Maybe discord counted that as something I’m still typing
#help-0
deep field
visual fjord
x^2 + 4y^2 = 40
xy = 6
how do I find the value of (x + 2y)^2 ?
rigid smelt
Can you expand (x+2y)^2 for me?
sullen nova
@visual fjord Expand
green urchin
elfin snow
e x p a n d
proud burrow
@visual fjord it's simple just expand (x+y) ^2 then you will get answer
sullen nova
@visual fjord Where are you at?
eternal spindle
the notation {a} means the fractional part of a
alpine sable
Dream what is the whole problem
visual fjord
nevermind i got it
the answer is apparently 64 because there was a formula that i never knew existed
glass lichen
nevermind i got it
the answer is apparently 64 because there was a formula that...
your question was just expanding the brackets. .
visual fjord
yes and substitution was involved
glass lichen
Oh no, not subbing in stuff
eternal spindle
bruh
nvm wait
{a} = a - floor of a
floor a means the greatest integer smaller than a
glass lichen
$a=\floor{a}+{a}, a\in\mathbb{R}^+$
ocean sealBOT
Mosh
eternal spindle
Pls anybody help me. What is {(2x+3x-9y)-7z}
what is the context of this?
hybrid ridge
what is the context of this?
It's just a basic question
I mean I wanna plus plsu and minus it
alpine sable
Add 2x and 3x
eternal spindle
ya
hybrid ridge
{(2x+3x-9y)-7z}
alpine sable
You get 5x - 9y - 7z
alpine sable
Yw
silent raft
this some beta ass shit but can someone explain im in fucking 10th grade and i dont remember this shit from year 8 😭
manic quail
this some beta ass shit but can someone explain im in fucking 10th grade and i d...
Do you know what a denominator is?
silent raft
yeah ofc
sweet mural
14*9
silent raft
i just forgot how to work it out
manic quail
multiplying the denominators (14*9) always gives you a "common" denominator
It isn't necessarily the smallest though.
sweet mural
you need to find least common denominator in this case it's their multiplication
so for the first one you will do 14*9 + 2 you can figure out for second one
silent raft
wait wdym by 14*9 + 2
sweet mural
you need to find upper value for first one to i showed you the way
glass lichen
you really need to work on your explanation if that's what you meant
"do 14*9+2" doesnt explain anything you meant
sweet mural
didn't wanted to write him the solution but basically he need to find least common denominator for those 2 given values
silent raft
bruh i just wanna know the fastest way to work it out cause my brain is dead
its like 4 am
and i havent slept for ages
glass lichen
14 and 9 are coprime so 14*9 is the smallest denominator
silent raft
i
sweet mural
do you know how to calculate your numerator for the first one ?
glass lichen
$\frac{2}{14}=\frac{2}{14}\cdot\frac{9}{9}$
ocean sealBOT
Mosh
lilac lantern
x=23.43356414207485
lilac lantern
yes
lofty kelp
is it not tan opp/adj ?
lofty kelp
yes
lilac lantern
x=39/tan(59)
tan(59)=1.66427
in degrees, maybe you have your calculator in radians
lilac lantern
39/1.66427=23.433
lofty kelp
to cancel it out?
lofty kelp
O
lilac lantern
wait i can show you
dry berry
can anyone help?
lilac lantern
can anyone help?
let me see
really easy problem
you know what a consecutive number is right?
dry berry
like x and x+1?
lilac lantern
yup
so just do the difference of those cubes
and thats equal to 1812
did you understand or should i write it?
dry berry
(x+1)^3 - x^3 = 1812?
lilac lantern
well
proud burrow
@dry berry yes solve it you will get answer
lilac lantern
x^3-(x+1)^3=1812
if that doesnt work
try the one you put
or viceversa
just in case
lilac lantern
x^3-(x+1)^3=1812
so try this one
proud burrow
@dry berry don't use vice versa case it's given difference of cubes of two consecutive terms is 1812 which is positive if you use x3-(x+1)3 then answer would be negative
lilac lantern
hmmmm
the weird thing is that it isnt in here the answer
you would get 24.07 and -25.07
and it also says integers
proud burrow
So use 24 as answer
dry berry
ohhh
proud burrow
So consecutive term will be 25
dry berry
man i've typed in wrong function 😳
alpine sable
is it free here already?
