and I was actually wondering what it meant here
prime bramble
can you show the original problem?
tropic saddle
is it sin^2 or some other trig?
cloud sky
Problem is Turkish tho
tropic saddle
then its squared
prime bramble
Problem is Turkish tho
that's okay, I just want a sense of the problem at hand
and what Denascite said is true
for the trig functions, it's common to use the exponent on the function name to indicate a square instead of composition
cloud sky
In short and public math language, i was trying to deal with this equation in derivative
So the "n" in here is?
cloud sky
Oh oky this took my whole day tryin to ask and find every math teacher i know 🥲
Thx dude have a nice day
pearl pondBOT
@cloud sky Has your question been resolved?
pearl pondBOT
dire snow
(the line drawn in green is my attempt of drawing the odd extension)
pearl pondBOT
pearl pondBOT
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bitter herald
Can we define integration as a linear map of $I: \mathcal{F} \to\mathbb{R}$ where $\mathcal F$ is a space of functions
jolly parrotBOT
Aero
bitter herald
I feel like this is incomplete though...
plush bramble
bitter herald
https://math.stackexchange.com/a/4437654
why was W defined with a circled plus and dot?
I thought vector spaces only had addition and multiplication defined on them
plush bramble
The addition in W need not be the same as the addition in V
Same for multiplication
That becomes irrelevant in the following paragraph. Keep reading
bitter herald
Woah that's cool. So interesting that you can write something such as
D(sin) = cos
You'd think that'd be an incomplete statement as a novice
But okay, I see. Integration and differentiation are basically linear maps between vector spaces. Thanks!
.close
pearl pondBOT
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lament geyser
Can anyone explain me how pi was found?
pearl pondBOT
Can anyone explain me how pi was found?
lament geyser
why pi * 2r = diameter
frozen lantern
$\pi=\frac{\text{Circumference}}{\text{Diameter}}$ by definition.
jolly parrotBOT
Percy
midnight haven
why pi * 2r = diameter
2r is diameter- pi * 2r = pi * diameter = circumference if that's what you mean
lament geyser
how to find area?
midnight haven
Area is pi * r^2
frozen lantern
It's $\int^R_0 2\pi r dr$ but yo don't need to know that yet actually.
jolly parrotBOT
Percy
lament geyser
why is radious squared?
frozen lantern
why is radious squared?
$\int^R_0 2\pi r dr= \pi R^2 - \pi 0^2 = \pi R^2$.
jolly parrotBOT
Percy
autumn fossil
There are simpler visualizations
midnight haven
I think its a geometry question lol dont use integrals unless Im wrong
frozen lantern
oh but that's less intimidating /lh
frozen lantern
I think its a geometry question lol dont use integrals unless Im wrong
integrals is geometry lmao
autumn fossil
I think its a geometry question lol dont use integrals unless Im wrong
Integrals are the better way to do it, because simple visualization doesnt prove anything
but idt the OP can understand them
lament geyser
i dont
frozen lantern
Yeah
midnight haven
but idt the OP can understand them
yeah thats my point lmao
lament geyser
im in 1st grade
chillax
i have yet to learn it
im starting to learn triogonometry
midnight haven
okay go off 🔥 dont be telling people online ur that young though lol
autumn fossil
Okay, so take a look at this. You can split up the circle into many sectors liek this and arrange them in something that almost looks like a rectangle
the more you split it, the more its gonna look like a rectangle
so if you imagine splitting it infinitely many times, its gonna be a perfect rectnagle
it's height is gonna be the radius (1r)
frozen lantern
parallelogram* which has the same area as a rectangle though
autumn fossil
because that's height of one of the sectors
autumn fossil
parallelogram* which has the same area as a rectangle though
its gonna approach a rectangle
its actually neither a rectangle nor a parallelogram
frozen lantern
yeah obviously not
autumn fossil
its some weird undescribable shape
lament geyser
Okay, so take a look at this. You can split up the circle into many sectors liek...
its not rectengale
autumn fossil
if you imagine decreasing the angle, its still gonna approach a rectangle tho
lament geyser
though
autumn fossil
its not rectengale
Imagine splitting it even more
its gonna look more and more like a rectnagle
lament geyser
also why is it pi * r?
autumn fossil
also why is it pi * r?
the top and bottom together make the circumfence
circumfence is 2pi * r
so top and bottom are both pi * r
lament geyser
yes
autumn fossil
or which r?
frozen lantern
if you imagine decreasing the angle, its still gonna approach a rectangle tho
okay yeah fair
i just thought ||gm for some reason
uff
lament geyser
@autumn fossil
lament geyser
so
autumn fossil
so the total area of the circle will be same as the one of the almost-rectangle
lament geyser
Circumference = pi * 2r
Area = pi * r^2?
autumn fossil
and area of that rectangle is (pi * r) * r
autumn fossil
Circumference = pi * 2r
Area = pi * r^2?
