So then what do you have putting all of it together
#help-49
wet grail
That's pretty much it I think
Thank you
midnight plankBOT
Available help channel!
dark locust
hellooo guysss in order to do graphical method, and find the graph of a function
i need to have two limits to evaluate right??
For example:
lim as it approaches to 4
and lim as it approaches to -4
and then i can check if the limit exists or if its DNE
or is it okay if i only evaluate one? Like only lim as it approaches to 4?
midnight plankBOT
hellooo guysss in order to do graphical method, and find the graph of a function...
dark locust
the question is weird i know but our task is to create word problems so i have questions abt this haha
thank u guys
snow pumice
Not sure I understand the question. You mean that if you were given, for example arctan([x^5 - x^2]/6), how to go about graphing it? As in, you need the asympotes etc?
dark locust
Not sure I understand the question. You mean that if you were given, for example...
Waitwaitt the example would be 5x^2-3x+3
ive already found the limit as it approaches 4, which is 71
but im asking if i should give another limit to evaluate (for example -4) in order to find out if the limit exists or nott?
or is it completely fine if i only have positive four alone?
snow pumice
Waitwaitt the example would be 5x^2-3x+3
ive already found the limit as it appr...
Umm, the polynom has a limit everywhere, since it is continuous everywhere, so no, I'd say that there is absolutely no need to do any of that. Even with positive 4, there is not any real reason to do that
dark locust
Umm, the polynom has a limit everywhere, since it is continuous everywhere, so n...
ohh but i can still graph the positive four one right? with my answer?
btw thank you!
snow pumice
ohh but i can still graph the positive four one right? with my answer?
You can definitely use it as a point there, as in [4; 71], yes
dark locust
You can definitely use it as a point there, as in [4; 71], yes
thank you so muchhh!!!
snow pumice
npnp
midnight plankBOT
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fair elbow
can someone explain why we choose min of delta_1 and delta_2 instead of the maximum, specifically, would we not want the maximum such that |x-x_0| < delta, so we need the maximum for both to satisfy this?
midnight plankBOT
can someone explain why we choose min of delta_1 and delta_2 instead of the maxi...
@fair elbow Has your question been resolved?
fair elbow
<@&286206848099549185>
spring wave
basically you want both f(x) and g(x) to be within range
midnight plankBOT
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Available help channel!
twilit field
midnight plankBOT
dawn dagger
status
twilit field
I was thinking of stating by factorising the curve
dawn dagger
factorising the curve?
grand pondBOT
What a wonderful world!
dawn dagger
seems right
twilit field
Then I start with 2x+y = u, and x-y=t
u=4, y=7, t=2, t=-1 become teh limits
so $\int_{4}^{7} \int_{-1}^{2} ut du Jdt$
?
grand pondBOT
What a wonderful world!
twilit field
how did you come up with that sub?
wdym
dawn dagger
was it suggested or you came up with that yourself?
twilit field
I came up with it based on experience
midnight plankBOT
midnight plankBOT
Available help channel!
last slate
so [
N = (D < 1.5) \times (A \in [30^\circ, 45^\circ]) \times (T < 1) \times (P \geq 8)
]
midnight plankBOT
so \[
N = (D < 1.5) \times (A \in [30^\circ, 45^\circ]) \times (T < 1) \times (P...
grand pondBOT
𝕺𝓷𝓮_99x 💥
drifting birch
? what
last slate
[
N = 1 \times 1 \times 0 \times 1 = 0
]
grand pondBOT
𝕺𝓷𝓮_99x 💥
heady plume
3x = 🐟 + 🍎 + 🍰
last slate
$c_1(x-1) +c_2(x-1)^2+c_3(x-1)^3 = b_1x^3+b_2x^2+b_3x^2+b_4x+b_5$
grand pondBOT
𝕺𝓷𝓮_99x 💥
midnight plankBOT
@last slate Has your question been resolved?
radiant roost
midnight plankBOT
next rover
intuitively there should be like 4 things you can do
left or right or a or b
maybe i'm missing other
yeah i guess there's more
radiant roost
left is the sixth table and right is the eighth
a is the first and i think b is isomorphic to that
next rover
max and min
so at least 6
trying to think of other
like "bx = a, ax = x" is that a new one
radiant roost
<@&268886789983436800>
graceful drum
SCAM
radiant roost
i think max and min are isomorphic to the fifth table
radiant roost
like "bx = a, ax = x" is that a new one
yeah that's the third table, it's new i think
next rover
i don't get it
like if you relabel 5th, it's not the same as itself
you get 3 b and one a
i can't even name an example where i see it's isomorphic tbh
well 5th stays itself okay
radiant roost
but if you have a table for max and a table for min, and you switch the labels in one of the tables, it will turn into the other table
next rover
ah
i'm lost
ok you didn't list b
so that makes sense
no special letters yes special sides
midnight plankBOT
@radiant roost Has your question been resolved?
