If k=0 it tells you 0+0=0, so it tells you nothing
#help-26
ruby tree
cinder oxide
so it would be wrong to say [k k k] = x+y=1 because it doesn't take into account the domain restriction, k cannot equal 0
ruby tree
I mean you can still continue when k=0, it just won't give you the same solutions
It gives you a different matrix
Yes a row like [k k k] means that either x+y=1 or that this row contributes nothing
cinder oxide
one unique solution: k = 0
infinitely many solutions: k = -4
is this the correct answer to this question?
there are no other answers?
if there are I will scream lol
ruby tree
There are
cinder oxide
cinder oxide
There are
but only for the infinitely many solutions?
unique solution is correct? k=0
ruby tree
What's incorrect is that the matrix also has solutions for other values of k
cinder oxide
unique solution is correct? `k=0`
^
that's the only answer to the unique solution right? when it's unique, there can only be one answer for k variable?
i just want to make sure on that part first
before I move on to the cluster___ of infinitely many solutions
thorny flameBOT
ruby tree
,w kx+y=-2, 4x-y=2, k=2
thorny flameBOT
ruby tree
,w kx+y=-2, 4x-y=2, k=pi
thorny flameBOT
cinder oxide
oh we are back to the (0,-2) again
no matter what k =
we always get that
,w kx+y=-2, 4x-y=2, k=-4
thorny flameBOT
cinder oxide
k=-4 does not give exact values for x and y
ruby tree
Correct
cinder oxide
k = -4 is the only value of k that will give the answer as another equation, right?
ruby tree
Correct
ruby tree
You can plug in infinitely many values for x and get a corresponding y so of course it's correct
cinder oxide
OK
ruby tree
If k = -4 you have a system of 2 identical linear equations with 2 unknowns, so really just one linear equation with 2 unknowns, so just a line, which is infinitely many solutions
If k =/= -4 you have a system of 2 linear equations with 2 unknowns, so one unique solution
cinder oxide
can what you just explained above, be described from looking at this matrix alone?
this is as best as I could make the matrix, in RREF form
to be as clear as possible
if k = 1, for example
wouldn't Row 1 indicate:
x = 0?
ruby tree
No, that just means y = -2 and [k = 0 or x = 0]
cinder oxide
so it's not helpful to get the matrix into RREF for this question?
let's just say k = 1 for a sec
I will re-write it
ruby tree
Ok I missed something
When you do k/(k+4) R2 -> R2, you also exclude k=0
Kind of
Because the operation would be 0*R2 -> R2 which is invalid
ruby tree
I'm talking about the last step
cinder oxide
then I multiplied by -1/5
oh
eek yeah
mb
yeah no matter what
we are gonna end up with (0,-2) for the last column
so that is a UNIQUE solution
x = 0
y = -2
but now let's try k = -4
not sure if that third matrix is necessary
if I EVER see a row of 0's, or a column of 0's..
I think that's a good indicator, right? we have infinite solutions
ruby tree
Yes well the third matrix just gives you x = 1/2 + 1/4 y
cinder oxide
interesting how k = -4 lines up for domain restriction
yet k = -4 is what gives infinite solutions
i guess because when k=-4 you get 0, and you can't divide by 0
this is interesting insight though. just because a variable's value provides domain restriction, does not mean it is impossible to use for solution(s) to the system of equations
ruby tree
I'm not sure what you mean by domain restriction
cinder oxide
if I EVER see a row of 0's, or a column of 0's..
this is not true?
I see cat emoji thinking about it
ruby tree
Not mine
cinder oxide
@vernal matrix?
cinder oxide
if I EVER see a row of 0's, or a column of 0's..
I need to make sure on this
column of 0's, I will assume, yes. always infinite solutions for that variable
ruby tree
I believe that if you have a square matrix before augmenting it, and you get a row or column of zeroes when reducing it, then you end up with either infinitely many or no solutions
cinder oxide
column of 0's, I will assume, yes. always infinite solutions for that variable
for row of 0's, does it depend on context?
vernal matrix
<@788085606483361802>?
Well be a bit careful: there are situations where you may have e.g. a row of zeros and yet a (0, …, 0 | 1) row, which would be a no solutions
cinder oxide
Well be a bit careful: there are situations where you may have e.g. a row of zer...
you mean after a row operation you turn 0 0 0 0 into 0 0 0 1?
vernal matrix
Similarly a column of zeros may not mean you don’t have a “0=1” column ofc
cinder oxide
Well be a bit careful: there are situations where you may have e.g. a row of zer...
OH. so it's whatever is lowest
I will illustrate
vernal matrix
you mean after a row operation you turn 0 0 0 0 into 0 0 0 1?