Yep
lament geyser
@orchid parrot you should really make an information channel in this server with all formulas and that so people can just send link to it.
frozen lynx
||i want proof through integration but i’ll wait||
south inlet
||i want proof through integration but i’ll wait||
What’s the point?
frozen lynx
What’s the point?
Fun
lament geyser
5 people in this chat! Nice!\
frozen lynx
But you do realise you will be proving it to yourself?
I tried and failed
south inlet
5 people in this chat! Nice!\
Yes and you have someone helping you, so you’re luckier than most
autumn fossil
it was already posted
lament geyser
Yes and you have someone helping you, so you’re luckier than most
cause im doing beginner high school math 🙂 and the rest of people are doing university/colleage math
frozen lynx
R because the circle will cover the whole area going half the distance in each direction right?
frozen lantern
<@102705166754549760> you should really make an information channel in this serv...
https://google.com is a great thing actually
lament geyser
with cotangens, i can find sin and con?
frozen lynx
With sin alone you can find all 6 trig functions
autumn fossil
R because the circle will cover the whole area going half the distance in each d...
It's basically summing up these rings.
Width of 1 ring is dr, radius is r ranging from 0 to R
frozen lynx
That’s my opinion tho, some say you need cos
autumn fossil
where R is the radius of the circle you are finding area of
autumn fossil
with cotangens, i can find sin and con?
Yes, given a cotangent you can find sin and cos
it's not gonna be particularly nice tho
and it can have multiple sols i believe
lament geyser
alr
frozen lantern
||i want proof through integration but i’ll wait||
imagine little circular concentric rings each with radius r and thickness dr.
Their area $dA$ is $2\pi r dr$,
$A=\int^R_0 2 \pi r dr$.
There.
frozen lantern
With sin alone you can find all 6 trig functions
no you can't.
jolly parrotBOT
Percy
autumn fossil
Yeah, so basically this.
Thickness - dr
radius - r
area ~ 2pir dr
and sum (integrate) them from 0 to R
frozen lantern
then you can do spheres and other fun stuff lmao.
frozen lynx
Yeah yeah i understand, what im saying is why R and not 2R
autumn fossil
Yeah yeah i understand, what im saying is why R and not 2R
why should it be 2R?
the largest ring is gonna have radius R
frozen lynx
Is it because the full ring will encompass the diameter when going to R?
autumn fossil
Is it because the full ring will encompass the diameter when going to R?
Yea
desert solar
Yeah yeah i understand, what im saying is why R and not 2R
The radius in a circle varies from 0 to R
autumn fossil
and you dont want to include rings with a diameter larger than than
pearl pondBOT
@lament geyser Has your question been resolved?
blazing shadow
So I got through the first part comfortably, but now I'm trying to take the inverse laplace of the g(t)u_9(t) part, which is just e^-9s/s(s-1)(s-3). My first instinct is to do partial decomp, which I've done as shown below. But the issue arises when I try to take the inverse laplace of this answer. It shouldn't be in terms of s, so I would need to somehow get rid of that, but also there's not really an inverse laplace of an exponential in my arsenal of laplace transforms.
Is it possible to somehow get everything in terms of e^-9s/s to get step functions? (or am I overlooking something here? I can't seem to figure it out)
blazing shadow
okay, so apparently lumen doesn't like U or u for the syntax, so it's likely that step functions isn't the answer here. I think I'm probably overlooking something
<@&268886789983436800>
opal lantern
screenshot are unnecessary fyi, we can read deleted messages
in fact we'd rather you not post them and perpetuate them
blazing shadow
screenshot are unnecessary fyi, we can read deleted messages
👍
pearl pondBOT
@blazing shadow Has your question been resolved?
lament geyser
<@&268886789983436800>
?
pearl pondBOT
@blazing shadow Has your question been resolved?
pearl pondBOT
pearl pondBOT
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faint shore
Once I saw da formula I sketched in the top left, but this just shows ( b/2 )^2
faint shore
Am I tripping?
mint wave
it's just (b/2)^2
warm grove
Can somebody please explain to me how to do this?
pearl pondBOT
Can somebody please explain to me how to do this?
burnt nova
Pls someone help
pearl pondBOT
Pls someone help
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
mint wave
Can somebody please explain to me how to do this?
it's kind of self explanatory. what is f(0)
warm grove
it's kind of self explanatory. what is f(0)
do I use cos(x)=x^3=0 and plug? or do I have to start with somethign else
mint wave
it tells you in the problem what f(x) is 🙂
mint wave
yep
mint wave
what is cos(1)
mint wave
going ok still?
warm grove
going ok still?