next rover
here is min, max and "opposite of min"
maybe two of them are equivalent but all three?
ok sorry i'll give up
storm spindle
I think 10 should be right. Looking through each of them, there seem to be 6 for which inversion results in a different structure
radiant roost
thanks 🙏
storm spindle
how is 3 and 4 different if aaaa ≠ bbbb
There’s 2 isomorphisms right? Inversion and identity
Neither of them are isomorphisms between 3 and 4
next rover
10 is right i googled it
storm spindle
3 is isomorphic to the opposite of 4 and vice versa, I think
next rover
why not have
ba
ab
storm spindle
Isomorphic to
ab
ba
by inverse isomorphism
next rover
nvm
storm spindle
I think the intuitive idea is to invert every result and then switch upper right with lower left and upper left with lower right
If it stays the same then the equivalence class has only one element
If not then it has two
next rover
thanks
oh it's like
1 nothing
2 opposite when equal
3 right when different
4 left when different
5 same when equal
6−9 left right and opposites
10 "is equal?"
ionic magnet
.close
midnight plankBOT
prime hornet
ionic magnet
oops
The base of a right parallelepiped is a rhombus with side 2. The angle between the planes of the side faces is 60°. The larger diagonal:
the parallelepiped makes an angle of 45° with the plane of the base. Calculate the volume of the parallelepiped.
guys help me
i dont understand
:(((
dawn dagger
maybe reopen your channel first?
ionic magnet
maybe reopen your channel first?
how
dawn dagger
.
midnight plankBOT
Available help channel!
rose mesa
midnight plankBOT
rose mesa
i do not know where to begin, i thought i did the correct thing doing 50% = 100(.975)^t and solving for t
but that was incorrect
rose mesa
50/100 = (.975)^t
ln(1/2) = ln(.975)^t
ln(1/2)/ln(.975) = t
28.5~ was my original answer
rose mesa
i tried 28 and 29
robust isle
or maybe 3 correct decimals idk
rose mesa
i tried that as well
robust isle
idk what your software is
rose mesa
webwork
midnight plankBOT
@rose mesa Has your question been resolved?
rose mesa
<@&286206848099549185>
midnight plankBOT
@rose mesa Has your question been resolved?
rose mesa
<@&286206848099549185>
midnight plankBOT
@rose mesa Has your question been resolved?
zinc leaf
midnight plankBOT
zinc leaf
using x=6sintheta
i did it but for some reason everything cancels out and i just get 1?? but the answer is pi/6
rain wasp
show your work?
zinc leaf
uhh like basically dx/dtheta is 6costheta and then
u sub in x
this
and then u factor out the 36
and bring it outside of the square root so its 6root 1-sin^2x
and doesnt that equal 6cosx...
silent elbow
I think you forgot to change integration boundries when you did the substitution
dusty portal
and doesnt that equal 6cosx...
Yes, it does.
zinc leaf
oh yeah oops i forgot that but like doesnt the bulk of it just cancel out to 1??
dusty portal
It's meant to cancel out.
dusty portal
$\int\frac{1}{\sqrt{36-x^2}}dx=\arcsin(\frac{x}{6})+C$.
grand pondBOT
;(
dusty portal
but how do i get that from like
Well, it's just the antiderivative. It's demonstrative as to why.
Try to solve for the antiderivative first.
dusty portal
Yeah.
zinc leaf
.
dusty portal
Again, change the bounds of integration.
midnight plankBOT
silent elbow
lol
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Available help channel!
lucid rivet
Solve 24
sleek cloud
I cannot see what are a and b labelled as
midnight plankBOT
@lucid rivet Has your question been resolved?
lucid rivet
.close
midnight plankBOT
oblique gyro
I’m so close i just keep on getting -sinx is there somewhere where i could’ve gotten rid of a sign so it gives me sinx not -sinx/cosx
midnight plankBOT
Available help channel!
sharp wave
can someone help im pretty sure we have to complete the squares but how do i start?
midnight plankBOT
can someone help im pretty sure we have to complete the squares but how do i sta...
white gate
can someone help im pretty sure we have to complete the squares but how do i sta...
expand the right-hand side
sharp wave
no shit bruh
old rampart
ok so do it
old rampart
can you send your work
sharp wave
i havent done much tbh i just expanded and took them all to one side thats where i need help
white gate
i did it after taking all the terms to the rhs how do i proceed
observe from the LHS: a^2 + (3b)^2 + (5c)^2 = 15bc + 5ac + 3ab
sharp wave
yes
white gate
hence, substitute x = 3b and y = 5c
white gate
no?
sharp wave
if youre trying to do (a + 3b+ 5c)^2?