No as in when you reduce you could have one of those rows, even if you have a row of zeros
cinder oxide
even though there is a row of 0's for the third matrix
it's still no solution because of 0 0 0 1
so the no solution takes precedence?
I think I get it, doesn't matter what the numbers in the top row are. if I ever see a row like this 0 0 0 1 on an augmented matrix that's a clear indicator that there is no solution
vernal matrix
so the no solution takes precedence?
Yep pretty much was my point 
cinder oxide
ty
cinder oxide
Yep pretty much was my point <:SCgoodjob2:750436894915166321>
lol, is this your website? https://nohello.net/
typical Keith...
vernal matrix
lol, is this your website? https://nohello.net/
Nope not mine, someone else’s 
north sparrow
help
topaz sinewBOT
@north sparrow Has your question been resolved?
north sparrow
<@&286206848099549185>
shadow olive
Actually you do not differentiate with respect to radius, try differentiating with respect to time instead, since that is what is given in the question
The rate of decreasing radius, which means: dr/dt (where r = radius)
In a crux, differentiate V = (4/3) pi r^3 w.r.t time,
You'll get,
dV/dt = (4/3)pi * 3r^2*(dr/dt)
Then simply put the values @north sparrow
north sparrow
In a crux, differentiate V = (4/3) *pi* r^3 w.r.t time,
You'll get,
dV/dt = (4/...
yeah and dr/dt = -3
4/3 * pi 3r^2 (-3) = -12*pi*r^2
r @ t=25 is 25 so dV/dt = 12*25^2*pi right?
thats what i got
and it says its wrong
@shadow olive
shadow olive
yeah and dr/dt = -3
4/3 \* pi 3r^2 (-3) = -12\*pi\*r^2
r @ t=25 is 25 so dV/dt =...
Yeah that should be it though
I don't think we missed anything?
what was your final answer?
value?
north sparrow
what was your final answer?
-12*pi*25^2 = -7500pi
shadow olive
yeah I'm getting the same value
hmm
lemme try it
do you know the answer though?
As in a reference?
@north sparrow
I think you gotta use integration on this one
north sparrow
do you know the answer though?
sadly no
shadow olive
And the function you get from there, you gotta put it in the equation
north sparrow
I think you gotta use integration on this one
integrate r you get r = 100-3t
doesnt help except for finding r at t= 25
also the syllabus hasnt done integration yet but ik how to do it
shadow olive
integrate r you get r = 100-3t
did you put the function into the volume equation, or simply put the value of t to get r?
and then used that r in the volume equation
north sparrow
did you put the function into the volume equation, or simply put the value of t ...
i found the value and then substituted but it should be the same
north sparrow
V = 4/3 pi r^3
V = 4/3 pi (100-3t)^3
dV/dt = 4/3 pi * 3(100-3t)^2 * -3
dV/dt = -12 pi (100-3t)^2
= -12pi*25^2 = -7500pi
same answer
north sparrow
Is the answer : 23571.428
ahould be negative
north sparrow
nah they need exact form
shadow olive
Yes that is the only answer you can get!
north sparrow
prob webwork being dumb
shadow olive
If you need the exact then
23,571.428571428571428571428571429
LOL PUT PI
Yeah the answer is same, I checked it on the internet as well
Oh it's 23561 not 23571
try checking it again
worked?
cyan mesa
,calc 7500pi
thorny flameBOT
Result:
23561.944901923
it worked 💀
stupid ass webwork
“ExaCt ForM” 🤓 until it just isnt
north sparrow
thanks
neon iron
topaz sinewBOT
neon iron
Is C's plot simply a circle, with center coordinates (T, 0) and radius a?
main shale
yes
main shale
you can see visually on the diagram that that isn't the case
neon iron
you can see visually on the diagram that that isn't the case
Am I supposed to plot this in 3D?
neon iron
as you've said, it's just a circle with centre (T,0) and radius a
Right, and it becomes a 3D solid when I rotate about the y-axis, as indicated in (b)?
main shale
yes
neon iron
yes
Oh, makes sense, rotating turns it into a donut
As for question (b), I need to use $V = \pi\int (R^2 - r^2) \dd x$, correct?
thorny flameBOT
Cash
main shale
I'm a bit rusty on shell integration, but that looks like the disk integral formula
and not shell
neon iron
you don't square stuff in shell integrals so I don't think that's quite right?
Not shells, disk
(b) is asking me to use disk
And (c) shells
main shale
looks good
that 4 looked a bit like an A to me though lol
was confused for a second
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
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Available help channel!
cinder oxide
topaz sinewBOT
cinder oxide
why is this true for matrix multiplication?
isn't it possible to get a different result?
if you multiply BC first, or AB first
cinder oxide
that doesn't affect the answer in the end at all?
either way you will get the exact same [2x1] matrix?
strange whale
yes
cinder oxide
no matter if it's 2x10 or 2x3 during the process
wow
which of these would be easier to calculate?
both would involve the exact same amount of work?