proud burrow
@alpine sable yes
alpine sable
can somebody help me with this question
😦
do we need to use differentiation here?
if yes is there any other method
?
dry berry
do we need to use differentiation here?
i think we need to use defferentiation
alpine sable
i think we need to use defferentiation
is there any other method
since i haven't learnt differentiation yet
😦
proud burrow
@hollow ravine use formula pi (outter radius square - inner radius square) h
dry berry
when it comes to tangent of a curve we often use defferentiation
alpine sable
fine the volume of the bigger one
fine the volume of the second one
and subtract them
nah nvm
im wrong
dry berry
since i haven't learnt differentiation yet
we have $y_{1,2} = \frac{-2 \pm \sqrt{-4x^2 + 12x +4}}{2}$
alpine sable
we have $y_{1,2} = \frac{-2 \pm \sqrt{-4x^2 + 12x +4}}{2}$
hmmm
ocean sealBOT
gansta
hollow ravine
@proud burrow I did it and I got it wrong so idk
dry berry
i don't understand cuz i haven't learnt yet
that's ok dude
alpine sable
there is no answer
thats why
i mean no answer sheet provided
what about this 😦
hollow ravine
ok I will try it now
but how do you get the height
since they only give the length
proud burrow
Length is the height
dry berry
what about this 😦
$-2h^2 - 6 =14$
ocean sealBOT
gansta
alpine sable
why tho
alpine sable
i think there might be smtg wrong
hollow ravine
alpine sable
cuz thats literally -14
hollow ravine
@proud burrow this is what I got
alpine sable
there must be smtg wrong with the question
dry berry
$-2h^2 - 6 =-14$
ocean sealBOT
gansta
dry berry
now is correct lol
alpine sable
this teacher is ridiculous
she simply sets question
and didn't provide us with any answer
D:
ember nest
Find the quadratic polynomial the sum of whose zeroes are root2 and their products is -12 . Find the zeroes too.
help
ember nest
ful explanation
hidden horizon
so polynomial will be x^2 - root2x - 12
alpine sable
that's fine if you have wrong solutions, just how you do it
btw why do we have to expand the equation
hidden horizon
ful explanation
do u know abt vietas relation of zeroes and coefficients ??
ember nest
nope bro
alpine sable
ember nest
in india it's different
ember nest
but i forgot
ember nest
cbse?
alpine sable
how does that work but i think thats correct
alpine sable
thanks ❤️ @dry berry
ember nest
class 10 ncert 2nd chap
ik but which excercise
dry berry
how does that work but i think thats correct
h is not only equals to 2 but also -2
hidden horizon
ik but which excercise
search the chap godamn it i forgot
dry berry
since (-2)^2 =4
ember nest
search the chap godamn it i forgot
i did i browsed but couldnt get the exact type of question
alpine sable
since (-2)^2 =4
yea?
hidden horizon
thanks
https://ncert.nic.in/ncerts/l/jemh102.pdf Pg 28 from bottom
see n understand coz vieta's used everywhere
ember nest
thanks bro
hidden horizon
thanks bro
cool bruh
ember nest
: D
dry berry
i mean how to get the first step
the graph show us it goes through the point (0;14) and (4;14)
alpine sable
i don't think so tho since the graph should only work under mapping x=2
so h must be 2
only
alpine sable
the graph show us it goes through the point (0;14) and (4;14)
yea
dry berry
since the graph has the function y=f(x) = -2(x-h)^2 -6
we can put the following two points into this function
(0;-14) and (4;-14)
alpine sable
ooh
dry berry
it seems like i've missed the point (4;-14) earlier
it those two function has the same root "h" you can only choose that root i guess?
btw im done here
the rest is yours
nimble mulch
Why is this solution wrong ?