For the 0.01 I got
0.99994
I just dont know hwo to make an interval for that
wait
no
thats just
(0.01, 0.99)
well
round to 2
thats basically 1
mint wave
that interval is not 0.01 apart
mint wave
there might be an algebraic way to do it, but you can always find the exact answer and subtract 0.005 for the lower bound and add 0.005 for the upper bound to get a difference of 0.01
warm grove
Oh okay so
For cos(0.01)-(0.01)^3 I get 0.99994
Then id subtract 0.005 for that
and add 0.005 also
am I correct?
warm grove
okay thank you let me try it out
okay i just got the values wrong for f1 and the interval
mint wave
that's what i get
mint wave
you may need to leave a few more decimal places
warm grove
okay
mint wave
oh that would be problematic
warm grove
just subtract 0.005 from the original values?
mint wave
use your graphing calculator
you want to find when the functions have a solution
so either graph them separately and see where they intersect or graph them together and find the zero
mint wave
either f(x) and find a 0 or each of the functions in the original problem and find an intersection
warm grove
okay tysm
warm grove
either f(x) and find a 0 or each of the functions in the original problem and fi...
I got (0.865474 , 0.6482793) as the intersection
mint wave
do they want you do do it in degrees? that's so weird
warm grove
i really dotn know honestly
mint wave
nah bc that would give you a positive answer
warm grove
ill just put the entire value
well taht didnt work either
yk waht whatever close enough
pearl pondBOT
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hoary blade
hi
hoary blade
help plz I hve a test tom and I am lost on the last lesson we learned
I dont get how this example aligns with the values of the graph that are written in the next photo below:
this is the pic that i DONT get the values for which are written on the left
like how is d 1.5
and a 2.5
and those other values
nova spindle
im just confused bc i have no idea what a paddle wheeler is. is the paddle also the wheel? the questions is written in a way that makes me think so
hoary blade
paddle wheeler is this
:
its just a wheel that spins
and part of the wheel goes under the water
I searched images for "paddle of a paddle wheeler"
and got a good idea
@nova spindle u there
pearl pondBOT
@hoary blade Has your question been resolved?
pearl pondBOT
@hoary blade Has your question been resolved?
pearl pondBOT
@hoary blade Has your question been resolved?
pearl pondBOT
fallen kindle
.close
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Available help channel!
marsh coral
when
jolly parrotBOT
ToggeldW
jolly parrotBOT
ToggeldW
jolly parrotBOT
ToggeldW
buoyant sandal
it has to be only linear or quadratic factors
so you can't do partial fractions anyways I believe
pearl pondBOT
@marsh coral Has your question been resolved?
marsh coral
it has to be only linear or quadratic factors
how u know kin??
buoyant sandal
sorry, wdym
marsh coral
sorry, wdym
pearl pondBOT
Available help channel!
low crystal
Why doesn't limit exist at 2?
pearl pondBOT
Why doesn't limit exist at 2?
lucid moth
pearl pondBOT
lucid moth
Im a bit confused about what to do here
sin(x) = cos(x)
tan(x) = 1
arctan(1)
= pi/4 + pi*k
So the points of intersection are pi/4 and 5pi/4
f(x) = sin(x) so F(x) = -cos(x)
g(x) = cos(x) so G(x) = sin(x)
timber tartan
Area enclosed is int f(x) - g(x)
notice how the first part, the tiny portion
when added to the third area, becomes equal to the 2nd area
so we just need twice of this area
which im sure you can calculate
lucid moth
I wanted to do a different method
lucid moth
when added to the third area, becomes equal to the 2nd area
Cause I would never notice this in an exam lol
But the last bit im stuck on
The actual calculation
timber tartan
its trivial
timber tartan
Cause I would never notice this in an exam lol
you gotta remember these are periodic functions
lucid moth
[(G(2pi) - F(2pi)) - (G(5pi/4) - F(5pi/4))] + [((F(5pi/4) - G(5pi/4)) - (F(pi/4) - G(pi/4))] + [(G(pi/4) - F(pi/4) - (G(0) - F(0))]
Is that correct?