A(BC) compared with (AB)C
drifting swift
cannot say without knowing what matrices A, B and C are
cinder oxide
just based on the sizes
drifting swift
there cannot and will not be one definitive answer as to which option is always easier
cinder oxide
looks like same work involved
but yeah, depends on how many zeros maybe
for each combination
I think (AB)C = (2x3[10x1] = [2x10][10x1]
would be easier
drifting swift
ok like
cinder oxide
because [2x10][10x1] is less work than ([3x10][10x1])
drifting swift
multiplying two matrices of dimensions m by n and n by p together
how many operations is that gonna involve
cinder oxide
how many operations is that gonna involve
depends on the size of the n-tuples
drifting swift
each of the mp entries in the product arises from the dot product of two vectors of size n, each of which requires n multiplications and n-1 additions
so overall you have
- mnp multiplications
- mp(n-1) additions
now if we have the product of three matrices, A [m by n] * B [n by p] * C [p by q]
doing it with AB first gives:
- mnp multiplications
- mp(n-1) additions
then multiplying AB [m by p] by C [p by q]: - mpq multiplications
- mq(p-1) additions
while doing it with BC first:
- npq multiplications
- nq(p-1) additions
and multiplying by A: - mnq multiplications
- mq(n-1) additions
so treating multiplication as the more costly operation
we are comparing mnp + mpq vs mnq + npq
mp(n+q) vs. (m+p)nq
im not sure there even is any clean condition that would ensure one is greater than the other
also this entire thing has an air of "who gives a shit" around it
it really doesn't matter
cinder oxide
OK
drifting swift
don't try to memorize a million rules for what's easier when
cinder oxide
drifting swift
just do whatever
drifting swift
so brackets don't really matter for multiplying matrices
easily misinterpretable.
cinder oxide
they do matter for distribution
but when no addition or subtraction is involved
only multipliplication
the brackets are basically pointless
cinder oxide
as I have illustrated above
drifting swift
sure.
cinder oxide
this is true for matrix multiplication, in same order of matrices
and scalar multiplication, in same order of matrices, but the scalar can go anywhere
.close
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sonic bone
why not tan^2(x)-sec^2(x)
topaz sinewBOT
why not tan^2(x)-sec^2(x)
sonic bone
.close
modern nexus
Hi, can someone explain why the gradient here is equal to 0?
topaz sinewBOT
Hi, can someone explain why the gradient here is equal to 0?
modern nexus
is it because there are multiple ways of going the direction of greatest increase in f
topaz sinewBOT
@modern nexus Has your question been resolved?
mellow zenith
hello
mellow zenith
i have a problem understand how the operations over the derivative notation dy/dx work
i've just started looking at DEs
and the first thing i'm learning is seperable DEs
and the video states that the way to solve them is by seperating x's and y's then multiplying both sides by dx then integrating
but i didn't know that it's even possible to do it with the notation
vernal vale
this is usually a thing you just plug your nose and do, fwiw
similarly to the chain rule thing of expanding the fraction
if you did that in calc iii
mellow zenith
this is usually a thing you just plug your nose and do, fwiw
what are other possible operations to do
and is it actually always true
or just related to this type of DEs
and is there a simple way to understand why is it possible to do such thing with the notation
vernal vale
its helpful to think of dy/dx as a fraction in the context of separable equations because its suggestive of the operations you need to do to get a solution
vernal vale
and is there a simple way to understand why is it possible to do such thing with...
well, its kind of a fraction right
i mean its the limit of a fraction
mellow zenith
how is that
vernal vale
quotient definition of a derivative
vernal vale
for single variable functions its equivalent
mellow zenith
quotient definition of a derivative
ik lim f(x) - f(a) / x -a as x approaches a is f'(a)
mellow zenith
i mean its the limit of a fraction
by this do you mean something like [lim y2-y1 / lim x2-x1]
vernal vale
by this do you mean something like [lim y2-y1 / lim x2-x1]
idk if its helpful to you to think of it that way
i was thinking of this
mellow zenith
ok nice but
what does dy represent and dx represent
so i can get what are the other operations that i may be able to apply
vernal vale
theyre differentials
vernal vale
so i can get what are the other operations that i may be able to apply
the only two that come to mind are chain rule and separable equations to be honest
mellow zenith
theyre differentials
isn't x just the variable we are diffentiating the function y wrt to
so how can we define it's "derivative"
vernal vale
yes
so really loosely you think of dx as a tiny change in x
and dy as a tiny change in y
so it should seem reasonable to write f' = dy/dx
how y changes as you change x
over a tiny tiny tiny interval
mellow zenith
so it should seem reasonable to write f' = dy/dx
i sort of get it now
i have another question if you don't mind
if we say like y=x^2
and we want to evaluate dy/d(x^2)
how can we do it and is there like a name for such things
vernal vale
theres nothing super special about the notation here
other than that it like
it can be a tool to help suggest how to work with things
but its easy to confuse the notation with the actual machinery or concepts
mellow zenith
yea i moved from using f' in math to using dy/dx in physics and i'm messing it up
vernal vale
there is tons and tons of calculus notation and its just a tool to help make whatever youre doing easier
mellow zenith
ill give it a go and try to fully understand the notation
thank you so much for your help brother
vernal vale
for sure
dont worry about it too much
theres a lot of other stuff to worry about in ODE
mellow zenith
.close
glad mango
Here is a physics question that i would love to know if i solved correctly:
An object is thrown vertically with initial velocity of 15m/s. At what height y, does its speed half.