I have checked multiple solutions online and none of them have considered that y cannot be 0
muted raft
why would it not be 0?
proud burrow
@nimble mulch use second equation as whole numerator >=0
@muted raft if it's zero then it would be infinite
muted raft
$\frac{0}{1+0^2} = \frac{0}{1} = 0$
ocean sealBOT
zslya
muted raft
apply log rules
proud burrow
@rustic hatch as base is 4 for both substitute both value equal then find value of x
rustic hatch
<@820725560505401395> as base is 4 for both substitute both value equal then fin...
wdym?
proud burrow
@hidden horizon yes that what I ment
rustic hatch
what about the log
hidden horizon
log will go coz its same both lhs and rhs
just like exponents when bases are equal
proud burrow
@hidden horizon yes
rustic hatch
just like exponents when bases are equal
ohh yeah thx bro
rustic hatch
<@828150220533137459> yes
thx bro
hidden horizon
cool bruh np
rustic hatch
hidden horizon
use basic trig
silk terrace
is this open now?
I got this problem. How do I find for a, a that is not 0, a solution? I can not have the null-vector. The matrix on the right is the inverse of the one on the left.
muted raft
I got this problem. How do I find for a, a that is not 0, a solution? I can not ...
So if A is the matrix on the left, then the augmented matrix [A, I] should produce [I, B] where B is the inverse matrix of A. I assume you can apply something like this here?
muted raft
Since A is supposed to be invertible like you said
hidden horizon
my guy thx so much
cool bruh
silk terrace
Since A is *supposed* to be invertible like you said
A is inverted and can be seen on the right hand side. I need to find solutions to T_a(x)=T_a^-1(x)
for a non zero "a" and non zero vector "x"
But I am not seeing an approach to the solution other than brute force?
muted raft
Hmm I think I have an idea one sec
There is a term called involutory matrices which is what I think is here
hidden horizon
my guy thx so much
@rustic hatch im goin 2sleep , so if u hv any more doubts , dont ping me , hv a great day
silk terrace
There is a term called involutory matrices which is what I think is here
Okay no problem. I was thinking about that as well
wary stream
A is inverted and can be seen on the right hand side. I need to find solutions t...
If a matrix is invertiable, then a special property of matrices will help a lot, do you know what property I'm referring to?
rustic hatch
equate 2x^2 + 1 = 10x - 7
if i simplify it, is it gonna be 4x instead of 2x^2
silk terrace
If a matrix is invertiable, then a special property of matrices will help a lot,...
not entirely. Been a while since I took linear algebra. I am helping someone with the problem.
muted raft
det is not 0?
silk terrace
nope
silk terrace
det is (a) and 1/a
I know that. I inverted the matrix which can be seen on the right hand side (since a is non zero)
wary stream
Do you know how to find the det of a 3 x 3?
silk terrace
Yes. Found for both.
wary stream
So set the det equal to 0, and find a
And a cannot equal that value, it can be any other value though
muted raft
Oh wait this is just a question about invertible matrix theorem
Which means you can pretty much apply any of the properties in the theorem
AKA it must have 3 pivots, it must have nullspace 0, it must be linearly independent, it must have det = 0, columns form basis, etc
silk terrace
I mean I am not sure on what dldh06 is refering to? Both determinants are found to be a and 1/a (of course) setting them to 0 does not do anything is it is non 0 (of course since it is invertible)
wary stream
Find the det of a 3 x 3
muted raft
Yes that should work as well
wary stream
This process
wary stream
The LHS matrix
And like I said, for a matrix to be invertiable, the det cannot be equal to 0
silk terrace
But that has already been done. The determinant is equal to a and a is then of course non 0
wary stream
So the solution to your problem, is a can be any value except for 0, so $a \neq 0$
ocean sealBOT
dldh06
silk terrace
yep but that is not the problem though?
