violet jetty
In this case the limit is just 1, so using 1 should suffice
#help-0
coral rune
lone heartBOT
lone heartBOT
Available help channel!
ivory eagle
How to factorise $28x - 35$
lone heartBOT
How to factorise $28x - 35$
ivory eagle
yes
vale wigeon
ok pull that common factor out then
ivory eagle
ok pull that common factor out then
$7 ( 4x - 5 )$
vale wigeon
how'd the plus sign end up a minus?
vale wigeon
ok there we go
ocean sealBOT
BrutalCandor
ivory eagle
Hmm this
ocean sealBOT
BrutalCandor
low mauve
When trying to factor a quintic equation over the rationals, If I rule out all linear and quadtratic factors, must I still check cubic and quartic factors?
low mauve
I would think that checking the linear and quadratic factors would also cover those cases
vale wigeon
if there was a cubic factor, the other factors would have a combined degree of 2
a quartic, 1
so no, you only need to check up to half the degree of the original rounded down.
lone heartBOT
@low mauve Has your question been resolved?
frail walrus
lone heartBOT
lone heartBOT
woven kestrel
u = cos3x -> du = -3sin3xdx -> -1/3du = sin3xdx -> -1/3 integral of e^u du
lone heartBOT
Available help channel!
alpine sable
bro
alpine sable
quick really quick
yes or no
i can still use bxhx1/2 for this triangle
it sounds really dumb ik
just yes or no
.close
lone heartBOT
patent vale
it sounds really dumb ik
bro isnt aura farming
vale wigeon
or was i supposed to multiple g by x
g(x) does not mean "multiply g by x" btw
calm rose
You substitute g(x) into f(x)
slender cairn
because there is?
tacit arch
<@&268886789983436800> quiz
lone heartBOT
vale wigeon
oh rip to that then huh
jolly notch
how do you mess it up that bad 😭
tacit arch
oh rip to that then huh
I didn't notice until he called me an ass
twin nimbus
hmm... he did dox his school in his photo. I wonder if his teacher would like to know that he's cheating.
🤔
nah, I'll delete it for him
tacit arch
If he tries again, do it
lone heartBOT
Available help channel!
tropic thistle
Combinatorics: Is there any algorithm more efficient than Heap's Algorithm?
I'm writing a program that needs to get the permutations of an array of a special data type called Unit. I've programmed an implementation of Heap's Algorithm, but I've been left wondering if there is any way I can make it more efficient because I know my data type and can specialize.
Are there any known cases of permutations algorithms that are specialized and consequently more efficient?
lone heartBOT
Combinatorics: Is there any algorithm more efficient than Heap's Algorithm?
I'm...
@tropic thistle Has your question been resolved?
mortal trellis
fwiw there is also the steiner johnson trotter algorithm but I dont know which of the two is more efficient
vale crag
Combinatorics: Is there any algorithm more efficient than Heap's Algorithm?
I'm...
doesn't the unit type only have one value ? or are you talking about something else ?
lone heartBOT
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hybrid zinc
hello, this isnt a homework problem of some sort, its from a book im reading about a theory called digital time theory. can someone explain to me what this means?
hushed locust
hybrid zinc
thank you, if i have further questions after the video can i still ask here?
hushed locust
yes
hushed locust
no problem
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Available help channel!
ebon hill
vale wigeon
is that a onedrive link?
ebon hill
Thats Word Link
jolly notch
that's sketchy
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
jolly notch
how do you think youd find the percentage
ebon hill
Uhh Hmm i Would First Find Calculate the radius of the circle Circumference (C) of a circle is C = 2πr, where r is the radius. We are given C = 28 Cm. So, 28 = 2 πr.
vale wigeon
ok then do it
ebon hill
So, Divide both sides by 2 π : r = 28 over 2 πr =14 over π
ebon hill
So Uhh Calculate the area of the circle.