Hard to read I know 😭
I always mix up what to add and what to take away
Cause some things are below the x axis so they need to be negative, yada yada
timber tartan
Cause some things are below the x axis so they need to be negative, yada yada
You can just do int (s - c) from pi/4 to pi/2 + int(s) from pi/2 to pi
that will give you this area
above the x-axis
just multiply that by 2 to get the full 2nd area
multiply that by 2 to get the answer
lucid moth
Bro pls 😭
I just want to know if THIS way is right
These are all things I learn after I get the basics
lucid moth
[(G(2pi) - F(2pi)) - (G(5pi/4) - F(5pi/4))] + [((F(5pi/4) - G(5pi/4)) - (F(pi/4)...
I need to know am I doing the basics right
timber tartan
[(G(2pi) - F(2pi)) - (G(5pi/4) - F(5pi/4))] + [((F(5pi/4) - G(5pi/4)) - (F(pi/4)...
can u just give me the integral expression
not the final one
lucid moth
can u just give me the integral expression
Whats that sry
timber tartan
like you integrating f to F
and then put the limits
you've given me this
i wanna see this
lucid moth
My handwriting is so bad 😭
lol
Like this?
Oh wait they are all supposed to be small f's and small g's in there
timber tartan
,w int (sinx - cosx) dx from pi/4 to 5pi/4
jolly parrotBOT
timber tartan
,w int (sinx - cosx) dx from pi/4 to pi/2 + int(sinx)dx from pi/2 to pi
jolly parrotBOT
timber tartan
Correct
pearl pondBOT
@lucid moth Has your question been resolved?
lucid moth
HI CHARTBIT!! ❤️
round lotus
pearl pondBOT
round lotus
this is impossbile to do
ember spear
do, you now the sine rule?
round lotus
yes
ember spear
what value did you get for theta
ember spear
you can
round lotus
i try to find the y side but when i solve it, on my calc it gave me a error
ember spear
theta is (180 - 54 - 40.33185)° or complement of that
round lotus
yea yea i just solve it
thanks
i didnt even know you could do that
but they not opposite tho?
pearl pondBOT
Available help channel!
tight charm
Hey so I’m trying to find the direction angle of <-11,6> but I got -28.6 degrees what do I do to find the direction angle from here
tight charm
Would it just be 180 -28.6?
?
To get 151.4 degrees
Would that be it
Nvm I figured it out
How would you go about telling if <10,20> and <2,4> were parallel
pearl pondBOT
@tight charm Has your question been resolved?
warm osprey
How would you go about telling if <10,20> and <2,4> were parallel
If two vectors are parallel, then they are multiples of eachother. So we must find c such that <10, 20> = c*<2, 4> = <2c, 4c>
10/2 = 5 therefore c = 5
Now test if 4c = 20, it does therefore they are parallel
midnight haven
Help.
oak quiver
!da2a
pearl pondBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
midnight haven
I wasn't waiting for anyone to respond to that.
The sides are (starting from the top one, going clockwise) 10, 6, 2 and 6.
It's to find for the radius.
Particularly, r/root5
oak quiver
what is B?
midnight haven
B is a point on the circle, which carries no significance.
LOL
Wait
Sorry
All sides are tangent, my bad.
oak quiver
DE is a tangent?
midnight haven
oak quiver
label the point of tangency
midnight haven
It looks like a trapezium in my book.
oak quiver
do you know the area of this quad?
midnight haven
no
If I knew, it would have been easier than saying the alphabet reversely.
I need help with this too.
<@&286206848099549185>
pearl pondBOT
@midnight haven Has your question been resolved?
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
bruh
<@&286206848099549185>
My teacher told to drop perpendicular from A and B on DC.
I am doubtful of the following:
Whether CD is parallel to BA.
Whether the line joining the point of tangency of CD and AB with the circle, passes through the centre or not.
O could be the centre which could not lie on the line joining the point of tangency as showing in black.
What I am asking is how we can prove that [the line joining the point of tangency as showing in black.] contains [the centre O of the circle].
If it was multiple choice, I wouldn't have faced any problem.
I think that AD = BC may be useful to this.
oak quiver
i think they forgot to mention that ABCD is a trapezium
midnight haven
nah
midnight haven
.close
pearl pondBOT
midnight haven
😦
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Available help channel!
jolly marsh
i need help with proof
pearl pondBOT
i need help with proof
jolly marsh
So i assume that f:X-Y is injective
So i have to prove that f^1(f(A))=A
let x be in f^1(f(A))
preimage definition
f(x) ∈ f(A)
image definition
x ∈ A
so f^1(f(A)) c A
let x ∈ A
so i know that function is defined as X-Y then f(x) ∈ A ?
preimage definition
x ∈ f^1(f(A))
A c f^1(f(A))
<=
I assume that f^1(f(A))=A
I have to show that f:X-Y is injective
So lets say objectily that f : X-Y is not injective
so x_1 != x_2 => f(x_1)=f(x_2)
So let A = {x_1}
so {x_1] != {x_2} => f(x_2)=f(x_2)
And this is against my assumption. because i can say from the definition that there is more elements in A than f^-1(f(A)) so the equality wont work. So f has to be injective
Is it good or some kind of logic
?
snow seal
f(x) ∈ f(A)
@jolly marsh you should say that it follow from injectivity
jolly marsh
Oh ok
snow seal
so i know that function is defined as X-Y then f(x) ∈ A ?