I need to find a vector x
that solves T_a(x)=T_a^-1(x)
silk terrace
(aka my first picture where the vector X=(x,y,z))
wary stream
But you said to find an "a" that has a solution?
silk terrace
A solution is not an "a". A solution is the vector
worded poorly I see.
i. e I need to find a vector x
that solves T_a(x)=T_a^-1(x), for "a" that is non zero
wary stream
So is the goal to find "a" or (x, y, z)?
silk terrace
(x,y,z), a not equal to 0 and (x,y,z) not equal to the null vector
wary stream
The thing is, if $a \neq 0$, you'll have infinity many (x, y, z) vector solutions
ocean sealBOT
dldh06
silk terrace
Yes. But which form do these vectors have. I need to argue for an approach and not just pick any random vector from brute force and show that it works
wary stream
I would assume RREF would be the best way to do that part
silk terrace
I would assume RREF would be the best way to do that part
but both would just be identity matrices in that case.
wary stream
Symbolically, keeping "a" in there
silk terrace
https://www.wolframalpha.com/input/?i=rref+{{1%2C+-2%2C+-1}%2C+{2%2C+-3%2C+-1}%2C+{1%2C+-1%2C+a}}^-1
wary stream
Where is this question from?
silk terrace
A pratice problem. Not from a book or anything special.
devout linden
Hi there.
I know that if
F(x) = a cos(px) + b sin (py) [1]
Then
F''+pF = 0 [2]
But assume we don't know anything about F(x). How can we solve it from [2] to get [1]? What should i know first if i want solve it in reverse??
wary stream
A pratice problem. Not from a book or anything special.
Something you created?
silk terrace
No not at all. A friend was given this in a cs lin alg class. I took lin alg last year.
wary stream
No not at all. A friend was given this in a cs lin alg class. I took lin alg las...
Do you have the solution? And the full problem, with what it's asking to find?
devout linden
<@&286206848099549185>
woven dock
Hello vondarkness
Did you mean
f(x)= a cos(px) + b sin(px)
And
f''+p²f=0
?
manic quail
How would i complete the square?
Can you identify an "a"?
viscid yacht
2
manic quail
I'd say $a=x\sqrt{2}$
viscid yacht
No
ocean sealBOT
𝔙eryhappyperson
manic quail
So am I.
viscid yacht
I sis this so far
ocean sealBOT
𝔙eryhappyperson
blazing oak
Easy 2
glacial pelican
does that mean 15d = 3/8
glacial pelican
its 7/8
glacial pelican
lol its ok
meager crescent
sure
outer elm
so d = 1/40
glacial pelican
but how do i figure out the first 3 terms??
outer elm
now you plug the d in one of the equations to find a1
then you just go:
a1
a1 +d
a1 + 2d
glacial pelican
then you just go:
a1
a1 +d
a1 + 2d
what is a1?
glacial pelican
sorry
meager crescent
sec ill re write it @alpine sable
outer elm
its a system of equation
alpine sable
no
alpine sable
outer elm
lmfao
meager crescent
Loool
in order to find ouut how much one thing cost
in this case M (Milk)
u would make the other variable (in this case bread) the same number
what i mean
a number that both 4 and 5 go in is 20
alpine sable
yes
meager crescent
12M+20B=44
20M+20B=50
now what we do is get rid of bread
so it is
kinda makes sense?
alpine sable
no
meager crescent
sorry did not even write properly
Ur goal is to find out what milk and bread cost
in order to do this u would make one factor in this case maybe bread the same
so u can figure out what milkk is
alpine sable
ohh
manic quail
,rotate
ocean sealBOT
manic quail
I need help with 5
Look where the 0s are on the graph, and the seek the one equation which is 0 at the same x values.
stiff quiver
Is this channel free?
manic quail
Is this channel free?
Probably.
devout linden
Hello vondarkness
Did you mean
f(x)= a cos(px) + b sin(px)
And
f''+p²f=0
?
Yess....but in reverse. How can i know
f''+pf = 0
Become f(x) = a cos px + b sin py
Without knowing what is f(x)?
Like how come a regular f'' somehow ended up as a trigonometric function??
If i start from f(x) to find f'', i can do that. But how about in reverse??
woven dock
I think it's a bit too long to explain it here, please check out the wiki
https://en.m.wikipedia.org/wiki/Characteristic_equation_(calculus)
devout linden
I think it's a bit too long to explain it here, please check out the wiki
https:...