The formula For the area is A of circle is A = πr²
Substitute r = 14 over π into the formula:
A = π( 14 over π) ² = π. 196 over π² =196 over π
ebon hill
Calculate The Area of The 2 Triangles. Since, The Area of One
Triangle Is 4cm², the area of 2 triangles is 2 × 4 = 8cm²
Helllo???
jolly notch
you're right so far there's only 1 thing left to do
if the total area is the circle, can you find how much of it is covered by the triangle?
and then convert it to a percentage
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
yeah looks correct
ebon hill
6
ocean sealBOT
jolly notch
ok yeah
ebon hill
Nah Not Wrong
jolly notch
!done
lone heartBOT
If you are done with this channel, please mark your problem as solved by typing .close
granite light
I need help with finding odd and even functions no question in particular just in general
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
It's just in general but I'll give an example
ebon hill
Okay.
vale wigeon
wdym by "finding odd and even functions"
granite light
Like if their odd or even
vale wigeon
do you mean like... given a function, determine whether it's odd or even or neither
granite light
Ye
vale wigeon
cause that's a matter of applying the definitions of both
you have to know and/or have in front of you the definitions of "odd function" and "even function" so that you check your function against either one
opal jolt
So pick a function and compute f(-x) and -f(-x)
opal jolt
Or I think -f(x)= f(-x) for odd
those are equivalent, it's just multiplying both sides by -1
granite light
The thing I'm stuck on is say x3-1
Sorry
X^3-1
Does it become -x^3-1 or -(x)^3-1
opal jolt
okay, so let's take your $f(x) = x^3-1$
ocean sealBOT
LordFelix
vale wigeon
to find f(-x) you replace all x's with (-x)
opal jolt
which means $f(-x) = (-x)^3-1$
ocean sealBOT
LordFelix
granite light
Do I simplify to x^3
ocean sealBOT
LordFelix
granite light
Ye so not even
granite light
**LordFelix**
Then u switch all signs for this equation
x^3+1
?
It's not neither is it
O it is right
opal jolt
now, you have $f(-x) = (-x)^3-1$
ocean sealBOT
LordFelix
ocean sealBOT
LordFelix
opal jolt
after simplifying, $-f(-x) = x^3+1$
ocean sealBOT
LordFelix
granite light
Ye neither
jolly notch
those are equivalent, it's just multiplying both sides by -1
again sorry side question uhh isn't -f(x) a reflection in the x axis and f(-x) a reflection in the y?
opal jolt
quick check: if it's a polynomial with only terms of even degree, it's even
if it's a polynomial with only terms of odd degree, it's odd
opal jolt
what are you referring to in that "it's"
jolly notch
i comprehended it as you saying that -f(x) is equivalent to f(-x) and got cnfused
oh i get whatyou meant
you meant the 2nd and 3rd system
mb
granite light
So it's neither right
opal jolt
in this case, it's not an odd OR even function
(it is symmetric, just not those two cases of symmetry)
vale wigeon
for polynomials, there's an easy way to determine parity
opal jolt
$f(-x)=(-x)^4-(-x)^2=x^4-x^2$
ocean sealBOT
LordFelix
vale wigeon
if you have terms only in even powers of x (including constants -- those are x^0), then the function is even
if you have terms only in odd powers of x (including just x -- that's x^1), then the function is odd
if you have a mix of both parities, then it's neither
opal jolt
you need to revise power rules, storm
granite light
I still have to show though
opal jolt
yes, but you made a few mistakes on computing the actual powers
rereading their rules would help
golden goblet
So what’s happening with -2(5-x) root5-x to turn into -4(5-x)^2
In first and second equation
lone heartBOT
@granite light Has your question been resolved?
granite light
.close
lone heartBOT
somber eagle
.reopen
this was not your channel
so you cant reopen it
if you want help, you have to open your own channel
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Available help channel!