white gate
15bc + 5ac + 3ab = (5b)(3c) + a(5c) + a(3b)
then it becomes a^2 + x^2 + y^2 = ax + ay + xy
im sure what you can do now
white gate
yea
midnight plankBOT
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Available help channel!
royal vigil
help again
midnight plankBOT
help again
royal vigil
if A, B and C are angles of a triangle
$\cos A+\cos B+\cos C-1=4\sin\left(\frac{A}{2}\right)\sin\left(\frac{B}{2}\right)\sin\left(\frac{C}{2}\right)$
grand pondBOT
♱
royal vigil
prove this
visual tiger
prove this
you know linearization formulas for sin(x)sin(y)? sin(x)cos(y)? cos(x)cos(y)?
royal vigil
you know linearization formulas for sin(x)sin(y)? sin(x)cos(y)? cos(x)cos(y)?
no?
im supposed to use factor formulae here i just have no clue how
visual tiger
im supposed to use factor formulae here i just have no clue how
ok, so can you tell me what they are so we can use them?
royal vigil
**♱**
cosA + cosB = 2cos(A + B/2)cos(A - B/2) ???
like idk what im even supposed to be grouping
visual tiger
we can start with that
visual tiger
like I'm not against trying to use those
buoyant yoke
cosA + cosB = 2cos(A + B/2)cos(A - B/2) ???
is that (a+b)/2 or a+(b/2)
royal vigil
is that (a+b)/2 or a+(b/2)
(a + b)/2
visual tiger
you see those formulae?
look at the RHS
4sin(A/2)sin(B/2)sin(C/2)
let's take 2sin(A/2)sin(B/2) for example
visual tiger
and now look at the RHS of those formulae
royal vigil
Dude ik the second set
visual tiger
let's take 2sin(A/2)sin(B/2) for example
compare them with this
royal vigil
its like
2sinAsinB = blahlah
But idk how u could even
Like ok ur gonna do the first pair
visual tiger
Dude ik the second set
so you do know linearization formula
royal vigil
and then sinC/2 is left alone
when i searched linearization on google it showed me calculus stuff sooo
royal vigil
and then sinC/2 is left alone
But like i said
sinC/2 ends up alone
say u have
(2sinA/2sinB/2)(2sinC/2)
second term doesn't have a pair
u can't use a formula on it
visual tiger
u can't use a formula on it
so don't use a formula yet for the second term
and wait until you apply product formula on the first
so
apply formula for 2sinA/2sinB/2
what do you get?
royal vigil
cos(A - B)/2) - cos((A + B)/2)
visual tiger
ok
so we now have
$\left(\cos\left(\frac{A-B}{2}\right)-\cos\left(\frac{A+B}{2}\right)\right)\left(2\sin\left(\frac{C}{2}\right)\right)$
royal vigil
2sinC/2
grand pondBOT
rafilou is not not born in 2003
royal vigil
idk
hold on
let me try
(cosA + cosB) / 2cos(A + B)/2) - (cosA + cosB) / (2cos(A - B)/2)
idk
it doesn't look like a solution
$\left(\cos A+\cos B\right)\left(2\cos\left(\frac{\left(A-B\right)}{2}\right)\right)-\left(\cos A-\cos B\right)\left(2\cos\left(\frac{\left(A+B\right)}{2}\right)\right)$
grand pondBOT
♱
royal vigil
its too complicated lol it does not make sense
visual tiger
**rafilou is not not born in 2003**
I think instead
you should expand the product
(x+y)*z
royal vigil
y tho
visual tiger
to linearize again?
royal vigil
o
wait
i see it
well
kinda
idk
nope
still nothing
$\left(\sin\left(\frac{\left(C+A-B\right)}{2}\right)+\sin\left(\frac{\left(C-A+B\right)}{2}\right)-\sin\left(\frac{\left(A+B+C\right)}{2}\right)+\sin\left(\frac{\left(A+B-C\right)}{2}\right)\right)$
grand pondBOT
♱
royal vigil
This is what u end up w
which makes no sense
its 4 terms which idk how to convert to cosA + cosB + cosC - 1
this is what chatgpt does which doesn't seem too bad
visual tiger
this is what chatgpt does which doesn't seem too bad
don't trust chatGPT
visual tiger
$\left(\sin\left(\frac{\left(C+A-B\right)}{2}\right)+\sin\left(\frac{\left(C-A+B...
when you get to this
remember what A+B+C =
visual tiger
and reexpress each term as sin or cos of a single angle
royal vigil
and reexpress each term as sin or cos of a single angle
how would u do this for the res tho
visual tiger
it doesn't hurt using A+B+C = 180 again
royal vigil
one of them is 180 and one of them isnt??
royal vigil
wdym
royal vigil
+2C
y wont my message send lord help me
+2C.