Soo should i know complex number in order to understand it?? Since the example already used complex conjugate and i don't know a thing about it
woven dock
Yea, you'll need knowledge of complex numbers to understand it
devout linden
Yea, you'll need knowledge of complex numbers to understand it
I already got this point but i dunno what should i do to get f(x)
covert glade
Is any number divided by infinity defined or undefined
like -4/oo
is that 0
or undefined
rustic hatch
Is any number divided by infinity defined or undefined
bro
covert glade
?
woven dock
I already got this point but i dunno what should i do to get f(x)
You can check the wiki site>>formation of the general solution >> complex root
hello uncle Rico you can say $$ \lim_{x \to \infty} \frac{-4}{x} = 0 $$
ocean sealBOT
Biscuit
timid wind
someone help explain this question please
<@&286206848099549185>
ping me when u can
outer elm
wtf looks hard
devout linden
You can check the wiki site>>formation of the general solution >> complex root
Almost got it.....but still wrong. Can you help me?? Why still get sqrt(p)??
Already followed that wiki method
woven dock
Hello vondarkness
Did you mean
f(x)= a cos(px) + b sin(px)
And
f''+p²f=0
?
As I have said here, there might be a typo
devout linden
Ahh yeahh....should be p^2
Okay....then i almost understand
Soo if it's 2 dimension, the sin px can be changed into sin py without anything to do??
woven dock
I don't think so, I think it's just a typo
devout linden
Ahh okay....after checking my book, i got misunderstanding.
However now i get it why it become like that. Thank you very much @Biscuit#5208
rustic hatch
crude eagle
rustic finch
$7\ =\ -1.79\sin\left(\frac{2\pi}{365}\left(x-79\right)\right)+6.3$
ocean sealBOT
Břāđ
rustic finch
how do you solve the multiple angles for something like this without graphing it
tight locust
sin
chilly night
Sorry for the easy question, but I'm not good at math:
Enter a number between 1 and 100:
Enter a number between 1 and 100:```
What are the chances to win?
edgy zealot
shell widget
@chilly night 1 in 100
@rustic finch take everyhing to the other side and write it in the form sin(...) = (some number)
then take arccsin on both sides
chilly night
<@!495504401436246018> 1 in 100
but three times
shell widget
did u enter 3 numbers?
alpine sable
hello, what is -i squared
shell widget
complex numbers?
alpine sable
yeah
shell widget
(-i^2) = (-1)^2 * (i)^2
edgy zealot
sterile beacon
i start with 60x and 3000y
every time i gain 100y
i lose 1x
how do i put this in equation format
rustic finch
so you just add +2npi
but like the supplemnetary one. like sin120 and sin60
silver bay
can someone help me solve this
quasi scarab
@silver baytry #multivariable-calculus
quasi scarab
how do i put this in equation format
60x+3000y +a(100y-x) ?
quasi scarab
silver bay
<@!778745077111455744>try <#496784996510466057>
just put it there, thanks
sterile beacon
60x+3000y +a(100y-x) ?
thx will check if worked
edgy zealot
@quasi scarab 176?
quasi scarab
yes
edgy zealot
Thank you bruh that made it so easy
worldly cliff
is this channel free?
sterile beacon
yes bruce
sterile beacon
sorr
worldly cliff
how would i find the two points the line y=4.2 through the parametric curve
sorry for the bad drawing
sterile beacon
it was (60y-x)(3000y+100x) not 60x +3000y + a(100y-x) @quasi scarab
quasi scarab
it was (60y-x)(3000y+100x) not 60x +3000y + a(100y-x) <@!424654701909377024>
? then u shouldve told us what the question was in detail
sterile beacon
i did i needed the numbers in equation format
lilac lantern
Sorry for the easy question, but I'm not good at math:
```Enter a number betwee...