I dont understand how you do other inclution?
snow seal
You can say A contains x then f(A) contains f(x) then f1(f(A)) contain subset f1(f(x)) but f is injective and f1(f(x)) contains only x
jolly marsh
is it because of image definiton there?(f(x) in f(A))
snow seal
Yeah
jolly marsh
then i use preimage definition?
jolly marsh
But how f^-1(f(x)) c f^-1(f(A))
do i have to say that in my proof or can i just say with preimage definition i know x is in f^-1(f(A))
snow seal
Oh you are right
f(A) contains f(x) and preimage is all element whose values in f(A) and x is that element
snow seal
<=
To prove other direction you could take A to be singleton and get that preimage of f(x) is x that is condition of injectivity
jolly marsh
so f({x_1}) = x_1 ?
snow seal
But yea you can do it with contradiction
jolly marsh
Only x take value f(x)
Oh ok
My meaning in contradiction is that if 2 different x give the same f(x) then from assumption there is no same amount of elements in both sets
So the = wont exist
Or i mean there is no same elements
snow seal
Yeah you would have that
|f1(f(x1))| => 2 but from assumption it is 1
But this proof is more indirect
But both are correct
snow seal
Bye
pearl pondBOT
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glass yacht
ok so I am not sure if this requires occupying a help channel, but my head is spinning, so I just learned about the refractive index and instead of going like this (299,792,458/1.3 water) I tried finding a way to get to the result using 0. times a number after it, so my noddle went like "its 1.3 so you probably could use 0.7x299,792,458 but then it didnt work, after that I tried the original way of just dividing like a human being and call it a day, so (299,792,458/1.3= 230,609,583.0769230769230676986936) huh!! so those decimals look rather suspicious, so I took the decimal and timed it by the speed of light and got the same answer. Finally the question is how TF is this working can't even think of this on a smaller scale to wrap my head around it. Please forgive me if this isn't worthy of occupying a channel for I am sorry.
plush bramble
can you ask your math question with fewer feelings
glass yacht
I guess not, sorry
pearl pondBOT
@glass yacht Has your question been resolved?
pearl pondBOT
ivory swallow
pearl pondBOT
@fervent meadow Has your question been resolved?
dim bobcat
Do you know about integral ?
What is an integral for ?
Poor samsy no one helped you 😭
Yeah !
So in your example, do you agree that we have to find the blue area thanks to the curves ?
Yes
Try to write every curve in function of x (y= ...)
It will be easier
Nope sqrt(y^2) != y
!= stands for not equal
What is sqrt(y²)?
Yes
So absolute value of y
Well no
It's sqrt (|x| + 2)
What don't you understand?
This absolute value of a number is its distance for 0
For example, -6 absolute value is 6
Just to know, how old are u?
pearl pondBOT
midnight haven
-a/x^(a-1) isn't the same, is it?
grim fractal
It's $-\frac{a}{x^{a+1}}$
jolly parrotBOT
Ari
grim fractal
because when you differentiate, you decrease the exponent by 1 so -a becomes -(a+1)
pearl pondBOT
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daring bay
so you have k(t) = ae^-0,04t
(t is in minutes and k(t) is something else i guess)
after 23 minutes the concentration is 30,07 mg/ml
what is the function?
wanton latch
thats ok
daring bay
so i put the point (23|30,07) in?
wanton latch
Plug in 23 for t and 30.07 for k(t)
daring bay
yeah
daring bay
raise both sides to LN so that you can get rid of the e
but i dont understand
my teacher did it like this
i was sick
during the day
they did it
and im confused on where the 1 comes from
wanton latch
that is a weird way to do it
so ill walk you through this
is it k(t)=a-ae^-0.04t?
or no
also is that ^ looking shape supposed to be a 1?? ur teacher's handwriting confuses me
daring bay
also is that ^ looking shape supposed to be a 1?? ur teacher's handwriting confu...
yeah
daring bay
so ill walk you through this
can u tell me how u would do it
pearl pondBOT
@daring bay Has your question been resolved?