golden goblet
Oops
zinc bolt
.close
potent mirage
lone heartBOT
potent mirage
can someone tell me how to do this without that grouping approach ( 6!/2!....stuff)
faint frost
can someone tell me how to do this without that grouping approach ( 6!/2!....stu...
as in with or without combinations
potent mirage
as in with or without combinations
what does that mean
faint frost
what does that mean
combinatorics. combinations and permutations
the ones that use factorial
potent mirage
combinatorics. combinations and permutations
oh yea i want to use that
faint frost
oh okay
potent mirage
could u tell me how
faint frost
what have u tried
faint frost
ok
sounds good
now how many permutations can u make of that
cuz u can do
2,2,1,1 or 1,2,1,2
watch out for duplicates asw brw
lone heartBOT
@potent mirage Has your question been resolved?
potent mirage
now how many permutations can u make of that
yeah so i did 6 C 4 to choose the 4 people who will get the 2bhk room and then from did 2! to arrangethem in each room
and then i did 2! to arrange the other 2 in the 1bhk
lone heartBOT
@potent mirage Has your question been resolved?
quiet atlas
this question is kindda complicated
potent mirage
this question is kindda complicated
h bhai 💀 advanced ka question h
<@&286206848099549185>
quiet atlas
lol
potent mirage
.close
lavish turtle
lone heartBOT
keen idol
do you know what the precise definition of a limit to infinity is
lavish turtle
do you know what the precise definition of a limit to infinity is
yes i am quite aware, if we are talking about the epsilon delta definition
keen idol
indeed
now we need to apply it to sequences
so we actually have
$\forall,\varepsilon>0;\exists,N\in\mathbb{N};\text{such that};\forall,n\ge N,;|x_n-L|<\varepsilon.$
ocean sealBOT
mia
keen idol
that is the definition of convergence
keen idol
that is okay
let us go step by step
first i will write it down in plain english if u arent familiar with the symbols
$For every \varepsilon>0 there exists an N such that for every n\ge N we have |x_n-L|<\varepsilon$
ocean sealBOT
mia
lavish turtle
oh no i am quite familiar with the symbols
lavish turtle
for all epsilon greater than 0 there exists N belonging to the set N such the for all n greater than or real for the set N (of natural number), the absolute value of x_n -L is greater than epsilon
pulsar aspen
For every $\varepsilon>0$ there exists an $N$ such that for every $n\ge N$ we have $|x_n-L|<\varepsilon$
ocean sealBOT
Xwtek
keen idol
no matter how small of an error tolerance u choose (epsilon), i can find a natural number N such that |x_N-L|<epsilon
pulsar aspen
You don't have to wrap an entire paragraph in dollar signs
lavish turtle
no matter how small of an error tolerance u choose (epsilon), i can find a natur...
shouldn't it be |x_n - L|
lavish turtle
oh alright
and L here would be the value of the function after taking the limit is that right?
well the value that the sequence converges to
keen idol
yes
keen idol
that is the definition of the convergence of the sequence
proving it is unique is a bit trickier
u need to assume that the limit converges to two different values for contradiction so
a_n -> p
a_n -> q
now u need to show that it must hold that p=q otherwise a contradiction exists
lavish turtle
This i had figured
keen idol
its actually a very absurd proof to do it in the first try
https://www.youtube.com/watch?v=A4LhIhI6tg4
u might refer here
lone heartBOT
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Available help channel!
tame nebula
lone heartBOT
tame nebula
are we looking at the y values here
modest robin
are we looking at the y values here
yes the yaxis shows the values of f(x) and g(x)
tame nebula
yes the yaxis shows the values of f(x) and g(x)
can you explain for b
why its - 1 -1
unique dune
${\lim_{x \to -1}f(x) - \lim_{x \to -1}g(x) = -1 - (1) = -1 - 1 = -2}$
ocean sealBOT
k
tame nebula
whered u get the -1 and 1
modest robin
whered u get the -1 and 1
on the graph of f(x) and g(x) they gave you
tame nebula
on the graph of f(x) and g(x) they gave you
for g(x)
this is the -1 we are looking at right
modest robin
x axis shows the imput and the curve gives the outputs f(x) or g(x)
modest robin
how about for the g primes and f primes
you don’t have the graph, but you could draw it from the one they gave you for f(x) and g(x)
tame nebula
you don’t have the graph, but you could draw it from the one they gave you for f...
