no
#help-0
dusty kayak
tardy steppe
first off, what are the triangle's dimensions?
mint peak
Or is it 76.5
dusty kayak
Or is it 76.5
correcto
tardy steppe
^
mint peak
Im so spedcial
tardy steppe
each length marks out only that line segment, not the dimension of the nearest shape
so the height of the middle rectangle isn't 7 miles, it's 7 miles + 6 miles
the left triangle requires a bit more work, since you have to also take away some length, but can you see what parts you have to add and subtract to get its height?
tardy steppe
there's 3 main segments to it
we're given 1 explicitly, the 6 miles on top
but then it is some of the middle rectangle's height
dusty kayak
but then you gotta subtract some
tardy steppe
those are all of the important numbers, but what order would you combine them in?
mint peak
but then you gotta subtract some
Which one? I'm so special
mint peak
7-5?
mint peak
Im so so sorry guys 😭 I js don't get my teacher's explanation
tardy steppe
you need to also account for the rest of the triangle's height
look at this section
the triangle's height is 6 miles, then it takes some from the height of the middle rectangle
so we can add that on, which is 13 extra miles, making 19 miles
but it doesn't take all of the height of the middle rectangle
so how much does it fall short by?
mint peak
so how much does it fall short by?
Can u please reword that 🥲
dusty kayak
think that section only
the 5 isn’t included and you found that that the 7 should be subtracted by the 5
so you got 2
now what ither measurements do you add to the 2?
mint peak
2+4+6
mint peak
2+6+6?
mint peak
14×22/2
dusty kayak
yee
mint peak
154
mint peak
24 is a lil rectangle right?
mint peak
I somehow got 55
mint peak
:3
dusty kayak
thats missing but
if we were to say there was a line there like line segment AB
what is congruent to it?
mint peak
6+7 is the line segment right or is it js 6?
mint peak
So is it 13×5 or no?
mint peak
Alr thank u sm
carmine topaz
how do i solve (d)?
lone heartBOT
how do i solve (d)?
buoyant saddle
how do i solve (d)?
alpine sable
erm what the sigma
carmine topaz
i dont know how to find the maximum amount of unprocessed gravel at that certain t like how do i set the equation down...?
wispy plaza
Mine now
alpine sable
ok
buoyant saddle
i dont know how to find the maximum amount of unprocessed gravel at that certain...
well did you do part c?
carmine topaz
well did you do part c?
yeah i've got 98.140 ton + some reasoning
buoyant saddle
so we know the rate at which unprocessed gravel accumulates in the processing plant is G(t) - 100 yea?
alpine sable
carmine topaz
so we know the rate at which unprocessed gravel accumulates in the processing pl...
yeah the amount entering - amount processed per hour...? right?
buoyant saddle
yes
alpine sable
i found the exact question online
buoyant saddle
so let’s call that some other function like f(t)
buoyant saddle
i found the exact question online
cool bro
alpine sable
so u need proof or smt
carmine topaz
i found the exact question online
its ap calc bc frq
buoyant saddle
we don’t care
carmine topaz
so let’s call that some other function like f(t)
and?
wispy plaza
so let’s call that some other function like f(t)
That’s so devious when the rate of processing is constant
buoyant saddle
That’s so devious when the rate of processing is constant
bro what
wispy plaza
Hold up, I misunderstood, my bad
buoyant saddle
and?
ok then we want the maximum amount of unprocessed gravel which means we want f(t) = 0 and f’(t) < 0 or we could also do first derivative test
since f(t) is the rate of "accumulation" in the plant
is this a calculator question btw?
carmine topaz
calculator is allowed
buoyant saddle
ok that makes more sense with the function they gave
patent vale
you need to numerically integrate?
buoyant saddle
ok then we want the maximum amount of unprocessed gravel which means we want f(t...
do you understand this
carmine topaz
ok then we want the maximum amount of unprocessed gravel which means we want f(t...
are we like using the max and min conditions,,,?
carmine topaz
so f(t)=0 (critical point)? and f'(t)<0 max?
buoyant saddle
$f(t) = 45\cos\left(\frac{t^2}{18}\right) - 10$
carmine topaz
wait shoudnt f'(t)=0?
ocean sealBOT
knief
carmine topaz
treat f(t) as the derivative
ok
buoyant saddle
for the "amount function"
buoyant saddle
i just think what usual max min are
sure but f(t) here is the rate
carmine topaz
i get it
buoyant saddle
and we want the rate to be zero since we want a stationary point
more specifically a maximum
carmine topaz
so f(t) should equal zero?
buoyant saddle
,w 45cos(x^2/18) = 10 for 0<= x <= 8
buoyant saddle
so f(t) should equal zero?
yep
ocean sealBOT
carmine topaz
and what should i do next...?
buoyant saddle
ahh i see why they asked t = 5 for part c
buoyant saddle
and what should i do next...?
use a calculator to find the exact value for t
carmine topaz
i checked the answer key and they said this
carmine topaz
use a calculator to find the exact value for t
what do i plug in...?
buoyant saddle
i checked the answer key and they said this
this is exactly what i said
buoyant saddle
what do i plug in...?
do you have a graphing calculator?
carmine topaz
do you have a graphing calculator?