Here is what i wrote:
Vo = 15m/s
Vf = 7.5m/s
t= ?
deltaY = ?
First, find the t:
Vf = Vo + at
7.5 = 15 + (-10)t
7.5 - 15 = -10t
(7.5-15)/-10 = t = 0.75
So from here, we find deltaY
deltaY = Yo + Vot + 1/2at^2
deltaY = 0 + 15 * 0.75 + 1/2 * (-10) * 0.75^2
deltaY = 11.25 - 2.8125
deltaY = 8.4375
topaz sinewBOT
Here is a physics question that i would love to know if i solved correctly:
An o...
@glad mango Has your question been resolved?
topaz sinewBOT
@glad mango Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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mild island
if p(θ) is the point at te intersection of the terminal arm of an angle θ and the unit circle, deterine the exact coordinate of p(3π/4)
topaz sinewBOT
if p(θ) is the point at te intersection of the terminal arm of an angle θ and th...
acoustic pecan
do you know polar coordinates?
acoustic pecan
hm dont worry about it then, have you drawn a diagram
mild island
no
acoustic pecan
we'll just do it the triggy triangle way, though its the same thing
mild island
how
acoustic pecan
its a circle of radius 1 centred at the origin (unit circle)
theres a line that makes an angle of 3pi/4 with the positive x axis that intersects that circles boundary - from the origin
mild island
so i use x^2=y^2=1
acoustic pecan
not really, that wont help unless you know either x or y
mild island
oh
acoustic pecan
its a circle of radius 1 centred at the origin (unit circle)
theres a line that ...
for now just try draw this
acoustic pecan
if you want to
mild island
i dont undertsand lol what
topaz sinewBOT
@mild island Has your question been resolved?
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real finch
Translated it says: 16. A cylindrical tank whose diameter measures 4 times squared root(3) and its height is 12 its five-sixths with wine. From its normal position, the tank is tilted until the wine is about to fall over the edge. Calculate the measure of the tilt angle.
topaz sinewBOT
Translated it says: 16. A cylindrical tank whose diameter measures 4 times squar...
real finch
I got 60 degrees by using triangles at both the wine's angles respect to the tank and the angle of the tank to the floor and measuring the length of both triangles (both being right triangles so it can be a special right triangle) and got 60 as a result
Just wanted to know if it's the answer and if there is another method with a faster way to get to the answer
topaz sinewBOT
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@real finch Has your question been resolved?
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neon iron
Translated it says: 16. A cylindrical tank whose diameter measures 4 times squar...
spanish right?
are you from spanish speaking country?
real finch
Yeah, but I understand quite well english so there is no problem if you don't talk spanish
topaz sinewBOT
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topaz sinewBOT
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Available help channel!
molten vine
Why when f is a linear mapping $\ f:E\to F \f(u_1)=f(u_2) \Longrightarrow f(u_1)=f(u_2)=0_F$
topaz sinewBOT
Why when f is a linear mapping $\\ f:E\to F \\f(u_1)=f(u_2) \Longrightarrow f(u_...
thorny flameBOT
Adam Chebil
molten vine
molten vine
where have you seen that ?
if that's not true then why: we prove that Ker f = {O} to prove that f is injective*
strange whale
injective you mean
molten vine
yeah srry
strange whale
it's not hard to show Ker f = {0} is equivalent to f injective
molten vine
So it's possible to have $f(u_1)=f(u_2)\neq 0_F$ where $u_1\neq u_2$ ??
thorny flameBOT
Adam Chebil
strange whale
yeah why not
consider T(x, y) = (x, 0)
(1, 1) and (1, 2) have the same image through T
and that image is not 0
molten vine
T is linear mapping ??
reef stratus
Hello how do i do this question?
topaz sinewBOT
Hello how do i do this question?
reef stratus
I dont even know where to start.
potent nova
Do you know how to complete a square?