daring bay
<@&286206848099549185>
daring bay
sorry
daring bay
yeah
wanton latch
there is a common factor of a in the problem
so what you do is seperate out a into a(1-e^0.04*23)
u understand?
daring bay
so what you do is seperate out a into a(1-e^0.04*23)
yeah
cuz its 2 a
like
a is there 2 times
but the - infront of the a doesnt matter?
daring bay
because a/a=1
why is it /
wanton latch
so by separating it out you get 1-(expression)
then divide both sides by (1-e^-0.04*23)
daring bay
then divide both sides by (1-e^-0.04*23)
yeah
daring bay
so by separating it out you get 1-(expression)
bro
i missed a day of math
and they start doing crazy stuff man
wanton latch
that isolates a on the right side. calculate and you get 49.99...
it happens
what math class is this
pearl pondBOT
@daring bay Has your question been resolved?
midnight haven
pearl pondBOT
midnight haven
For this equation, would I do KL+LM+KM=180?
unkempt yacht
can you label the vertices?
midnight haven
Can you give me a bit, help others in the discussion because it might take a bit for me
Is this it
Or is this the equation?
<@&286206848099549185>
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warm depot
let $\mathcal{S}$ be the portion of the elliptic cone $z^2 = x^2 + 4y^2$ with $x \geq 0, y\geq 0$ and $1\leq z \leq 4$ write the scalar surface integral as an iterated integral
jolly parrotBOT
syecko
warm depot
$\iint_{\mathcal{S}} x + yz dS$
jolly parrotBOT
syecko
warm depot
so
ive parameterized it as
$x(u,v) = (u\cos v, \frac{u}{2} \sin v, u)$ for $1\leq u \leq 4 \quad 0 \leq v \leq \frac{\pi}{2}$
jolly parrotBOT
syecko
warm depot
hence $x_u = (\cos v, \frac{1}{2} \sin v, 1)$ and $x_v = (-u\sin v, \frac{u}{2}\cos v, 0)$
jolly parrotBOT
syecko
warm depot
and i found the cross product
$x_u \cross x_v = (-\frac{u}{2}\cos v, u\sin v, \frac{u}{2})$
jolly parrotBOT
syecko
warm depot
so $\norm{x_u \cross x_v} = \sqrt{\frac{u^2}{4}\cos^2 v + u^2\sin^2 v + \frac{u^2}{4}}$
jolly parrotBOT
syecko
jolly parrotBOT
syecko
warm depot
so would be dS just be the norm written above dudv
like
$\iint_{\mathcal{S}} x + yz dS = \int_0^{\frac{\pi}{2}}\int_1^4 (x+yz)\norm{x_u \cross x_v} dudv$
jolly parrotBOT
syecko
warm depot
and substitute x y and z according to my parameterization of course
i just didnt want to write it to make it look like less of an eye sore
pearl pondBOT
@warm depot Has your question been resolved?
warm depot
@tall ruin sorry for the ping, im just wondering if you know
warm depot
**syecko**
just this really
like is dS just going to be dudv
and the norm of course
tall ruin
<@764342735732867072> sorry for the ping, im just wondering if you know
if i know what?
everything so far looks correct...
warm depot
everything so far looks correct...
like the last part is good?
when i change to the iterated integrals
tall ruin
like the last part is good?
yeah, why wouldn't it be?
you're just integrating the function with respect to the surface area
like you said you gottap lug in the parameterization but otherwise it looks good 💀
warm depot
ok thanks then, and yea i dont actually have to evaluate it
that would be hell
thanks though
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outer hare
You keep rolling a 6 sided die until you hit 3,4,5 consecutively. What is the probability it takes you odd rolls?
slim verge
If you in first try = 1/2
If you get in third try = (not in first not in second and in third ) = (1/2)^3
In fifth similarly= (1/2)^5
Similarly it will go to infinity
You need to add all these
So it is a sum of infinity GP
outer hare
OKOK wait
ops sorry for caps
mistake
okok wait so here is my logic so far
essancially, you either get it on the frist try
which means its odd
or the second try
even
and if its more than the first two you can just reset it
because its odd reguardless of if its 1, 3, 5
slim verge
I only add up when you get in the tries which are odd
outer hare
(1/6)^3
no worries ur good
So probability of getting it on the frist try would be (1/6)^3
then continuing lets say we got it on the second turn right
it would be (5/6)(1/6)^3
slim verge
I gtg right now
Some urgent task I had to do
I will get back to you in 30-35 minutes
I am sorry
outer hare
no worries
fast anvil
You keep rolling a 6 sided die until you hit 3,4,5 consecutively. What is the pr...