It wasn;t meant to be I;m not meant to solve this
nvm yes it was
visual tiger
yes it's +2C
so
A+B-C = A+B+C - 2C
now use that
and do the same with the other terms
visual tiger
A+B-C = A+B+C - 2C
you can rewrite A+B-C as this
visual tiger
yes
royal vigil
how does that change anything
visual tiger
that is sin((A+B-C)/2)
visual tiger
so we keep it
royal vigil
wait
royal vigil
sin((A + B + C - 2C)/2)
sin((A + B + C)/2 - 4C/2))
sin(90 - 2C)
cos(2C)
thats still 2c though
visual tiger
idk how you got 4C even
royal vigil
whered the
Oh
woops
Ohhh
i see the pattern
so u js do that for the rest like
C + A - B = A + B + C - 2B
cosB
manic bison
How to apply combinatorics here?
midnight plankBOT
How to apply combinatorics here?
manic bison
Huh?
modest star
treat x1,x2,x3,x4 as 4 groups
manic bison
Okay
modest star
G1 | G2 | G3 | G4
note how 3 barriers is enough to distinguish 4 groups
if we take a smaller example, say x_1 + x_2 + x_3 = 7, i want to count all ordered triplets
manic bison
2 barriers?
modest star
yes!
manic bison
Okay so what to do next?
modest star
if we take a smaller example, say x_1 + x_2 + x_3 = 7, i want to count all order...
a possible configuration is
••|•||••••
manic bison
ohhhh
modest star
then, notice that all you need to do is find the number of ways to arrange these objects
manic bison
Number of permutations?
modest star
yes
manic bison
Could you explain with an example
modest star
sure
lets take a small example so we can manually enumerate all possibliites
x_1 + x_2 = 3
one barrier
|•••
•|••
••|•
•••|
modest star
yes, or you can think of it as permuting AAAB
there are 4! ways to do this
but we dont want to overcount the permutations where the A's switch places
manic bison
4! / 3!
modest star
yes
manic bison
yes, or you can think of it as permuting AAAB
AAAB because 3 balls and 1 barrier right I think I get it
modest star
yes
the original question is a bit different since it says we need to deal with positive odd integer
manic bison
Yeah
modest star
the reg stars and bars thing accounted for nonnegative integers
so find a way to transform positive odd -> nonnegative
manic bison
maybe assume 2n-1?
manic bison
.close
midnight plankBOT
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Available help channel!
twilit field
midnight plankBOT
twilit field
I tried using $\abs{r(t)} = \sqrt{r(t) \cdot r(t)}$
grand pondBOT
What a wonderful world it is !
twilit field
But to no avail
robust isle
what happened ?
white gate
Are you sure, that works pretty fine
twilit field
Like that gave me $\frac{1}{2 \sqrt{ r(t) \cdot r(t)}} (r(t) \cdot r(t))'$
grand pondBOT
What a wonderful world it is !
white gate
|x| = (x²)^(1/2)
Use power rule:
y' = 1/2 (x²)^(-1/2) * 2x
robust isle
yeah and the derivative of that dot prod is exactly 2 r(t) . r'(t)
last arch
Nah nvm that's more wrong than I thought
modern sapphire
break into cases, and the first half is just sgn(r(t))
last arch
Should give you $\frac{2 \cdot r(t) \cdot r'(t) }{2 \sqrt{r(t) \cdot r(t)}}$
robust isle
the product rule is actually true for the dot product also
grand pondBOT
denzio321
robust isle
$\dv{}{t} \left(f(t) \cdot g(t)\right) = f(t) \cdot \dv{g}{t} + \dv{f}{t} \cdot g(t)$
grand pondBOT
aPlatypus
midnight plankBOT
midnight plankBOT
Available help channel!
formal shore
I have trouble understanding how these 2 equations work.
The question I got asked was, show that cos(-60 deg) = cos(660 deg). How could I prove that with these equations?
midnight plankBOT
I have trouble understanding how these 2 equations work.
The question I got ask...
kindred dagger
I have trouble understanding how these 2 equations work.
The question I got ask...
Whats the difference between -60 and 660
formal shore
600
sharp wave
are you sure
formal shore
or 720
kindred dagger
or 720
✅
Its also good to know know that $\sin$ and $\cos$ have a period of $360^\circ$.
grand pondBOT
King Leo
formal shore
So now I've found the difference between them, how could I proceed with proving that they're the same?
because the only way I can currently 'prove' it
kindred dagger
**King Leo**
Do you understand this @formal shore
formal shore
I like to believe i do, the only way I could describe is if alpha here is 60 degrees, and we were to go 360 deg around, we'd end up in the same spot
umbral mesa
-60 % 360 == 660 % 360
kindred dagger
I like to believe i do, the only way I could describe is if alpha here is 60 deg...