topaz sinewBOT
@reef stratus Has your question been resolved?
reef stratus
start by computing (m+6)^2
-6, 2 ?
reef stratus
m^2 6m 6m 36
clear lodge
and the signs?
you now have:
$m^2+12m-5 = m^2+12m+36+TRIANGLE$
What does TRIANGLE need to be for it to be equal?
thorny flameBOT
LordFelix
topaz sinewBOT
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warm kiln
topaz sinewBOT
tawny spade
I think the best thing to do here is the factorial approximation formula
Stirlings formula
warm kiln
then what test would i use after?
tawny spade
Root test
remote basin
topaz sinewBOT
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toxic aspen
Could someone explain what the difference is between lg, ln and log?
toxic aspen
and how do i change between them?
flat kindle
drifting swift
lg and ln are often used as abbreviated notations for log_10 and log_e respectively.
neon iron
Could someone explain what the difference is between lg, ln and log?
They are all logarithms with different bases
neon iron
What are their bases?
Lg is log_10
Ln is log_e
toxic aspen
Okay so
if i for example wanted to go from lgx to lnx
I would do
$\frac{lg(x)}{ln(x)}$
thorny flameBOT
Merineth
ruby tree
$log_b(x) = \frac{\log_a(x)}{\log_a(b)}$
thorny flameBOT
Nel
neon iron
$\log_{b}a = \frac{\log_{c}a}{\log_{c}b}$
keen matrix
$\log_{a}(x)=\frac{\ln(x)}{\ln(a)}$ is a special case
thorny flameBOT
PajamaMamaLlama
keen matrix
of the chanse of base formula
ruby tree
You have a special case where a = e
keen matrix
we can generalize it
toxic aspen
ruby tree
If you want to go from log_10 to log_e, that's
$log_e(x) = \frac{\log_{10}(x)}{\log_{10}(e)}$
thorny flameBOT
Nel
ruby tree
You divide by the log with the current base of the target base
toxic aspen
I'm super confused
Why is it a special case?
and how do i go from lg to ln
lg(x) = log10(x) ???
ruby tree
Yes lg is log_10
toxic aspen
**PajamaMamaLlama**
this?
ruby tree
Ask whoever made that table
thorny flameBOT
Merineth
toxic aspen
So this is how it's done?
ruby tree
Yes
toxic aspen
But that doesn't cover ln(x)
ruby tree
It does, ln = log_e
thorny flameBOT
Merineth
toxic aspen
So this would be the right answer?
toxic aspen
But that's not the right answer according to the answer in my book
change lg(x) to ln(x)
the answer is:
ln(x) / ln(10)
ruby tree
The answer to what?
toxic aspen
change lg(x) to ln(x)
ruby tree
Depending on how you read this, it can mean either going from lg to ln or going from ln to lg
If you want to substitute lg(x) with something that has ln(x) in it, then it's lg(x) = ln(x)/ln(10)
toxic aspen
Yes
lg(x) = ln(x)/ln(10) is the right answer
but i dont understand how to get there
toxic aspen
https://gyazo.com/78218bc842653de4460120287c861361
by using these
ruby tree
$\log_{a}(x)=\frac{\ln(x)}{\ln(a)} \implies \log_{10}(x)=\frac{\ln(x)}{\ln(10)}$
thorny flameBOT
Nel
toxic aspen
okayyyyyyyyyy
i get it nowww
That makes total sense
a becomes our desired base
which is 10
and since lg(x) = log10(x)
ruby tree
Yes
topaz sinewBOT
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wanton stirrup
I have to show the inequality is true but i stuck at itQQ
topaz sinewBOT
I have to show the inequality is true but i stuck at itQQ
wanton stirrup
$$\frac{2x}{\pi} < \sin(x) < x, \quad \text{for } x \in (0, \frac{\pi}{2})$$
thorny flameBOT
Yuuto☆チェラン
wanton stirrup
I think most likely i have to apply mean-value theorem but i cannot think of one good equation to solve this
round gust
divide by x i think
and find the minimum and maximum of sin(x)/x in 0<x<pi/2
or maybe you dont have to
bcuz sinx/x decreases in (0,pi/2)
wanton stirrup
But how do i know 2x/pi < sinx ??
plush glacier
Hello
plush glacier
Does anyone know how to solve no.6?