May we discuss it together?
I'm not a master of probability but I would like to find the answer with trials
Getting it consecutively on the first three turns would be (1/6)³
fast anvil
Hello
outer hare
I agree
and then for the second turn
it would be
5/6 times (1/6)^3
lets say the probability is odd
fast anvil
5/6 times (1/6)^3
However that's an even number of rolls
outer hare
and represent that as n
outer hare
However that's an even number of rolls
yup
With my logic, the probability of even would be (5/6) n
fast anvil
There are other considerations though if I'm not mistaken
As we need it consecutively
Let's say we get it in 4 rolls
It may be either in first 3 or the last 3
Won't it be 2 cases
outer hare
Its either odd or even tho
so there should only be 2 cases, and the probability of odd + even = 1
so even if you get it in 4 cases
thats 5/6 times the probability of odd
as you could have gotten it in 3 for odd
thats the only two we care about no?
fast anvil
We do and you would be correct that odd + even = 1 but these cases have further cases which we probably need to consider to calculate the probability
outer hare
what would be a different case
hmm
ok wait
what about this
Lets say it takes you 216 rolls on avg to reach this condition
fast anvil
For example if I ask you what's the probability of getting '3' consecutively three times if you roll the dice 4 times. What would be the probability of the event
outer hare
Within those 216 rolls, the probability of odd is (5/6)^2 (1/6)^3 + (5/6)^4 (1/6)^3 .....
and proabaility of even would be (5/6)^1 (1/6)^3 + (5/6)^3 (1/6)^3 .....
until 216 turns
does that make sense
fast anvil
It does but you're missing a key thing
If we say we roll the die 4 times and get 3,4,5 consecutively
outer hare
ok
fast anvil
It's not (5/6)(1/6)³ but 2(5/6)(1/6)³
Because there are two probable ways
3,4,5,x or x,3,4,5
outer hare
the game would end after so the final x would not count
outer hare
ok so probability of odd would be
fast anvil
(1/6)³+(5/6)²(1/6)³ +(5/6)⁴(1/6)³...
outer hare
((5/6)^2 + (5/6)^4 + (5/6)^6 .. (5/6)^212)(1/6)^3
fast anvil
Yes
outer hare
over all the total possibilities, ie
i think this would be just for odd tho
we dont need to continue for even because this should just be the answer no
fast anvil
It is the answer
fast anvil
((5/6)^2 + (5/6)^4 + (5/6)^6 .. (5/6)^212)(1/6)^3
This series will go indefinitely
If the die is rolled
outer hare
fast anvil
Indefinitely
fast anvil
They are used in probability quite alot
outer hare
makes sense
fast anvil
Sum of infinite series that is
outer hare
ans is 216/431
fast anvil
Let us try to find it
Sum of a geometric series has the formula
a(1 - r^n)/1 - r
a is the first term of the series
r is the common ratio of difference
In our case a = (5/6)²
and r = (5/6)² as well as it's multiplied after each number
n = ∞
r^n = (5/6)^∞
There's no absolute answer but we can take this as 0
Because as the power increases the fraction gets smaller and smaller to 0
So putting the values in the formula
[(5/6)²(1 - 0)] / [1 - (5/6)²]
pearl pondBOT
@outer hare Has your question been resolved?
fast anvil
May you elaborate
outer hare
check the video
fast anvil
Okay I will
slim verge
Just give me some minutes
I will solve all your queries
outer hare
ok
fast anvil
<@785148097533313085> we are still lost lmao
Fr well I'm trying to understand what they did and find the flaw in the explanation I formed in my mind but I cannot sadly
I'm hopeful y'all will figure it out
outer hare
nw
pearl pondBOT
outer hare
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outer hare
@slim verge any updates?
outer hare
no worries I was curious lol
slim verge
its an interesting one for sure
pearl pondBOT
@outer hare Has your question been resolved?
slim verge
Guys
My answer is coming out to be 646/863
outer hare
uh is that simplified?
slim verge
I will show you my solution
outer hare
Guys
My answer is coming out to be 646/863
its incorrect
slim verge
Yeah
I will show you my solution
Check if I made a silly mistake or some calculation error
Wait a minute
Guys you need to bear with my bad hand writing
outer hare
hmm ok let me take a look
no worries
I had a similar solution
but its aparently incorrect
slim verge
what?
slim verge
let me try another way then
i will get back to you in some minutes
pearl pondBOT
@outer hare Has your question been resolved?