yes
buoyant saddle
**knief**
ok so just graph this
and use the zero option
do you have a ti-84
you hit 2nd trace zero
carmine topaz
i have casio not ti84 😭
buoyant saddle
bro invest in a ti-84
i’m sure you can with a casio
you need to figure out how to or get a ti-84 before the ap exam
carmine topaz
you can also use desmos in the exam
carmine topaz
the test is now digital you only write the answer (frq) in paper
buoyant saddle
this is a new thing this year
carmine topaz
so they allowed desmos
buoyant saddle
the test is now digital you only write the answer (frq) in paper
this is crazy
ok desmos works just fine then
do you know how to use desmos
carmine topaz
im kinda learning it now cause its sometimes faster then graphing calculator
buoyant saddle
i checked the answer key and they said this
see if you can get that value for t
carmine topaz
whats that G(s) in solution...?
buoyant saddle
whats that G(s) in solution...?
the rate at which unprocessed gravel comes in
they used a dummy variable
because you can’t use t in the limit of integration and as the variable you’re integrating with respect to
buoyant saddle
no same function, just used a different variable
patent vale
i checked the answer key and they said this
would this be considered an integral equation?
buoyant saddle
wait wasnt that G(t)?
yes G(s), G(t) same thing
carmine topaz
because you can’t use t in the limit of integration and as the variable you’re i...
what do you mean by this?
buoyant saddle
also, writing that out explicitly isn’t necessary
buoyant saddle
what do you mean by this?
like $\int_0^x f(x) \dd{x}$ makes no sense
ocean sealBOT
knief
carmine topaz
i get it
carmine topaz
is that 500 the initial amount?
buoyant saddle
also you don’t have to write the A(t) function explicitly
you can
but
don’t have to
buoyant saddle
is that 500 the initial amount?
yes
carmine topaz
why did they state A'(t)=0 like dervative of the amount...?
buoyant saddle
why did they state A'(t)=0 like dervative of the amount...?
yes it’s the same as how i stated f(t) = 0
because we’re looking for a maximum
carmine topaz
oh
buoyant saddle
we find the critical point
buoyant saddle
why did they state A'(t)=0 like dervative of the amount...?
the rate at which the amount of unprocessed gravel accumulates in the plant is zero because it’s at a maximum
carmine topaz
so their A(t) is the total amount of unprocessed gravel... and they took A'(t)=0 to find the t where the rate (unprocessed gravel) is at maximum? and then they plugged in the found t value to the equation A(t) that finds the total amount? and the answer is maximum because we used the t that leads to maximum...?
buoyant saddle
precisely
and then they had to check it of course against the endpoints
extreme value theorem
we want the absolute maximum so it’s not sufficient to conclude that the local max is the absolute max
in this case it did happen to be the absolute max though of course
carmine topaz
why does EVT make testing endpoints necessary is it cause the endpoint could either pop up or down...?
buoyant saddle
why does EVT make testing endpoints necessary is it cause the endpoint could eit...
well i think the simplest reason to see why is to consider an example
let me create a graph for you
consider the interval -2 to 2
carmine topaz
oh the other end could go up
buoyant saddle
clearly the function has a local max that isn’t the absolute max
carmine topaz
clearly the function has a local max that isn’t the absolute max
yea
buoyant saddle
oh the other end could go up
yes
so like it’s entirely possible to have a couple of stationary points with the endpoints still being the absolute max or min based on the behavior of how the function is increasing/decreasing in the entire interval
buoyant saddle
i don’t think desmos does that
it won’t just tell you the value
plot A’(t)
and then look at the graph for the zero
it’ll show the point
buoyant saddle
write d/dt A(t)
buoyant saddle
maybe y =?
turbid gyro
i checked the answer key and they said this
hello, excuse me, could u also give me the a b c keys? 
carmine topaz
also since this is a simple graph you can just plot what i did
do i try this in desmos?
carmine topaz
i get the right answer
buoyant saddle
nice
buoyant saddle
yea tbh i think the entire test should be no calc
calculator section was just dumb
just annoying
carmine topaz
calculator section was just dumb
if there is no calculator how am i supposed to find answer for a b c like those
its too much math
to do it without calcu.
buoyant saddle
if there is no calculator how am i supposed to find answer for a b c like those
by making questions that you don’t need a calculator for
carmine topaz
that make sense
buoyant saddle
there’s a reason why the questions on no calc look drastically different
they wouldn’t give a complicated function like this on no calc
carmine topaz
most of the polar curve questions are calculator
buoyant saddle
true
for frqs
mcq have a fair bit of just "what is the correct integral for the area"
or whatever
lone heartBOT
buoyant saddle
anyways thanks for helping 🙏
you’re welcome
molten plover
c?
lone heartBOT
@molten plover Has your question been resolved?
fickle musk
median is less effected by varying data?
to measure dispersion however ud use variance or standard deviation
molten plover
.close
lone heartBOT
plain bronze
input vector is
A
B
C
D
E
output vector is
B
A
C
D
E
by the way, I have a very strong hunch it is not possible, but im going for proof or strong argument for why its not
possible
So basically im looking to see if any string of matrix multiplication between these two matrices gets the matrix
lone heartBOT
lone heartBOT
Available help channel!
molten plover
lone heartBOT
molten plover
homogeneous?
cause its better to use median and mode for skewed distributions
@lunar robin what ye cookin?
lunar robin
my own question lol
molten plover
oh.
glacial mesa
homogeneous?
cause its better to use median and mode for skewed distributions
Yea what you're saying makes sense..