I think the answer is 500
But cant seem to know why
plush glacier
Is a = 2 and b = 3?
round gust
no
plush glacier
Ohh
round gust
if this doesnt work you gotta put in numbers in x until you find a pattern
because of f(3) = 4
fortunately f(x) = x+1
plush glacier
So these type of questions follow a pattern?
plush glacier
Its not something where you can derive a function and input any number into the function
?
round gust
assume f(x) is a polynomial
first
so f(x) = ax^n + bx^(n-1) + ....
use the given equation to find n
after that coefficients should come out easily
but there are questions where this is difficult
round gust
you need to find n first
plush glacier
Very sorry but I cant seem to find n
Would it be okay if you can demonstrate it for me?
round gust
f(x) + f(x+1) = 2x+3
its likely that n=1
because the result is a first degree polynomial
round gust
you dont need f(3)
f(x) = ax+b then
f(x) + f(x+1) = (ax+b) + (ax+a+b) = 2x + 3
2ax + a + 2b = 2x + 3
2a = 2
a+2b = 3
a=1,b=1
now if f(3)=4 then you can use this
which fortunately is true
plush glacier
Ohhh
So if we plug in a and b into f(x) = ax + b
Then it becomes f(x)= x + 1 basically
Hence f(499) = 499 + 1
= 500
round gust
yes
plush glacier
f(x) = ax+b then
f(x) + f(x+1) = (ax+b) + (ax+a+b) = 2x + 3
In this line
How does f(x+1) be equal to (ax + a +b)?
round gust
a(x+1) + b
round gust
nice
plush glacier
Do you happen to know what kind of questions these are sir:
?
Like the topics?
Its because I am joining an online math challenge for the first time and I have zero experience
round gust
id say theyre related to sequences
plush glacier
The topics are familiar however the questions are kind of advanced and requires so much manipulation (like the first one)
Do you happen to know where I can start learning?
round gust
i would start with arithmetic and geometric sequences
and get used to recognizing patterns in given relations
by experiencing alot of problem solving
plush glacier
I understand I will start practicing noww
Thank you so much sir @round gust and I hope you can hel0 me again (if fate allows)
.close
raven comet
Help, i don't know why the answer of the book and mine are not the same. Where did I go wrong?
My final answer is 0.34 while the book says 0.11
topaz sinewBOT
Help, i don't know why the answer of the book and mine are not the same. Where d...
topaz sinewBOT
@raven comet Has your question been resolved?
raven comet
i just input it in the calculator, but my answer is not the same with the book
upbeat crypt
explain what u did
first
like explain
i just did it using calculater and the answer is 0.11555
i dont know where you failed
haughty hornet
I was given assistance the other day trying to find a formula to draw a shape based on some data but I think I'm messing up my Order of Ops on it possibly.
The original question is that I have 1000 points of Radius data of a shape from the center measured in mm. I need to convert that into X,Y coords to draw said shape in an application. The data is organized as just raw measurements sequentially of radii from the center.
The formulat I was given for polar representation (as they called it) is as follows:
for each number:
x = radius × cos(1.5pi − (n*pi)/500)
y = radius x sin(same angle)
for programming I have to split the OOO up and force them properly
for X I am doing npi (n is incremented by 1 per loop)
then dividing that by 500
then 1.5pi
then 1.5pi -angle
then Cos of that number
Cos * Radius and using that
for Y I am doing n*pi
then dividing by 500
then Sin of that
then * radius
I end up with pretty much a straight line at the end
topaz sinewBOT
I was given assistance the other day trying to find a formula to draw a shape ba...
@haughty hornet Has your question been resolved?
haughty hornet
<@&286206848099549185>
topaz sinewBOT
@haughty hornet Has your question been resolved?
placid drum
$\cos²x=1$
topaz sinewBOT
$\cos²x=1$
thorny flameBOT
Jash
thorny flameBOT
Jash
placid drum
so $\cos 2x=2(1)-1$
thorny flameBOT
Jash
rigid ivy
do i have to use double angle identity
To do what?
placid drum
To do what?
i need to solve for x
neon iron
what is the initial question pls ?
rigid ivy
i need to solve for x
Square root both sides
placid drum
in [0,2π]
neon iron
what is the question pls
placid drum
Square root both sides
but then you get ± and then it’s not a function
placid drum
what is the question pls
solve sin²x=1 for x in [0,2π]
neon iron
solve sin²x=1 for x in [0,2π]
ok ,
rigid ivy
but then you get ± and then it’s not a function
That is correct. You end up with two separate cases you need to solve for.
placid drum
doesn’t cos(2x)=1 tho
neon iron
placid drum
x=0?
placid drum
cos^2(π/2)=0 tho
neon iron
Now just find the particular values that fit in your interval
was i wrong ?
neon iron
solve sin²x=1 for x in [0,2π]
because this is the initial questio
maybe i should revise ...
rigid ivy
$\cos²x=1$
Are you solving for cos?
rigid ivy
solve sin²x=1 for x in [0,2π]
Or sin?
topaz sinewBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
rigid ivy
i was solving for (sinx)^2 = 0
Why
neon iron
Also
you are solving for (cosx)^2 = 0 ?
ah , ok , wait
i was solving for (sinx)^2 = 1
sorry
I'll solve for that
is it ok ?