1/100 * 1/100 * 1/100 = 1/1000000 = 0.0001%
quasi scarab
u said this: i start with 60x and 3000y
every time i gain 100y
i lose 1x
how do i put this in equation format
quasi scarab
and u got this : (60y-x)(3000y+100x)?? how
quasi scarab
Is this right ?
no
sterile beacon
i didn't think i assumed
quasi scarab
u didnt pay attention to the rules, so i advised u to read them, i didnt go around telling ppl what to do
quasi scarab
wdym
silver bay
can someone help me with these
im not too sure if this is math or physics
but its in my math class
remote heron
its rotational kinematics right
but basically math
which problem were you having a hard time with @silver bay
silver bay
which problem were you having a hard time with <@!778745077111455744>
do i just use the equation for simple harmonic motion of a pendulum
remote heron
id imagine so
silver bay
but im not sure if its right because i dont know gravity, should i just assume its 10 m/s^2
remote heron
usually yea whatever convention you use for your glass
sorry class
usually for problems like this i think youd just use g
silver bay
we haven't really done this before
remote heron
or if you all are using 10
silver bay
and i dont have a teacher :/ so i have no clue
remote heron
youre lucky theres a lot of resources for physics at this level
at least lecture-wise
if you can wrap your head around simple harmonic motion really
this is just a subset of that
silver bay
this isnt even physics 😭 its for my diffeq class and im not sure whether im supposed to do something different for that
remote heron
oh
remote heron
idk id just answer it however you can figure it out
silver bay
math class
remote heron
idk at that point id just pick the easiest way
since theyre not really clear
you can state/solve the SHM equation
which is uhh
silver bay
2pi sqrt(L/g) right
remote heron
silver bay
oh nvm i found it in my book
remote heron
ye
remote heron
i mean yea
remote heron
its not really exactly clear what youre supposed to do
remote heron
but it seems like youre on the way
idk if you state the original one, then the small angle approximation
maybe if you feel like solving it
so solve the IVP on that solution, then use calculus to maximize it
thats probably overkill for what this problem is asking but i guess thats the mathy thing to do
remote heron
since they give you an initial position and velocity
silver bay
ummm
silver bay
ok ok makes sense
edgy zealot
remote heron
then whatever procedure you typically use for maximizing things
silver bay
so i just use the equation, plug in a value for length, and solve?
remote heron
i would state the equation, state the small angle approximation
without subbing in anything
then for part 2, use the given length, IV's state the specific SHM eq for that situation
then do calc stuff to maximize
or whatever handwavey 'it is known' blah blah stuff youre allowed to do for periodic functions
does that all make sense
remote heron
which part seems confusing
silver bay
so
verbal sigil
Hi guys, im using excel and im trying to represent a large amount of data, i thought a line graph might be the best option but im struggling to create it on excel, would anyone be able to assist me? Thanks
silver bay
say this equation but with a sin(theta) instead of theta
then i say because its a small angle, sin theta~~theta
remote heron
idk thats probably overkill but i would state it just for shits and giggles
remote heron
i mean they're constants so you can leave them for as long as you want but whatever works
remote heron
id solve it fully with all constants just left but thats just me
silver bay
oh okay
silver bay
okay makes sense
remote heron
😄
remote heron
lol im gonna have to review
alpine sable
yknow how differentiating velocity gets acceleration and differentiating that gets displacement, what does integrating velocity get you?
silver bay
yknow how differentiating velocity gets acceleration and differentiating that ge...
displacement
alpine sable
oooo so its like a cycle
silver bay
yeah
alpine sable
thank u
silver bay
should i solve it with a laplace transform
because thats my current unit
i have no clue whether that makes any sense though
remote heron
if you know how yea
remote heron
haha
silver bay
random square roots and stuff
verbal sigil
will anyone be able to help on statistics?
plush goblet
misty path
I need help. What is 1+5
remote heron
yall can u not see were having a conversation
misty path
no
remote heron
please use a channel that doesnt have a active ppl in it
misty path
Bruh
silver bay
i swear i remember this stuff
hahaha me too i did it last sem but i forgot everything
broo i have a physics ap test tomorrow 🤯
remote heron
damn i forgot how involved solving these things can be
silver bay
can you say what you got for the first one once you finish
because i did it
like the easy way
but i have absolutely no clue if its right
remote heron
so
you use
characteristic polynomial
you have imaginary solutions
but the imaginary part falls away when you determine the coefficient?
remote heron
but i have absolutely no clue if its right
i mean you know the answer
remote heron
silver bay
idk if its 19 or 38
because
like
it says returning to original posiiton
not a full swing
silver bay
oh
wait
thats what makes it tick
that or its mirror image
so wouldnt that happen twice in one period
remote heron
were getting the position function arent we
so it should be positive, become negative at the bottom, be maximum negative on the other side, then positive again when it comes back
i am dumb so grain of salt but i dont think this function is giving vertical displacement
i think its angular displacement
cloud kiln
remote heron
?