Depends on what you define "has relevance" no?
glacial mesa
Ye suitable to homogeneous
molten plover
thanks!
lone heartBOT
Available help channel!
hushed compass
How do I do this?
lone heartBOT
How do I do this?
opal portal
is that the entire question?
hushed compass
is that the entire question?
Yes
golden canyon
I guess it is though, since both exponents need to be 0
lunar saddle
I guess it is though, since both exponents need to be 0
Smart
golden canyon
notice that square roots are always positive
lone heartBOT
@hushed compass Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
fervent timber
How can I convert a recurrence relation to a generating function?
fierce cipher
idk, there's lots of ways to do that, but some of them have to go through the step of finding closed form of the recurrence relation
some method assumes a generating function exists rightaway to find the closed form
some of them just doesnt follow any rules at all
lone heartBOT
@fervent timber Has your question been resolved?
fierce cipher
for example, a common way to solve a_n = h * a_(n-1) + k * a_(n-2) is to assume a generating function exists and do some changes so that the RHS will be something familiar
fervent timber
for example, a common way to solve a_n = h * a\_(n-1) + k * a\_(n-2) is to assum...
do I need to know the initial conditions as well to figure out the generating function?
fierce cipher
if you switch everything to LHS it becomes a_n - h * a_(n-1) - k * a_(n-2) = 0
so you can imagine that the way to do is to perform the subtraction:
f(x) - hx * f(x) - kx^2 * f(x)
fervent timber
if you switch everything to LHS it becomes a_n - h * a\_(n-1) - k * a\_(n-2) = 0...
is this right?
fierce cipher
i think thats correct
i never tried finding a general formula before but that seems alright
lone heartBOT
lone heartBOT
Available help channel!
austere shore
Really confused about where to put the y axis.. did convert the intervals into exclusive format and took each as 1 unit but stuck at where to place the y axis between x= -1.5 and 0.5
austere shore
Please help
lunar robin
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
alpine sable
here's how you do it mate:
- find the midpoint of each of the intervals
- add those midpoints as ticks on the x-axis
- plot the subsequent value for the number of runs for each team
lunar robin
austere shore
https://www.youtube.com/watch?v=QL-uWhuQEzs
That’s already exclusive.. my problem is it starts with 0.5 and idk where to close it on the left side
mental python
,rccw
ocean sealBOT
austere shore
Gosh i hate these polygons
A quick question: can I just put the class marks on the x axis instead of the class intervals? And then plot the points accordingly?
If I can then I think I got my answer
carmine topaz
part (b) asked to find the absolute minimum value so that means you have to test the local minimum and both endpoints right? but i dont get why the calculation in the solution goes like that...? why are we using f(8) to find those...?
fierce cipher
part (b) asked to find the absolute minimum value so that means you have to test...
yep, check both endpoints and the extrema
remember, that graph is f'(x)
not f(x)
so you need to calculate the relative minimum/maximum through integrating
carmine topaz
so i have to integrate? kinda reverse back to that f(x)?
fierce cipher
i mean, why do u think they give you areas
carmine topaz
but is it like we dont know that equation for f stuff so we are using the areas?
fierce cipher
exactly
carmine topaz
but why do we do f(8) + some integral or f(8) - some integral...?
i dont get that part
fierce cipher
well, what is that integral evaluated to by definition?
carmine topaz
well, what is that integral evaluated to ***by definition***?
what do you mean?
oh
area under the curve
?
carmine topaz
what is the integral of f(x) from a to b
[f(a)-f(b)]?
fierce cipher
it's the opposite, F(b) - F(a) where F(x) is the antiderivative of f(x)
so if you look at the integral, it's just f(8) - f(0)
carmine topaz
i confused the limit 😅
fierce cipher
lol
carmine topaz
but we're trying to find f(0) not when x is from 0 to 8 or something but if we use 0 as both limit the answer gonna be zero
this whole thing doesnt make sense in my brain
fierce cipher
but we're trying to find f(0) not when x is from 0 to 8 or something but if we u...
no
isnt the function continuous at x=0?
carmine topaz
what do you mean
carmine topaz
yeah
carmine topaz
cause that's what f(0) should be like in my head but that doesn't make sense mathematically
fierce cipher
no
a = b = 0 -> f(0) = f(0)
that's just it
sure, the integral is 0, but that means f(b) - f(a) = 0, not f(0) = 0
carmine topaz
i mean like when finding f(0) you're using when x=0 and in my brain both ends in the integral should be like 0 and 0 but that doesn't work
i think im kinda confusing myself
fierce cipher
why would you make both bounds be 0
you are running in a circle without even knowing
carmine topaz
sorry im kinda slow
but the whole equation in the solution for f(0) make zero sense to me
also f(6)
fierce cipher
if you are given f(8) and you are assigned to find f(0), you find the integral from 0 to 8
which is just the area, isnt it
but the integral of f'(x) from 0 to 8 is also f(8) - f(0)
suppose the area you just calculated be something like, A
then f(8) - f(0) = A
f(0) = f(8) - A
carmine topaz
but should you do like f(8) - integral from f(8)-f(1) so you get f(0)?
i dont know what im thinking
😭
fierce cipher
but should you do like f(8) - integral from f(8)-f(1) so you get f(0)?