topaz sinewBOT
neon iron
ok 👍
topaz sinewBOT
Available help channel!
vital pawn
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vital pawn
Where's my mistake?
vital pawn
I solved it using elliptical coordinates
topaz sinewBOT
@vital pawn Has your question been resolved?
topaz sinewBOT
@vital pawn Has your question been resolved?
topaz sinewBOT
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Available help channel!
pure frigate
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ivory wave
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@pure frigate Has your question been resolved?
pure frigate
catfan i watched the examples and still don't understand how to transfer it from nf to uf
neon iron
topaz sinewBOT
neon iron
His logic is that I is the only variable and the rest are constants
but how does he derive I without making everything 0
does he take everything else out of d/dt? how is that allowed? i feel like that cant be right
if someone can remind me of a property of a derivative thatd be great
rigid ivy
if someone can remind me of a property of a derivative thatd be great
You can move constants out of derivatives
topaz sinewBOT
neon iron
.reopen
topaz sinewBOT
✅
neon iron
You can move constants out of derivatives
ok wait wait
how is that true
if you have like d/dx [2x] u can just do 2 * d/dx [x] and get 2... oh fuck
what the shit
im so dumb
.close
astral blaze
topaz sinewBOT
astral blaze
domain is x element of all reals z is element of all reals and y is
0?
or all reals?
broken niche
or all reals?
all. It can be any value, they just all map to the same value (assuming x and z are the same)
astral blaze
all. It can be any value, they just all map to the same value (assuming x and z ...
uh can you give an example?
broken niche
f(1, 0, 1) = 1^2+1^2 = 2
f(1, ln(3)*sqrt(e)+7/3, 1) = 1^2+1^2 = 2
astral blaze
ahh
yeah i get it
for range
x is (0 to all reals)
y is 0
and z is (0 to all reals)
?
broken niche
range is the set of possible output values, so you do not need to separate x,y,z
broken niche
Can you get negative values as an output?
broken niche
Yeah
broken niche
Idrk how to explain it, but if I had to try I would say its the shape you get from taking a "slice" of the graph, which in this case is 4d, so you will get a 3d shape as a slice
and you can determine the shape by looking at the function
astral blaze
uhh
expand?
since
x is x^2
and z is x^2
oh wait a slice
let me check
my notes rq
astral blaze
and you can determine the shape by looking at the function
is it a cylinder?
a cylinder on the y axis?
broken niche
a cylinder on the y axis?
I don't think so. My reasoning is that f(x, y, z) changes as x and z change. If you wanted a cylinder along y, you would need something like a=x^2+z^2, where a is constant, because then you are forcing the distance to be a fixed value.
broken niche
Disclaimer: I am not 100% sure I know what it is, but I think you should consider that as x and z get bigger, f(x,y,z) gets further from the y axis
and this is at a quadratic rate
broken niche
Oh I think then it would be cylinder
supple rampart
Limit of [e - (1+x)^(1/x)][e - e^(sqrt(1+x))]/[e^(x^2) + sin(x^2) - cos(x^2)] as x tends to 0
seems like l hospital will complicate it, and it doesnt even seem solvable using it
topaz sinewBOT
Limit of [e - (1+x)^(1/x)][e - e^(sqrt(1+x))]/[e^(x^2) + sin(x^2) - cos(x^2)] as...
supple rampart
hey, this is my thread 🤨
vapid bolt
cyan mesa
$\frac{\left(e-\left(1+x\right)^{\frac{1}{x}}\right)\left(e-e^{\sqrt{1+x}}\right)}{e^{x^{2}}+\sin\left(x^{2}\right)-\cos\left(x^{2}\right)}$
thorny flameBOT
Combustion
cyan mesa
is that it?
supple rampart
is that it?
yeah thats it
cyan mesa
pain
supple rampart
yeah
strange whale
pain or taylor expansion
supple rampart
it looks tedious
supple rampart
pain or taylor expansion
whats that?
cyan mesa
pain it is
supple rampart
pain it is
pain as in using l hospital?
cyan mesa
guess so
supple rampart
how? it seems unsolvable. you get rid of the sin then the cos turns to sin in denominator
and in numerator you wouldn't be able to get rid of e as well
,w derivative of [e - (1+x)^(1/x)][e - e^(sqrt(1+x))]
thorny flameBOT
supple rampart
the fak
derivative of (e - (1+x)^(1/x))(e - e^(sqrt(1+x)))
maybe square brackets messed it up
,w derivative of (e - (1+x)^(1/x))(e - e^(sqrt(1+x)))
cyan mesa
probably yeah
thorny flameBOT
supple rampart
💀
cyan mesa
strange whale
,w lim x -> 0 ((e-(1+x)^(1/x))(e-e^(sqrt(1+x))))/(e^(x^2)+sin(x^2)-cos(x^2))
thorny flameBOT
strange whale
ofc it's not something like 0
supple rampart
I tried on wolfram alpha but it doesn't show steps
supple rampart
hm whats this taylor stuff just tell me definition or something and i'll try to apply it
supple rampart
I wouldn't even try w/o taylor stuff tbh
do you mean series for sin and cos
cyan mesa
oh shit you do know it
supple rampart
thats just e, no?