✅
formal shore
Do that 2 times and you get 660 degrees
kindred dagger
Do that 2 times and you get 660 degrees
Theres youre proof
formal shore
But how could I mathematically write this down?
Ah alright
So it doesnt even really need to be done with an equation?
kindred dagger
But how could I mathematically write this down?
So how many times do you rotate 360 degrees?
formal shore
2x
umbral mesa
Cosine has a period of 360 degrees so I’ve always just modulo it
kindred dagger
So in your equation $\cos(v + n \cdot 360^\circ) = \cos(x)$, what variable is $2$?
grand pondBOT
King Leo
formal shore
n
kindred dagger
$$\cos(v + 2 \cdot 360^\circ) = \cos(v)$$
grand pondBOT
King Leo
kindred dagger
And what is v
umbral mesa
And -60 and 660 modulos are the same
formal shore
Ah alright
So
I'm not sure if this is allowed, but we can take out the core which we can put as
660 = -60 + n * 360, and then simply solve for n
kindred dagger
I'm not sure if this is allowed, but we can take out the core which we can put a...
Yes, thats what youre supposed to do
And if you find that n is an integer, then you can say the cosine of both angles are equal
dusty aspen
midnight plankBOT
dusty aspen
How do I finish this?
kindred dagger
No l'hopital?
white gate
i mean he's trying
sharp wave
oops
dusty aspen
this is good start or no?
white gate
The (x+2) is kinda hurting my eyes, so try taking ln both sides
The thing in bracket is also obviously simplify-able
white gate
we must have (1+1/x)^x to get e
that is not necessarily a way to get e
You can take ln both sides and evaluate an entirely new limit
which i think might be easier
dusty aspen
I did all like this and feel better continuing doing it the old way 🙂
I know the procedure roughly, just stuck
white gate
RHS might be easier to do now ig
dusty aspen
How do I do it with e
white gate
you just need to evaluate the RHS limit then e^ everything
RHS approaches -2, so L -> e^(-2)
(does that count as an usage of e?)
white gate
why do you have to be so hesitant about simplifying the thing in the bracket
all can be divided by 2
wouldn't that make the calculation easier
anyways if doing it your way then:
white gate
No?
white gate
why do you have to be so hesitant about simplifying the thing in the bracket
^
I have emphasized that so many times yet you treat it like its nothing
dusty aspen
sorry, I am brain-fried also, just had an exam
white gate
oof
white gate
yeah
dusty aspen
.solved
vocal mauve
$(-1) * (-1)^2 * (-1)^3 * (-1)^4 * .... * (-1)^{2019}$
midnight plankBOT
$(-1) * (-1)^2 * (-1)^3 * (-1)^4 * .... * (-1)^{2019}$
grand pondBOT
Simon James B
vocal mauve
idk how to solve this or what to do i never did problems like these before
i need guidance
i don't know how to solve problems with ... at all
runic hamlet
cut off the ... and everything after that
what happens if you only have the first four terms
vocal mauve
what happens if you only have the first four terms
-1 * 1 * -1 * 1 = 1
vocal mauve
-1
runic hamlet
what if you include the (-1)^6 ?
runic hamlet
not quite sure what you mean
runic hamlet
no
vocal mauve
ok. if you include the next one
1
then ^7 gives us -1
^8 gives us 1 again
and so on
runic hamlet
can you write a table?
number of terms | result
vocal mauve
can you write a table?
number of terms | result
how do i write a table on discord?
or not on discord?
runic hamlet
just write the rows as individual messages
dont worry too much about the formatting
vocal mauve
ok
runic hamlet
or shift-enter for newline without sending it
vocal mauve
Power | result
1 | -1
2 | 1
3 | -1
4 | 1
5 | -1
6 | 1
7| -1
8| 1
9 | -1
10 |1
runic hamlet
no
runic hamlet
if you have two terms, what is the result
youre trying to jump too fast at guessing the pattern
vocal mauve
(-1)(-1)^2 = -1 * 1 = -1
runic hamlet
yes
runic hamlet
yes
vocal mauve
(-1)(-1)^2 (-1)^3 (-1)^4 (-1)^5 = -1 * 1 * -1 * 1 * -1 = -1?
(-1)(-1)^2 (-1)^3 (-1)^4 (-1)^5 (-1)^6 = -1 * 1 * -1 * 1 * -1 * 1 = -1 ?
(-1)(-1)^2 (-1)^3 (-1)^4 (-1)^5 (-1)^6 (-1)^7 = -1 * 1 * -1 * 1 * -1 * 1 * -1 = 1
runic hamlet
yes
so with each new odd exponent, what happens?
with each new even exponent, what happens?
runic hamlet
no
runic hamlet
(-1)(-1)^2 (-1)^3 (-1)^4 (-1)^5 = -1 * 1 * -1 * 1 * -1 = -1?