how do i do that?
tame nebula
you don’t have the graph, but you could draw it from the one they gave you for f...
i cant solve this without drawing a new graph:?
tame nebula
what’s the derivative (definition or geometrically)
i dont know how
modest robin
you are not forced for c) but imo you have to have the intuition that comes from this graph, might as well do it this time and after that skip the details if you’re comfortable
modest robin
i dont know how
it’s the local slope of f(x) and g(x)
modest robin
i dont know how
you know how to get the slope of a line
buoyant saddle
are you sure
modest robin
ha yes -
buoyant saddle
are you still sure
ocean sealBOT
Banana Steeler
modest robin
i’ll just scrap this
modest robin
i dont know how
sorry for the fumbling the derivative definition. now, f(x) and g(x) are piecewise linear functions (different lines depending on the x) the derivative will give you the slope of these lines for each x.
so for instance evaluating f’(-3) should give you the slope of this blue line
lone heartBOT
@tame nebula Has your question been resolved?
modest robin
**Banana Steeler**
Because the derivative is defined by a limit, for it to exist you need both the limit approaching from the left and from the right to exist (thm on limits) and to have the same value but at g’(-2) approaching from the left gives one slope and from the right another so the limit does not exists
in general functions with sharp corners don’t have derivative defined on theses corners
hybrid halo
need help to get the variance and standard deviation
lone heartBOT
need help to get the variance and standard deviation
hybrid halo
I know that I have to add them and each one of them should be squared 2 and then divide by something
what’s the number that should be subtracted by 1
I hope that made sense
Help pls
@buoyant saddle
buoyant saddle
need help to get the variance and standard deviation
you cut off the actual question
i cant read this
buoyant saddle
ok do you know the formula for variance
hybrid halo
yes I think so
u mean
For sd?
isn’t variance just squared
Or is it the opposite
Ughhh
buoyant saddle
well variance is sd^2 but it’s nicer to write the formula for variance since we can omit the sqrt
buoyant saddle
isn’t variance just squared
yes
but what is the formula
youll need some additional information
hybrid halo
idk how to write it but I know each number s^2 and then add them
buoyant saddle
have you found the mean
hybrid halo
and then divide by a number -1
hybrid halo
have you found the mean
No I don’t think it’s necessary
hybrid halo
lecturer didn’t do it when teaching the formula
buoyant saddle
the mean is built into the formula for variance
hybrid halo
this is how I learned to find it
my question is what is 4-1 where did the 4 come from
buoyant saddle
you do not take the sum of the terms and divide by n-1
that is not the variance
the terms you’ve listed are likely (x_i - mean)^2
buoyant saddle
$s^2 = \frac{\sum_{i = 1}^n (x_i - \overline{x})^2}{n-1}$
ocean sealBOT
knief
buoyant saddle
the number of terms in your list
hybrid halo
so this would be 9-1?
ocean sealBOT
knief
hybrid halo
I thought it’s 8
hybrid halo
51.1
buoyant saddle
,calc (19 + 21 + 17 + 25 + 299 + 17 + 18 + 29 + 15)/9
ocean sealBOT
Result:
51.111111111111
yep
hybrid halo
ayeee
ocean sealBOT
knief
hybrid halo
what does this mean
buoyant saddle
are you familiar with summation notation?