no, why is x=1 relevant here 
carmine topaz
i dont know
fierce cipher
ok ok
fierce cipher
we will do another way different from the given key
(its not that different, it's just more elaborated)
carmine topaz
oh i get it so its like from the solution its basically f(8) - f(8) + f(0) so we get the f(0) at the end?
carmine topaz
i hate my brain
fierce cipher
ITS THAT SIMPLE 😭
carmine topaz
thanks for helping 🥹
lone heartBOT
lone heartBOT
Available help channel!
untold oriole
hiya, Im a super linear algebra newbie, trying to wrap my head around vectors. I know its a 'direction and magnitude' and have heard that likle 1000 times, but that doesnt like make sense for me in a concrete way. Would it make sense to say that, one image here is the vector points like vec6(1, 2, 3, 4...) and the arrow represents the vector of those points? like thats just me drawing the arrow this is not accurate just an arbitrary example
lone heartBOT
hiya, Im a super linear algebra newbie, trying to wrap my head around vectors. I...
@untold oriole Has your question been resolved?
twin nimbus
Oh gosh ok, so yes you can think of this graph as a single vector, but in order to do so you cannot think of it as residing in 2 dimensions
Instead you have to imagine a 6d configuration space
And the vector lies in this space
Assuming that the x values of the coordinates are fixed
This would be approximately the vector (1,3,2,4,3,5)
@untold oriole
This is perhaps not the best example to begin with
untold oriole
I think I might have gotten it now, this a lot of text but do u mind just skimming through it and let me know if I got the general idea?
"Vectors are quantities that have both magnitude and direction.
Vectors basically describe relationsship between points of data, and how they are related to one another.
A vector is essentially an array of numbers or a list of numbers that represent some quantity in a specific context. Each number in the vector can be thought of as a "coordinate" in a particular dimension.
Linear algebra can either be a physical representation or an abstract one, as physically we can understand linear algebra as related numbers in space (magnitude and direction), whereas we can also understand linear algebra as numbers related to each other in a more abstract way, just as numbers (not representing magnitude and direction, rather just numbers.)
In machine learning (ML) and many other abstract contexts, vectors aren’t typically about direction and magnitude in the physical sense. Instead, vectors are simply groupings of numbers that represent data points or features.
This represents the points the vector arrow can be drawn in to visualize the magnitude and direction, but it is not the magnitude and direction itself, those can be calculated by different formula."
twin nimbus
Well, yes to a point.
Even if you do just have a list of numbers, which is a perfectly valid way of thinking about a vector, it doesn't mean that it doesn't also describe a magnitude and direction
untold oriole
Right
twin nimbus
And perhaps by thinking of this as a magnitude and direction you can get some insight
But perhaps not
untold oriole
The idea about a physical vector as opposed to a list of numbers is what confuses me really
twin nimbus
It's two ways of representing the same thing, like 1/2 and 0.5
The list of numbers is useful because it's easy to calculate with, but it requires defining a specific coordinate system
untold oriole
Okay, yeah. Would that mean like, if we had an abstract concept, for example ML, that just deals with numbers and not physics, we could still represnt those numbers in a physical space as points connected?
twin nimbus
So let's say we have a neural network, it has 30 billion parameters
We can think of this entire neural network as being a single vector in 30 billion dimensional space
And this is actually what we do
Because then we consider a function on this entire space
And ask questions about the gradient of this function
Which is also a vector
Then we wander through this space following the gradient to optimize the value of the function
This is how training a neural network works
Just the way we represent these concepts is via a list of numbers, instead of a magnitude and direction
@untold oriole does this make sense?
(I'm not sure what you meant by "points connected" btw)
lone heartBOT
twin nimbus
.reopen
lone heartBOT
✅
untold oriole
The words definetly makes sense, its just the visualization that I cant wrap my head around. I think am a very visual thinker, so when I can't see it for me, it makes less sense.
twin nimbus
Well, visualizing higher dimensions is quite difficult
untold oriole
I suppose, something beyond 3 dimensions doesnt make sense
Anyway, the general idea is just about grouping related numbers together to form complex systems, or like describe them? Is that somewhat accurate?
twin nimbus
Well, vectors can do a lot of things. I don't know if I would say that is the "general idea" because even that is somewhat limiting. But sure! A vector can be used to describe the state of certain types of complex systems.
Also certain types of simple systems
For instance, you can use a vector to represent a pendulum.
untold oriole
like vec4 for RGBA or vec3() for X, Y, and Z in space, is that accurate?
twin nimbus
Where our space is 2 dimensional angle vs angular momentum
twin nimbus
like vec4 for RGBA or vec3() for X, Y, and Z in space, is that accurate?
This works as well, yeah
untold oriole
Do you mind boiling it down to a general idea, if you can? Mine says its relationsship between specific numbers that can represent anything.
twin nimbus
So the formal definition of a vector is a good deal more general
untold oriole
What is the formal definition?
"a mathematical object that has both a magnitude (length) and a direction" ?
twin nimbus
So a vector is an element of a vector space.
A vector space V over a field F is a set equipped with a binary operation (addition) V×V->V and a binary function (scalar multiplication) V×F->V that satisfies the following criteria:
Using a,b,c as vector elements and x,y,z as field elements.
- Associativity of addition: a+(b+c) = (a+b)+c
- Commutativity of addition: a+b = b+a
- Identity element of addition: there exists a vector element 0 such that 0+a = a for any a in V.