silver bay
so it should be positive, become negative at the bottom, be maximum negative on ...
thats true but i didnt use the diffeq at all
i just used the equation for period
remote heron
you can use whatever you want
remote heron
unless the question is specific
silver bay
which is the time for a right swing and a left swing
remote heron
i mean you can do it however you want i think
if you are not comfortable with that way find the roots of the velocity equation?
which is gonna be the same thing but longer
remote heron
how do you get the velocity given a position equation
remote heron
you solved the diff eq right
silver bay
ah shoot gtg can i ask again in like half an hour
remote heron
if you just want the first derivative
silver bay
there is a way to turn a second order into a first order right
i think
remote heron
just define the first derivative as a function
idk im being dumb
but i wanna review how to solve it now
just lazy
strong furnace
the way they do it in introductory physics is multiply left side by dx/dx or d(theta)/d(theta)
you get a variable seperable ODE I think
and you use the relation to solve it
tawdry mantle
how does the first equation turn into the second equation?
<@&286206848099549185>
remote heron
you shouldnt ping right away
tawdry mantle
oh sorry
remote heron
its a two step algebraic process
you should try to track it, its good practice
but its division and exponentiation
ionic jewel
but its division and exponentiation
this is pretty much the biggest hint outside of the answer
remote heron
tawdry mantle
divide both sides by 10
then turn the log into something like... little to the power of right equals middle
thanks 🙂
remote heron
😄
alpine sable
I have N=20, k=4 (m1=4, m2=8, m3=12,m4=7) and SSB=22. How do i find the value of SSW? I tried SST=SSB +SSW. And MSB=SSB/K-1 (4) but i'm stuck.
loud folio
Help pls I’ll give you a 🍪!
civic crypt
Which of these looks like an area formula?
scenic sable
????
timid wind
hey, can someone help me with this question
scenic sable
why does 0^0 equal 1
noble sinew
but i thing google is tripping
silver bay
the way they do it in introductory physics is multiply left side by dx/dx or d(t...
sorry i just saw this
how would that work?
shut elk
@gilded gazelle i think we want some system of equation to solve for how many weeks it takes to make 10,000$ correct? EDIT: make 10,000$ more than its expenses
so it's linear, and linear relationships have form $y = kx$ right?
ocean sealBOT
EL145
shut elk
furthermore, the average weekly income is roughly 4,500, the average weekly spend is roughly 3,200.
gilded gazelle
ah ok i get it now
i knew the answer but i couldnt figure out why
i didnt use averages
gilded gazelle
i am studying, this has an answer sheet and once you mentioned averages i solved it by just getting both and doing simple math
spending + 10000 = revenue
so this
shut elk
well that's not what i was thinking
strong furnace
how would that work?
did you try doing it ?
silver bay
i'm not sure what you meant tbh
shut elk
i know it's the same thing bigweld, but my thought process was 4500x-3200x=10000 hence 1300x=10000
i'll drop out the channel
sorry t o interrupt.
strong furnace
i'm not sure what you meant tbh
ok so you have a second order differential equation in x right?
silver bay
yeah, its just theta'' = -g/L theta
strong furnace
but this is a first order differential equation in v or dx/dt
strong furnace
and you know condition at some point
silver bay
yeah i think
wait
can i check number 1 with you
because i think i dont need the diffeqs for that
but i also dont know if i did it right
strong furnace
sure
ocean sealBOT
oreo
strong furnace
if you are allowed to use this
then that is alright
but this result requires differential equation
so if this is a result you're allowed
silver bay
I'm not sure if im allowed to use it
strong furnace
you have the time period of oscillation
silver bay
so i should probably use a differential equation
strong furnace
if this is an introductory physics course
they probably don't expect you to solve the diff eq
silver bay
its a differential equations coures
*course
like a really intro level one but we've covered the things i should know to solve it
like 2nd order linear
strong furnace
you can solve 2nd order differential equations?