hybrid halo
no
buoyant saddle
ok so i’d recommend watching a video on that but i’ll walk you through this one
hybrid halo
I just memorize the steps
buoyant saddle
$s^2 = \frac{\sum_{i = 1}^9 (x_i - 51.1)^2}{9-1} = \frac{(19 - 51.1)^2 + (21 - 51.1)^2 + \dots + (15 - 51.1)^2}{9-1}$
ocean sealBOT
knief
hybrid halo
this isn’t how it was taught
it was just 19^2 21^2 17^2 and so on and then divided by 9-1
buoyant saddle
your teacher is either wrong or you misunderstood the lecture
buoyant saddle
as i said before, given that the terms in the list are listed as squares id assume they wrote down each (x_i - mean)^2
hybrid halo
and got the answer
modest robin
the formula you were shown in class here and the one knief propose will produce the same number
hybrid halo
the formula you were shown in class here and the one knief propose will produce ...
ahhhh
modest robin
hybrid halo
guys what’s the answer
buoyant saddle
lmao
hybrid halo
pls
modest robin
yeah compute either of them
I think the one your teacher showed is quicker to compute but is less interpretable
hybrid halo
it’s not the only step
then u have to add them all and ^2 divided by n (n -1)
then subtract
hybrid halo
and square to find the variance
modest robin
i mean you do you i just chipped in to clarify that what your teacher does is not bs
hybrid halo
ITS STILL WRONGGG
hybrid halo
i mean you do you i just chipped in to clarify that what your teacher does is no...
yes thanks for that!!!
buoyant saddle
ITS STILL WRONGGG
you didn’t do it right then
buoyant saddle
yea that’s not correct
hybrid halo
I deadass spent a hour on this question
lone heartBOT
@hybrid halo Has your question been resolved?
clear linden
Hi! I have some newbie questions about the discrete Fourier transform.
clear linden
My background is CS and some math, so you can assume e.g. linear algebra and functional analysis. Never done signal processing at all though. I understand the continuous Fourier transform as a statement about functional analysis, where the basis vectors are complex exponentials.
I'm trying to understand the discrete version. Here's what I've been playing with:
from numpy import allclose, array, sin, cos, pi, linspace, floor, fft, zeros, linspace, arange, exp
import matplotlib.pyplot as plt
def f1(x):
return 3 * sin(2 * pi * 1 * x) # - 0.5 * cos(2 * pi * 1 * x)
def f2(x):
return 1.5 * sin(2 * pi * 3 * x) # - 0.8 * cos(2 * pi * 3 * x)
def f3(x):
return 1 * sin(2 * pi * 15 * x) # + 0.1 * cos(2 * pi * 15 * x)
def f(x):
return f1(x) + f2(x) + f3(x)
total_time = 2.0 # second
sampling_rate = 200 # Hz
time_interval = total_time / sampling_rate # seconds
t = linspace(start=0, stop=total_time, num=sampling_rate)
freqs = arange(0, sampling_rate)
nyquist_frequency = len(freqs) // 2
def dft(x, inverse: bool = False):
X = []
N = len(x)
expo = -1.0 if inverse else 1.0
coeff = 1.0 / N if inverse else 1.0
for i in range(N):
r = 0
for j in range(N):
r += x[j] * exp(expo * 2j * pi * i * j / N) * coeff
X.append(r)
return array(X)
fhat = dft(f(t))
fhathat = dft(fhat, inverse=True)
fig, ((ax1, ax3, ax5, _), (ax2, ax4, ax6, _)) = plt.subplots(2, 4, figsize=(16, 8))
fig.suptitle('Signal and decomposition')
ax2.plot(t, f1(t), t, f2(t), t, f3(t))
ax2.set_title("Components")
ax1.plot(t, f(t))
ax1.set_title("Signal")
ax3.stem(freqs[:nyquist_frequency], fhat.real[:nyquist_frequency])
ax3.set_title("Real Fourier coefficients")
ax4.stem(freqs[:nyquist_frequency], fhat.imag[:nyquist_frequency])
ax4.set_title("Imaginary Fourier coefficients")
ax5.set_title("Reconstructed signal (real)")
ax5.plot(t, fhathat.real)
ax6.set_title("Reconstructed signal (imag)")
ax6.plot(t, fhathat.imag)
assert allclose(fhathat.imag, 0.0)
Two questions:
-
Why are my real Fourier coefficients not exact? Since I have sines of frequencies 1, 3, and 15, why do I see anything but absolute zero in the other parts of the frequency spectrum? It also seems like they're doubled (e.g. a peak at 30 instead of 15)? They go to the correct places (e.g. peak at 15) if
total_time = 1.0instead oftotal_time = 2.0. -
Why are the imaginary Fourier coefficients so large, at the frequencies where the real coefficients have large values? And why are the values in the frequency domain not the amplitudes of the signals (3, 1.5, 1)?