.
write the table again
vocal mauve
Type | result
even | -1
odd | 1
even |1
odd | -1
even |-1
odd|-1
even | 1
i don't understand this at all srry
runic hamlet
thats not the table headings I gave you
and the second to last row is wrong
1 | -1
2 | -1
3 | 1
4 | 1
5 | -1
6 | -1
7 | 1
8 | 1
9 | -1
10 | -1
11 | 1
vocal mauve
the firt number means the number of terms right?
runic hamlet
yes
runic hamlet
what is the pattern?
vocal mauve
2 negatives 2 positives
runic hamlet
so with each new odd exponent, what happens?
with each new even exponent, what h...
what about this?
vocal mauve
let me think
first odd exponent gave us -1
first even exponent gave us (-1)(-1)^2 = -1 * 1 = -1 still -1
that means the next odd exponent will give us 2 negatives and the next even exponent will give us 2 positives? maybe i am wrong
runic hamlet
wdym give 2 negatives
vocal mauve
like the next 2 exponenets will be negative
^1 = -1
^2 = -1
^1 gave us 2 negatives
^3 = 1
^4 = 1
the first even gave us 2 positives
runic hamlet
but the 2 gives you the -1
vocal mauve
but the 2 gives you the -1
ok then can u help me
this confuses me so badly
don't tell me i gotta do this until 2019 cuz imma explode
runic hamlet
so, the first term gives us the -1
then the next term doesnt change it, still -1
the third term changes it to 1
the fourth term doesnt change it, still 1
the fifth term changes it to -1
the next one doesnt change it, still -1
then change to 1 again
so at each odd exponent we switch
vocal mauve
yes
runic hamlet
and at each even exponent we stay the same
white gate
I mean the whole (-1)(-1) doesnt matter since there is always odd (-1) if the exponent is odd
runic hamlet
we need to count how often we switched
aka, how many odd numbers we have encountered
white gate
aka, how many odd numbers we have encountered
Oh yeah i made a mistake 
vocal mauve
can i see the formula-
i doubt in my exam i will take 1 hour to check for the pattern-
runic hamlet
n | number of odd numbers encountered
1 | 1
3 | 2
5 | 3
can you guess a formula from that?
you need to learn do analyse patterns like this. there is no use in me telling you the formula
vocal mauve
let me think
runic hamlet
if you cant guess it yet then continue the table
white gate
wait am i missing something
Cant u just do sum of all the powers
runic hamlet
wait am i missing something
Cant u just do sum of all the powers
thats another way, yes
vocal mauve
wait am i missing something
Cant u just do sum of all the powers
don't know it
runic hamlet
forget that sum idea for now
vocal mauve
fine
runic hamlet
n | number of odd numbers encountered
1 | 1
3 | 2
5 | 3
continue this table
runic hamlet
yes
you can also include the rows with the even numbers but I think that would be distracting
vocal mauve
i need to think of a common rule
but idk how to formulate it for the formula
nope no idea
runic hamlet
the left number is always nearly twice the right number
vocal mauve
nearly
runic hamlet
in fact, left = 2*right-1
vocal mauve
2 * even - 1
?
but no
yes actually nvm
but how does this help to figure it out for 2019
runic hamlet
adding 1 on both sides gives
2020 = 2*right
dividing by 2 on both sides gives
1010 = right
so the number on the right is 1010
2019 | 1010
runic hamlet
$(-1)\cdot(-1)^2\cdot(-1)^3\cdot(-1)^4\cdots(-1)^{2019} = (-1)^{1+2+3+4+\ldots+2019}$
grand pondBOT
Denascite
runic hamlet
by exponent laws
vocal mauve
yep
vocal mauve
(n*n+1)/2?
runic hamlet
yes
vocal mauve
gauss formula?
vocal mauve
this one is much easier
i don't think i will ever understand ... problems
I have lots more problems like this and i will never get them right
ty
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gaunt jetty
Let $G$ be a finitely generated group such that every normal subgroup of $G$ is either trivial or finite index. Prove that $G$ is either finite or simple.
midnight plankBOT
Let $G$ be a finitely generated group such that every normal subgroup of $G$ is ...
grand pondBOT
Aero
gaunt jetty
Just a quick confirmation i need about this, but if G is not simple then there exists a unique maximal normal subgroup M such that G/M is simple and finite, is that correct?
grizzled coyote
@smoky coral
gaunt jetty
I think the structure must eventually collapse to either a unique maximal normal subgroup or a simple quotient no matter
midnight plankBOT
@gaunt jetty Has your question been resolved?