slim verge
the mistake was that we also imcluded two more cases multiple times
these were when 3 and 4 came in 6k+5th and 6k+6 term
and also when we take 3 in 6kth term
our sol will be correct if we did that thing till 12 numbers
but we will obviously die that way
i will do that question now after some time
i will dm you when i gets it
is it fine by you ??
thnx
it was a good question
@outer hare
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hoary blade
help plz
hoary blade
i dont get how to do this
how do u get the 7pi/4?
and isnt root 2/2 the reference angle so to find the blue angle in standard position isnt it just 2pi- root 2/2?
midnight haven
why are you subtracting root(2)/2
hoary blade
to find angle in q4 dont u do 2pi minus reference angle
midnight haven
root(2)/2 is not an angle
hoary blade
wait i thought when u do sin of 5pi/4 u get the reference angle of it?
hoary blade
i thought x is standard position and y is reference angle
midnight haven
no
hoary blade
where u get pi/4 from
midnight haven
i dont get how to do this
hoary blade
wait i dont get why i am confused rn
i thought it was always x was standard position and y was reference angle
like sin of 45 and sin of 135 is the same cause they have same reference angle
ohhhh
wait i think ik what I did wrong
can i use the root 2 over 2 to get pi over 4
i think if i can do that then it would make sense
@midnight haven
midnight haven
yes
pearl pondBOT
@hoary blade Has your question been resolved?
viral moat
I know the answer is correct, but are the calculations correct?
smoky musk
I guess it's correct. Exponentiation is a continuous function after all.
You have to be careful if you're dealing with a discontinuous function, though.
pearl pondBOT
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torpid river
Hi
warm current
pearl pondBOT
@torpid river Has your question been resolved?
hazy dome
hello
hazy dome
i need help w something very confusing (for me)
so i need to find the distance of an object using the angle and height of the object itself
however what comes up in the calculator is very different to when i actually measured the distance itself
the angle is 77 degrees, height is 15 inches, and distance around 60 inch
i dont know if the error is with the solving or the actual measuring itself
<@&286206848099549185>
ember spear
,calc tan 77deg
jolly parrotBOT
The following error occured while calculating:
Error: Unexpected type of argument in function multiplyScalar (expected: number or Complex or BigNumber or bigint or Fraction or Unit or string or boolean, actual: function, index: 0)
ember spear
i think the angle may not be 77 degrees
hazy dome
😭 i think so too
my classmates convinced me it was 77 so
i do not know how to read this thing
ember spear
distance should be about 65 inches
hazy dome
so if i wanted to know the height it should be 65tan(77)?
hazy dome
how do i input cot?
ember spear
1/tan(77deg)
ember spear
ember spear
de nada
hazy dome
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red spire
I'm trying to solve this AMC10 problem via factoring, but I ran into 2 possible solutions
here is my work in process
2mn-15m-15n=0
4mn-30m-30n=0
4mn-30m-30n+225=225
(2m-15)(2n-15) = 225
after some testing
m=120,n=8 fulfills
m=20,n=12 also fulfills
the answer is 32, I do not know why
compact ridge
I'm trying to solve this AMC10 problem via factoring, but I ran into 2 possible ...
read the question, m is not a multiple of n
120 is a multiple of 8
sly plover
Yeah
compact ridge
so yeah 20 + 12 = 32 that's right
red spire
how did I just assume it wasnt....
sly plover
You should always verify whatever you get at the end
Cuz sometimes some answers don't work
red spire
yea, thank you lots, I think im gonna go back to 2nd grade math just to practice reading
sly plover
red spire
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red spire
This is a AMC10 question about arithmatic sequences
From its 15 terms and 3060 as sum, the middle term is 3060/15 = 204
I now work out all the values possible for a1, which not only have to be even but also have to fulfill (204-a1)mod14=0
since 204 is the eighth term, this just means d(common difference) will be a even integer.
now after I work out the numbers
(8, 22, 36, 50, 64, 78, 92, 106, 120, 134, 148, 162, 176, 190)
I caculate their first four terms to check for squares
red spire
8-36-64-92
true
22-48-74-100
true
36-60-84-108
false
50-72-94-116
false
64-84-104-124
true
78-96-114-132
false
92-108-124-140
false
106-120-134-148
false
120-132-144-156
true
134-144-154-164
true
148-156-164-172
false
162-168-174-180
false
176-180-184-188
false
190-192-194-196
true
8+22+64+120+134+190=538
Answer:538
I do not know where it went wrong
thanks in advance btw
I have been trying to solve this for the past 2 hours and anyhelp is appreciated!
supple knoll
The third one
pearl pondBOT
@red spire Has your question been resolved?
pearl pondBOT
supple knoll