- Inverse elements of addition: for each a there exists an element -a such that a + -a = 0
- Compatibility with scalar multiplication: x(ya) = (xy)a
- Identity element of scalar multiplication: there exists a field element 1 such that 1a = a for all a.
- Distributive property of vectors: x(a+b) = xa + xb
- Distributive property of field elements: (x+y)a = xa + ya
Under this definition, we can identify even things like polynomials as residing in a vector space
@untold oriole
(thus we can even define the derivative as a particular infinite matrix)
raven void
hi i need help
twin nimbus
! occupied
lone heartBOT
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).
untold oriole
So a vector is an element of a vector space.
A vector space V over a field F is...
I'll write that down for later use, hopefully as I work with this it slowly settles. I appreciate you taking your time out to explain me this, that's really awesome. I might come back at a later time, to follow up, eventually settling bit by bit.
raven void
sorry i get
untold oriole
Go to either of the channels under (available) and then the bot will assign you your own channel 🙂
tough relic
You can probably solve it by computing A² and A³ and then solving for a and b after simplifying both sides of the equation.
But is there a faster way to get to the answer?
tribal geyser
Can you find the roots of the polynomial ?
tough relic
Can you find the roots of the polynomial ?
I could treat it as a cubic equation and find one of its factors. Then divide it by the factor to get a 2nd degree polynomial, then solve the quadratic.
Is that what you mean?
tribal geyser
Yup
By doing that you find the spectrum
By finding the spectrum you can easily solve for a and b by choosing relevant vectors
Actually wait …
tough relic
By finding the spectrum you can easily solve for a and b by choosing relevant ve...
I haven't gone that far into linear algebra yet, so I don't know what you mean 😅
Sorry 😭
But I understand the basics of matrix operations.
Like, multiplication, inverse, adjugate or determinant.
tribal geyser
Ah sorry ok
dire hollow
mmmh why don't you just perform the multiplication?
tough relic
mmmh why don't you just perform the multiplication?
That will take a fair bit of time. I'm looking for a way to get to the answer in less steps.
dire hollow
That will take a fair bit of time. I'm looking for a way to get to the answer in...
not that much time, I'm trying to think about something tho
glacial mesa
I'm not sure but if you could find the eigenvalues in terms of a and b, then you can define matrix B=-A^3+4A^2-A-21I_3 and there's a theorem that says if B=f(A) then f(lambda_A)=lambda_b (lambda is an eigenvalue) so then you can plug then eigenvalues with the a and b and get an equation, then solve it for them(?)
I'm just writing my thoughts out I'm not sure at all this helps
I don't think this helps
dire hollow
Idk, is this easier than just doing two times a 3x3 matrix multiplication T.T
tough relic
I'm not sure but if you could find the eigenvalues in terms of a and b, then you...
I'm sorry, what are eigevalues? 🥲
I'm only starting with this topic, seems like I haven't even touched the tip of the iceberg.
I think I'll stick to solving it by computing A³ and A². Thanks for all your help though. Appreciate it 👍!
glacial mesa
it is pretty simple
tough relic
Idk, is this easier than just doing two times a 3x3 matrix multiplication T.T
Seems like it. Thanks.
glacial mesa
I'm sorry, what are eigevalues? 🥲
I'm only starting with this topic, seems lik...
Of course, once you learn you could come back to the question I'm pretty sure it could be solved in a simplier way using them but not sure how!
tough relic
Of course, once you learn you could come back to the question I'm pretty sure it...
Thank you very much 🙏!
dire hollow
Of course, once you learn you could come back to the question I'm pretty sure it...
but finding eigenvalue with parameters is more difficult IMO
you need to solve for $det( λI-A)=0$
ocean sealBOT
nico.alesi
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dire hollow
it doesn't show lambda I don't know why
tough relic
it doesn't show lambda I don't know why
$\lambda$
ocean sealBOT
GoldBarley
glacial mesa
I'm thinking you could play with the matrix to make it triangular and then the diagonal is just the eigenvalues..
dire hollow
I'm thinking you could play with the matrix to make it triangular and then the d...
I guess it's easier to just do the multiplication
glacial mesa
Could be
dire hollow
taking into account that @tough relic hasn't gone too much deeply into linear algebra, I think that is the goal of the exercise
pure meadow
this question is driving me crazy
lone heartBOT
this question is driving me crazy
pure meadow
theres something stupid im not seeing
g' when z=2 is 31/2
g(2)= 21/2+ln2
y-(21/2+ln2)=31/2(z-2)
so y=31/2z-19.807
oh i see it
im dumb
.closed
.close
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muted anchor
hi,
muted anchor
is there a mistake in this question?
It would be an exact differential if there was y in the second LHS term
buoyant saddle
It would be an exact differential if there was y in the second LHS term
what?
lone heartBOT
muted anchor
i got side tracked by something, was focusing on the wrong thing
pure meadow
happens to all of us man
buoyant saddle
$(\sin y \cdot \sec^2 x - \cot x)\dd{x} + \cos y \tan x \dd{y} = 0$
ocean sealBOT
knief
buoyant saddle
i got side tracked by something, was focusing on the wrong thing
ahh ok
no worries
silver vine
,tex \int x^2 \sqrt{3 + 2x - x^2} ,dx
ocean sealBOT
regular cam
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silver vine
help plz
lone heartBOT
mental python
!msgdel
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mental python
just open a new channel
lone heartBOT
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onyx trout
Who wanna grind with me on khan academy the pre-algebra section, i'm trying to pick up math.
onyx trout
.close
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untold hollow
anyone interested in solving some algebra questions with me? im thinking of doing some exercises from the chapter: complex number, mathematical induction and combinatorics (they are all mixed in one chapter)
lone heartBOT
anyone interested in solving some algebra questions with me? im thinking of doin...