hard umbra
Just a quick confirmation i need about this, but if G is not simple then there e...
unique seems sus
gaunt jetty
unique seems sus
Well like
u r gonna have an infinite chain of infinite normal subgroups right
hard umbra
you need that G f.g. + M f.i. => M f.g.
gaunt jetty
so like
Ok wait i think im a bit unconvinced still
so lets assume G has two distinct normal subgroups M_1 and M_2 right
their intersection must also be normal in G
but isnt M_1 \cap M_2 a proper normal subgroup of each M_i? so like u contradict the fact that they are maximal unless they're nonunique
hard umbra
how does that contradict maximal
gaunt jetty
<@&268886789983436800> lmao
hard umbra
ty hayley
gaunt jetty
how does that contradict maximal
ok yeah u r right
i get it now dw
ty boss
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karmic trench
is a = 1.5
midnight plankBOT
is a = 1.5
karmic trench
since r is max when sin pheta is -1
which makes r = 4 +a
and 5.5 = 4 + a
a = 1.5
or am i tweaking
<@&286206848099549185>
rigid zenith
Looks correct
rigid zenith
oh shruber doobers
karmic trench
@rigid zenith i assume i just sub the equivlanet of 5cos3pheta + cos5pheta
rigid zenith
wait which one r u doing
rigid zenith
Yeah honestly idk 😭 it’d take me a while to figure this out
karmic trench
rigid zenith
Also how in the world do you show such a thing
karmic trench
have u learnt de moivres theorem
rigid zenith
Nope not yet
I kinda skipped precalc 😢
Might wanna go back to that in the near future
karmic trench
well then you probably havent learnt about expressing sin and cos in terms of cosnx or sinnx
it has you scratching your head a lot
rigid zenith
well then you probably havent learnt about expressing sin and cos in terms of co...
Well the theorem looks familiar
But idk
I can’t really help you out confidently with this one
Sorry 😞
karmic trench
but maths wouldnt be interesting if it was not difficult
no prob
<@&286206848099549185>
midnight plankBOT
@karmic trench Has your question been resolved?
midnight plankBOT
@karmic trench Has your question been resolved?
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@karmic trench Has your question been resolved?
vocal briar
does this make sense?
midnight plankBOT
does this make sense?
vocal briar
i cant help but feel like its totally wrong
i was calculating the surface area of a banana leaf
and I did that by uploading the pic to geogebra and creating a couple points around the edge of the photosynthetic region of the leaf and calculated from the points the equations of the upper and lower functions and found area by subtracting the two areas
and then i tried to apply a conversion factor but is 6400cm^2 a reasonable number?
fallow scarab
does this make sense?
Where's the question
vocal briar
Where's the question
js wondering if it makes sense
i dont have a lot of experience with this
fallow scarab
can't tell without the question
vocal briar
oh the research question was to determine if larger leaf surface area was correlated with a larger tree height
so like to determine if trees have bigger leaves so they can photosynthesize more and grow taller than other trees
like as an adaptation
if thats what you mean by question
midnight plankBOT
@vocal briar Has your question been resolved?
midnight plankBOT
@vocal briar Has your question been resolved?
midnight plankBOT
@vocal briar Has your question been resolved?
midnight plankBOT
@vocal briar Has your question been resolved?
latent elk
Do a P test then
latent elk
so like to determine if trees have bigger leaves so they can photosynthesize mor...
You just collect as much data as possible
Then do a P test to determine whether to accept or reject the null hypothesis
@vocal briar
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remote halo
quick question here shall i make two transition graph for each process ? i have posted my attmept to sketsh the system
midnight plankBOT
quick question here shall i make two transition graph for each process ? i have ...
@remote halo Has your question been resolved?
midnight plankBOT
@remote halo Has your question been resolved?
remote halo
<@&286206848099549185>
i wanna also calacute the number of reachble states
i have calacuted the number of states for each comp shall i add or multiply them ?
any hint ?
thin nova
midnight plankBOT
@remote halo Has your question been resolved?
midnight plankBOT
@remote halo Has your question been resolved?
midnight plankBOT
@remote halo Has your question been resolved?
last slate
quick question here shall i make two transition graph for each process ? i have ...
Yeah you should
remote halo
Yeah you should
so for each component one transition graph fo you know if i have to connect them all
last slate
so for each component one transition graph fo you know if i have to connect them...
Yes, each component should have its own transition graph to represent their behavior
Then you connect them to a global transition graph using the shared events
noble cedar
hiii nice meet you im newer here xd i could make a question this is like my frist time in discord, i want to make a proyect with mathematics, the unific of theorems xd i will like to said so many theorems and use togheter for have an analysis more specific, is possible???
remote halo
i wanna also to formally justify the ack1 transition in addition one tau transition
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mint ravine
Can someone please help me on this question:
midnight plankBOT
Can someone please help me on this question:
mint ravine
I don't how to get started because idk how I'm supposed to draw it out
mint ravine
Yes
brisk iris
What is it ?
mint ravine
$\pi \cdot r^2 \cdot \frac {h}{3}$
grand pondBOT
RamenNoodleMan21
brisk iris
Nice
Now let's focus on the base of radius r ...