silver bay
i think? i dont really remember 😭
strong furnace
general solution Ae^(a_1x)+Be^(a_2x)?
strong furnace
yeah
silver bay
okayy, so
my equation is
$$\theta '' = -\frac{g}{L}(\theta)$$
i think?
or that should be a sin(theta) on the right but im using small angle approx
i should probably just keep it as sin
strong furnace
nah they use theta to get the result
silver bay
oh okay
ocean sealBOT
oreo
silver bay
im confused about how id solve that though
should i just plug in numbers and then try>
but then i get like
okay if i plug in numbers
i get
$$\theta '' + \frac{10}{0.6} \theta = 0$$
ocean sealBOT
oreo
silver bay
and to factor that i get like imaginary numbers right
strong furnace
yes
silver bay
sooo
uh
$$(D+\sqrt{\frac{10}{0.6}}i)(D-\sqrt{\frac{10}{0.6}}i)\theta=0$$
oops
no
ocean sealBOT
oreo
silver bay
okay that
strong furnace
yes
ocean sealBOT
oreo
strong furnace
theta in this case but yes
strong furnace
to get it in the desired form you need to actually do that
silver bay
okay sounds good, so itll be
wait what is my dependent variable here
oh nvm
theta is dependent, t is independent
silver bay
theta in this case but yes
wait would it even be theta then
because theta is the dependent variable
silver bay
$$\theta=c_1 cos(\sqrt{\frac{10}{0.6}}t)+c_2 sin(\sqrt{\frac{10}{0.6}}t)$$
does that look right? im not sure if i did the euler thing right
ocean sealBOT
oreo
strong furnace
does not look right
strong furnace
e^(wit) would be cos(wt)+isin(wt) right?
silver bay
i think so
strong furnace
don't you think there are two terms missing from your solution ?
strong furnace
you c1.exp(iwt)+c2.exp(-iwt) right?
ocean sealBOT
silver bay
yeah
so i think what i have is right
wait no
uhhh
wait
no
i need to check again
ok yeah i think what i had is right then
i think the other two terms cancel out or something?
strong furnace
I am really tired
silver bay
i think so
i have the equation for theta
so i have to find out how many times it equals 0 between t=0 and t=30
i have no clue how to do that
strong furnace
you can use something called R-method to convert this into a single sinusoidal function
strong furnace
so you would get a sin function with the same period
silver bay
that makes sense but at the same time we have like constants right
and i dont knwo what the constants are
strong furnace
the constants affect the phase and amplitude of the sinusoid not the period
silver bay
oh okay makes sense
strong furnace
so after you have theta as a function of time with period this
you can use that as time period
and now you have a simple arithmetic problem with time period total time and number of ticks
strong furnace
so what would the method be?
for?
silver bay
the R-method you mentioned
strong furnace
the idea is to divide by sqrt(c1^2+c2^2) and you'll have terms similar to he terms in sin(A+B)
but here's a link for more info
strong furnace
theres no way we have to do that
why would you think that?
silver bay
well
its nowhere in our textbook
and i really dont know how im supposed to solve this but theres no way its supposed to be this long
because i have 10 of these as 1/10 of my assignment
strong furnace
also R-method is trigonometry so precalculus that would be a pre-requisite, no?
silver bay
yeah i guess
i dont think ive ever seen it though
in precal
but i could be wrong because i took precal like
3 years ago
almost 4
how would i do this though
because my constants are really arbitrary
theres no given values
these are my questions
strong furnace
you have to use the condition
like they say it is released from rest
at an angle of .1 radians
so that is your initial conditions
strong furnace
for 1 the constants don't matter
since the time period does not depend on the constants
strong furnace
so that is your initial conditions
you need to differentiate to get all the information from the initial condition btw
silver bay
since the time period does not depend on the constants
yeah i understand
silver bay
you need to differentiate to get all the information from the initial condition ...
im confused, differentiate what?
the equation i got?
alpine sable
I know this is a math channel but can someone help me in my english please?
strong furnace
#discussion might help
silver bay
the relation you get yes
okay so id get the angular velocity equals something right
since the left hand right now is theta
edgy zealot
4?