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brittle lake
Can someone tell me how the equation at the bottom simplifies to the one at the top?
brittle lake
Are you just able to take the square root of something and multiply it without consequence?
like
brittle lake
Can someone tell me how the equation at the bottom simplifies to the one at the ...
I thought this could only happen if 4-x^2 wasnt square rooted on the outside
if that makes snese
prob not
does it
ocean whale
Can someone tell me how the equation at the bottom simplifies to the one at the ...
Because $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$
ocean sealBOT
CaptainNova22
brittle lake
thank u
ocean whale
So $\sqrt{4 - x^2} \cdot \sqrt{1 + \frac{x^2}{4-x^2}} = \sqrt{(4-x^2) \cdot \left(1 + \frac{x^2}{4-x^2}\right)}$
brittle lake
makes sens
ocean sealBOT
CaptainNova22
ocean whale
makes sens
Just a basic exponent rule
lone heartBOT
brittle lake
.reopen
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✅
stiff falcon
Yes 🙂
brittle lake
how do i deal with the sqrt{1+e^x}?
tight pier
how are you canceling out?
tight pier
tight pier
but you have a double square root
brittle lake
Can someone tell me how the equation at the bottom simplifies to the one at the ...
arent what i doing
the same as that
ocean sealBOT
ocean sealBOT
brittle lake
ah i see
didnt know i could do that
I did make a mistake because I forgot to carry the squared from above
But assuming this is correct where would I go from here?
How do I rid of the square root
tight pier
but how did the x get down
ocean sealBOT
tight pier
agreeable, right?
brittle lake
yes
brittle lake
thaknkthasfasf
tight pier
thank
lone heartBOT
brittle lake
https://www.youtube.com/shorts/OUGDlKnRLOI
idk what this is btw
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willow stone
Hey guys, I'm stuck to this point. How old i solve?
lone heartBOT
Hey guys, I'm stuck to this point. How old i solve?
modest robin
modest robin
Hey guys, I'm stuck to this point. How old i solve?
Wolfram says you need to use the lambert W function (the inverse of xe^x if I remember correctly) to explicitly solve for y in your equation.
Anyway, sometimes you can't solve for y with elementary functions in ODEs, you get implicit equation for y like the one you have here.
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ionic vale
Which of the following is the Lewis structure for CO2? - Anyone know if this is A or D?
jagged cobalt
pallid scarab
Which of the following is the Lewis structure for CO2? - Anyone know if this is ...
many ways to solve this. One way is to just count the amount of valence electrons for each atom and see if it matches
simply looking at the carbon atom is enough here
pallid scarab
https://discord.gg/eexdsFw
For future chemistry questions though, I invite you to go in the appropriate network server linked here
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alpine sable
Which of the following is the Lewis structure for CO2? - Anyone know if this is ...
İts d
pulsar badge
Start by separating the fractions, then perform Euclidean division, and finally calculate the integral of each term individually.
junior vigil
y(y^2-17y+72)
wary fable
y(y-8)(y-9)
brittle lake
THis might be a dumb question whcih it is but can someone explain to me how you would realize this is a perfect square
brittle lake
(the left part)
tacit arch
factor out 4x^2 from the denominator in all terms
brittle lake
i see
hushed locust
a major clue is the fact that if you were to multiply out the two outside terms, you would get a constant
brittle lake
.close
small nimbus
delicate osprey
patent vale
probably should ping them
plain bronze
tryna see if for any vector b and a where the values are all eithere zero or one, this is true
plain bronze
this is also equivalent to asking for a proof that for any number in base 2, there is a different number that when added to the sum of its own digits, equals the original base 2 number
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plain bronze
<@&286206848099549185>
covert galleon
I think it works for n >= 2
For a = (10)_2, there exists b=1
For a = (11)_2, there exists b=(10)_2
Wait, it doesn't work for $a = (100)_2$
ocean sealBOT
timuko
covert galleon
@plain bronze
plain bronze
oh hello
uh
@covert galleon the problem was to prove that for any number in base 2 (b in our case), there is a number in base 2 (a) such that a + the sum of the digits of a is equal to b
so Im not sure how you showed that it was not possible
covert galleon
I couldn't find examples for number (100)_2 = 4 on the left side
plain bronze
Oh, i realize
the problem is different than what i just said
@covert galleon the problem is to prove that for any number in base 2 (b in our case), there is a number in base 2 (lets call it a) such that the number, ignoring its first digit + the sum of the digits of the number is equal to b
so in our case we can use (11)_2
wait
no, we can use 110
.close
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alpine sable
The resultant force acting on the support shown in (Figure 1) is to be 1600 lb directed horizontally to the right.
Determine the magnitude of the force F
in rope A
.
Determine the corresponding angle θ
.