Can you tell me anything about that base ?
What information do we know about it ?
brisk iris
so radius is 7
brisk iris
side length of triangle is 14
Side of triangle is 14 ...
So what does the side of a triangle become in your cone
mint ravine
So what does the side of a triangle become in your cone
slant height?
mint ravine
the equilateral triangle was revolved about an altitude to make the cone
so the base of the triangle and the base of the cone is equivalent
brisk iris
brisk iris
so the base of the triangle and the base of the cone is equivalent
What can you derive from that
can you find the radius ?
mint ravine
two times the right triangle makes our equilateral triangle, right?
brisk iris
two times the right triangle makes our equilateral triangle, right?
No
Look at the base
we're not thinking about the height yet
Can you find a formula for r ? the radius of the base
the circumference of your base is equal to one side of the triangle. Can you see it ?
dusty portal
so radius is 7
Good.
dusty portal
the circumference of your base is equal to one side of the triangle. Can you see...
Hm?
mint ravine
we can find h if we know radius = 7 using the formula
brisk iris
Look at the little circle in the base. That used to be a triangle side
dusty portal
we can find h if we know radius = 7 using the formula
Not necessarily, since we need to know the volume.
brisk iris
I know, but if you wan tot know the volume, you need to figure out the radius of the base AND the height
dusty portal
Since you already asserted that one side length will be the slant height, what can we do to find the height?
brisk iris
Dude
mint ravine
Since you already asserted that one side length will be the slant height, what c...
pythagorean theorem?
dusty portal
pythagorean theorem?
Good.
brisk iris
The radius is NOT 7
brisk iris
Your statement about the circumference did not make sense.
What ??
brisk iris
Your statement about the circumference did not make sense.
How do you figure out the radius ?
dusty portal
How do you figure out the radius ?
It’s half of the side length of the triangle. It’s rotated about an altitude.
The circle will have radius 7. Read the problem again.
Do not send server invites.
brisk iris
It’s half of the side length of the triangle. It’s rotated *about an altitude*.
I read it and I'm positive
mint ravine
Since you already asserted that one side length will be the slant height, what c...
height is square root of 147
fallow scarab
<@&268886789983436800> spam
dusty portal
<@&268886789983436800> If it’s not supposed to be pingable, sorry.
brisk iris
2Pir = 14
r = 7/Pi
dusty portal
height is square root of 147
Show your calculation.
brisk iris
It’s half of the side length of the triangle. It’s rotated *about an altitude*.
This is wrong. Again check how the cone is formed
mint ravine
take the square root and you can root 147
dusty portal
take the square root and you can root 147
Good.
dusty portal
This is wrong. Again check how the cone is formed
Just wait for another helper to come.
Or, @mint ravine , how do you interpret it?
mint ravine
I just imagined that the side lengths of the triangle and the cone stayed constant and equivalent throughout the entire process of being revolved about the altitude
I just sort of imagined the triangle being like rotated in a 360 degree to form a cone
dusty portal
Which is what I thought as well.
I don’t know how else this could be interpreted, really.
Anyways, if you want to continue with my method and see if it’s right, go ahead.
mint ravine
ok!
dusty portal
Your radius and height are correct; all you have to do is plug it in now.
midnight plankBOT
dusty portal
thanks for helping
👍
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faint tree
hello, can someone explain to me why this set of choices is not correct?
midnight plankBOT
hello, can someone explain to me why this set of choices is not correct?
faint tree
the answers i chose either have zero volume in R^2 or they are not part of the event space Σ
here's the definition im using
cobalt nest
hello, can someone explain to me why this set of choices is not correct?
The choices are incorrect?
faint tree
yeah this is apparently incorrect
cobalt nest
which one
ancient ridge
Is C true the way you have it set up?
cobalt nest
Omega is the square
faint tree
if it's outside the square then it's not in the event space right?
cobalt nest
apparently
faint tree
so i thought the probability should just be 0
ancient ridge
I'm asking if a vector outside of the square is sigma measurable, of if your definitions just by default assign it a probability of zero
*or if
cobalt nest
I'm asking if a vector outside of the square is sigma measurable, of if your def...
It should be by default of probability zero
$1=P(\omega) = 1 - P(\omega^c)$
grand pondBOT
Goëtia
faint tree
actually if it's outside the square it is in Σ because Σ contains the empty set
cobalt nest
but whats the probability
faint tree
i dont know