strange whale
but yeah it's series expansion
strange whale
sure
that doesn't tell you a lot of info though
expansions tell you what the functions look like around 0
supple rampart
oh shit you do know it
I didnt know tht term name
cyan mesa
it should be MUCH easier now
just expand e^x^2 , sin(x^2), -cos(x^2) and split the limit into 2 and those should be easy to l'hopital or something
strange whale
(1+x)^(1/x) = exp(ln(1+x)/x)
thorny flameBOT
supple rampart
too much effort for a twitter fight
strange whale
AH
cyan mesa
lmao
supple rampart
i mean not really a fight this guy is always posting ezpz geometry problems so i asked him to post calculus
then he gave that problem
cyan mesa
based
supple rampart
this is the type of shi he keeps posting
south tapir
topaz sinewBOT
keen thistle
idk wth is this linear algebra
grim violet
yes
keen thistle
no offense
grim violet
matlab 💀 
south tapir
matlab 💀 <:devastation:898725325335298088>
yeah lol
how to do exponential
is it the same as polynomial?
topaz sinewBOT
@south tapir Has your question been resolved?
topaz sinewBOT
@south tapir Has your question been resolved?
woeful depot
what's the trick to solve :
limpid mica
I have this transform and I need find the value if given other values. But im lost on how to find what the transform is
topaz sinewBOT
I have this transform and I need find the value if given other values. But im lo...
keen venture
I assume T is linear, because we wouldn't be able to solve this otherwise
That means there exists some matrix such that:
[a b][1] = [0]
[c d][2] [1]
And... Also does that with (-1,1) to (0,1)
.
Actually, nvm. It might be easier to get T inverse
I'll call that U. We have that:
U(1,0) = (1,2)
U(0,1) = (-1,1)
limpid mica
hm, i see. U is just the inverse transform?
topaz sinewBOT
Available help channel!
edgy cosmos
This mgiht make no sense but:
a) for a span in Rn that forms a line, all the vectors are a scalar multiple of each other right? (so in a ref form matrix it's rank 1)
b) For a span in Rn that forms a plane it would form a matrix thats rank 2?
c) And for a span that that is Rn the matrix is rank n?
edgy cosmos
For a/b does that only apply for r3 or?
topaz sinewBOT
@edgy cosmos Has your question been resolved?
toxic fjord
topaz sinewBOT
toxic fjord
i didnt know how to graph it so i used desmos
but im not sure why it goes up to 9
the y intercept is (0,8)
the x intercept is (-4,0) and (2,0)
the axis of symetry is -1
and the vertex is (1,5)
so why does the graph go up to 9 and curve like that
?
drifting swift
how did you get (1, 5) as the vertex
are you 100% sure you didn't fuck up your arithmetic at any point
toxic fjord
how did you get (1, 5) as the vertex
sub in -1 as x in the equation
toxic fjord
8 - (-2) - 1
wait
thats 9
erm
how did i get 5
oopsie
wait
i got axis of symetry is 1
toxic fjord
OH
oh yea
i messedup
now it makes more sense
wait
that means i was right the first time
flip
.close
bye bye
topaz sinewBOT
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empty fossil
If I have n^2-k objects, and k-2 boxes how many objects will each box atleast have in terms of n?
topaz sinewBOT
If I have n^2-k objects, and k-2 boxes how many objects will each box atleast ha...
empty fossil
2≤k≤n√2
long stirrup
none?
empty fossil
Why?
Maybe its important but n>2, and k and n are both integers
Wont the minimum be reached for k=n√2?
empty fossil
.close
neon iron
Please, is there a person to respond to me in #elementary-number-theory ? It is about the congruence
topaz sinewBOT
Please, is there a person to respond to me in <#418981682117345288> ? It is abou...
topaz sinewBOT
Please, is there a person to respond to me in <#418981682117345288> ? It is abou...
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@neon iron Has your question been resolved?
topaz sinewBOT
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hexed spindle
A ball is thrown, with a vertical distance (h meters) expressed by the formula h(t)=10t-t². where t represents time (in seconds). Draw the ball's trajectory and determine the time it takes for the ball to reach a height of 25 meters!
topaz sinewBOT
A ball is thrown, with a vertical distance (h meters) expressed by the formula h...
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@hexed spindle Has your question been resolved?