Express your answer in degrees.
alpine sable
alpine sable
can i ask why
wild umbra
900 cos 60 would be the blue component, but we need the red one which will be 900 cos 30
alpine sable
so both of them are 450 sqrt(3)?
alpine sable
900 cos 60 would be the blue component, but we need the red one which will be 90...
i see okay
but that would mean both are 450 sqrt(3)
wild umbra
which one is the second one?
you have to make two equations-\
$F\cos\theta+900\cos 30 = 900\
F\sin\theta=900\sin 30$
ocean sealBOT
yajat
alpine sable
you have to make two equations-\\
$F\cos\theta+900\cos 30 = 900\\
F\sin\theta=90...
900cos30 = 900?
im confused
wild umbra
900cos30 = 900?
where did i write that?
alpine sable
wild umbra
i mean there's F cos theta as well???
alpine sable
but why does it equal 900
wild umbra
yea since resultant force in y direction is 0
alpine sable
yea since resultant force in y direction is 0
what about the other question
im lost on that too
finding theta
<@&286206848099549185>
rich light
you have two relations, Fcos theta = 900 - 900 cos 30
and F sin theta = 900 sin 30
is there a way to solve for theta?
alpine sable
is there a way to solve for theta?
there is not
rich light
is there a trig identity involving sin and cos that you think may be helpful?
wild umbra
you have two relations, Fcos theta = 900 - 900 cos 30
and F sin theta = 900 sin ...
"Fcos theta = 900 cos 30" how?
rich light
"Fcos theta = 900 cos 30" how?
mb, misread your image up there
Fcos theta = 900 - 900 cos 30
alpine sable
is there a trig identity involving sin and cos that you think may be helpful?
i dont think so
rich light
try sin^2 + cos^2 = 1
is there a way we can manipulate the two equations given above to have that form?
alpine sable
move to one side
rich light
that is true
rich light
however, we currently only have sin and cos, not sin^2 + cos^2
alpine sable
square it all?
rich light
yes
alpine sable
but how would i get 1
rich light
no, this would not eliminate theta
we need something of the form sin^2 + cos^2, which we can then equate to 1, eliminating theta, one of the unknown variables
notice how we have sin^2 in the first equation and cos^2 in the second equation
how we would bring them together?
rich light
the two equations are not equal to each other
try adding the two equations to each other
alpine sable
im sorry i cant visualize this
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@alpine sable Has your question been resolved?
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junior kraken
Hii
junior kraken
it doesn't
Ik it doesn't
modern pagoda
I want help with that too. How do u even begin to solve something like that
wintry wadi
I think they meant + instead of multiply
so sqrt(5), sqrt(5 + sqrt(5)), sqrt(5 + sqrt(5 + sqrt(5))), ...
junior kraken
But how do I find the value of the series
fierce cipher
what
prime badge
yeah it works with +
mortal trellis
assuming that it does exist you can use the self-similarity of the expression and get an equation x = (something in terms of x)
junior kraken
I think they meant + instead of multiply
so sqrt(5), sqrt(5 + sqrt(5)), sqrt(5 +...
Ah I see !
mortal trellis
but you first have to show that it does indeed converge
junior kraken
but you first have to show that it does indeed converge
For the + sequence right ?
fierce cipher
you need to show a_n converges then you can show the series converges next
junior kraken
you need to show a_n converges then you can show the series converges next
a_n should tend to 0 for the series to converge, right ?
fierce cipher
... no, it just need to tend to L
junior kraken
I think they meant + instead of multiply
so sqrt(5), sqrt(5 + sqrt(5)), sqrt(5 +...
As sepdron said, if we assume that I think then the series converges
fierce cipher
dont mix things up
sorry
little drum
$a_k = \underbrace{\sqrt{5 + \sqrt{5 + \sqrt{5 + \cdots }}}}_{k \text{times}}$
ocean sealBOT
fierce cipher
LMAO
junior kraken
$a_k = \underbrace{\sqrt{5 + \sqrt{5 + \sqrt{5 + \cdots }}}}_{k \text{times}}$
Thanks everyone!!!!
little drum
Uh, do you also need help proving it's convergence?
It's monotonic increasing so you should be able to use MCT
junior kraken
Uh, do you also need help proving it's convergence?
Yeeah
junior kraken
Uh, do you also need help proving it's convergence?
THE sequence has a upper bound
So it does converge right ??
little drum
Yeah
junior kraken
Else how can we do it ?
junior kraken
```A monotonic sequence will converge if it's bounded```
Ohh !
Thank you so much !
Another q
When we solve for the upper bound
Is it possible in some cases both roots of the quadratic equation is positive
?
I gtg, will close the channel as of now !
Ty ,everyone again !
.close
lone heartBOT
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leaden zenith
Im trying to know how much % of souls% im gaining because when i get that is +10% +21% +31% and so on, but when you have 110 and after that you add again the 10'68% is not a real 10'68% it would be less and less each time for the same reason that is different if you have 400% and you add a +2% it would be 402% not a real 2% but i dont know how to calculate that
leaden zenith
On the table that says Souls% is adding to 100% like it would be +110'68% not only 10'68%
lone heartBOT
@leaden zenith Has your question been resolved?
leaden zenith
I just noticed i pinged a guy named helper and not the helpers tag 😭
alpine sable
.reopen
lone heartBOT
@leaden zenith Has your question been resolved?
leaden zenith
<@&286206848099549185>
Or i dont know im trying to figure it out if i can put it in a graphic to understand it better and play with the numbers to find what i want
But im pretty sure there's a way to know it TT
leaden zenith
Is fine dw
static arch
Could you elaborate on a bit on table
leaden zenith
Ill put it on another way with less numbers
static arch
What exactly you need?
static arch
Ill put it on another way with less numbers
I find the names confusing
Not the numbers tbh
leaden zenith
Imagine you have 400% and you add +2%
Would be 402% but is not a real 2% of the number
static arch
Okay
leaden zenith
I want to calculate how real is the % im adding when i add more and more
As higher the number will go the real% will be lower
static arch
Okay
leaden zenith
But i dont know how to TT
static arch
Percentage is calculated by principal * (percentage+100)/100
Its just that but if you could give me a example of your values
I would be able to tell you exactly how it is applied
leaden zenith
The examples are the table
When i start i have 110,68%
And the next one will be 121,36%
It always att 10,68% but the problem is that number is not real on the % you have of the number each time you're adding less and less
To the point I reach for example 1000% and i add 10% that is like a 1% of total and it always go lower
static arch
10,68% implies what
leaden zenith
I want to know how much i lose value of the number for each time i add the 10,68%
static arch
Its 10 at 68% ?
leaden zenith
Its a calculation i made of the raw bonus% you get from that and the souls per achievement you get
This would be the entire table
static arch
It means 10.68% ?
leaden zenith
It means 10.68% ?
10'68% is when you summ all the soul bonus and the souls per achievement
static arch
I will try to answer your question by looking at values but i honestly don't follow
leaden zenith
What part you dont follow?
static arch
To the point I reach for example 1000% and i add 10% that is like a 1% of total ...
Oh you made it so complex when explaining
Let me write on paper an explanation
leaden zenith
Sure
static arch
To the point I reach for example 1000% and i add 10% that is like a 1% of total ...
Is it that each time you add percentage (assuming each time 10) you receive a constant increment?
leaden zenith
Noup
Always you add a percentage you decrease the value of the % from the initial %
static arch
@leaden zenith i am sorry if i am taking too long but what the heck does commas in the table mean
It should be whole numbers or decimals
leaden zenith
Just look the first image i sent TT
static arch
Im trying to know how much % of souls% im gaining because when i get that is +10...
This too ks like 10,68%
leaden zenith
Yes
static arch
<@&286206848099549185>
leaden zenith
I just want to know if there's any way to calculate how much loss you have from each time you do a % on something again and again TT
stable cove
It always att 10,68% but the problem is that number is not real on the % you hav...
Ah, you mean you want to figure out what % of the new total is being added?
leaden zenith
I want to figure out what % of the new total i lost
stable cove
$(100+10.68)^n-(100+n*10.68)$
static arch
$(100+10.68)^n-(100+n*10.68)$
So that was just 10.68??
I was so confused to see the comma
static arch
Please take over, i will just stalk the channel
leaden zenith
Thats it? :0 that way you can know how much you lost from how much you had before?
Let me check its kinda cool ngl
stable cove
However this would be % of the initial amount
If you want it as a percent of the new amount...
$\dfrac{[(100+10.68)^n-(100+n10.68)]*100}{(100+n10.68)}$
If i'm not mistaken
leaden zenith
n is how much times you do it right?
leaden zenith
Let me try to put it in excel so he does it
stable cove
Hold on, silly mistake
leaden zenith
Okay dw
ocean sealBOT
A miscellaneous Fern
stable cove
There we go
ocean sealBOT
A miscellaneous Fern
leaden zenith
And it would be 100% or 1?
stable cove
You know what.
leaden zenith
Because i was having crazy numbers ngl
stable cove
to avoid having to be concerned about what gets interpreted as a percentage and how
Let's just do it the right way
leaden zenith
But before all of that its giving me strange numbers D:
stable cove
$\dfrac{[1+0.1068]^n-(1+n0.1068)}{(1+n0.1068)}$
ocean sealBOT
A miscellaneous Fern
stable cove
Thats its for the formula that shows how much i lose right?
Yes.
It (should) be the percentage that is "lost"
Due to the bonuses stacking additively instead of multiplicatively
stable cove
In what way?
leaden zenith
Its adding exponentially
stable cove
Yeah.
stable cove
This is comparing it, at each step, to having added 10% multiplicatively in each previous step
If you want to find the loss only step by step...
leaden zenith
I thought we were losing like 9'3% and 26% not 0'93% and 2'6% respective
stable cove
If you want to find the loss only step by step...
$\dfrac{[1+(n-1)0.1068]*(1+0.1068)-(1+n0.1068)}{(1+(n-1)0.1068)}$
ocean sealBOT
A miscellaneous Fern
snow geyser
,help
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leaden zenith
**A miscellaneous Fern**
Hmm what do you mean step by step?
stable cove
Right, so.
leaden zenith
Like in the step 3 would only check the step 2?
stable cove
The first time we add 10.68%, there's no loss
leaden zenith
Gotcha
stable cove
The second time, we're losing some due to the fact that we're adding 10.68% of the initial amount, instead of 10.68% of 110.68%
leaden zenith
Right
stable cove
The next time we do it, we're incurring two losses
Because the "correct" amount would not only multiply by 10.68%, it'd be working with a higher number from the second step
The multiplicative approach increases more and more with every step
leaden zenith
Yes i understand that