-
The reconstructed signal is fine, and for that I grabbed the real coefficients of my inverse discrete Fourier transform (
fhathat.real). What semantics should I assign to the imaginary component of the reconstructed signal (fhathat.imag)? Just numerical noise? -
How would I deal with waves that are not pure-sines, but sine + cosine?
clear linden
lone heartBOT
@clear linden Has your question been resolved?
clear linden
<@&286206848099549185> just in case 🙂
tacit arch
lone heartBOT
lone heartBOT
Available help channel!
coarse elm
Can someone help me visualize this better
lone heartBOT
Can someone help me visualize this better
coarse elm
Im a little confused because how am I supposed to know how to do this without drawing it
slate vortex
what's stopping you from drawing it 🤔
coarse elm
well im kinda confused on what to draw other than the two points
I know (6,3)and (11,-6)
but how do i continue
patent vale
Can someone help me visualize this better
just draw it in your mind
hushed locust
the parallelogram law of vector addition is useful here
coral steeple
real skiff
help
real skiff
patent vale
this is the type of problem i would see only in my head
do you have the full problem?
real skiff
do you have the full problem?
that's supposed to be it
solar pebble
? i doubt this for some reason
ABC and ADC are the same
solar pebble
? i doubt this for some reason
oh I was referring to the image I sent
real skiff
? i doubt this for some reason
I'm supposed to find the length of the missing sides in each circumscribed quadrilateral
proven leaf
Hint: ||For any tangential quadrilateral formed by points ABCD, it follows that: AB+CD=DA+BC.||
real skiff
Hint: ||For any tangential quadrilateral formed by points `ABCD`, it follows tha...
I know what I want to know is how the procedure would be. I haven't paid attention to math classes.
Step-by-step solution using Pitot's Theorem (Circumscribed Quadrilateral):
Given sides:
AB = 2x + 1
BC = 3x - 2
CD = 5x - 3
DA = 3x + 2
Apply Pitot’s Theorem:
In any circumscribed quadrilateral (with an inscribed circle touching all four sides), the sum of opposite sides is equal:
AB + CD = BC + DA
Substitute the expressions:
(2x + 1) + (5x - 3) = (3x - 2) + (3x + 2)
Simplify both sides:
Left side:
2x + 5x + 1 - 3 = 7x - 2
Right side:
3x + 3x - 2 + 2 = 6x
Solve the equation:
7x - 2 = 6x
Subtract 6x from both sides:
x - 2 = 0
So, x = 2
Substitute x = 2 back into each side:
AB = 2(2) + 1 = 5
BC = 3(2) - 2 = 4
CD = 5(2) - 3 = 7
DA = 3(2) + 2 = 8
Final side lengths:
AB = 5
BC = 4
CD = 7
DA = 8
✅ The opposite sides add up correctly:
AB + CD = 5 + 7 = 12
BC + DA = 4 + 8 = 12
The theorem is satisfied.
would this be okay?
patent vale
!nogpt
lone heartBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
real skiff
eu
lone heartBOT
@real skiff Has your question been resolved?
lone heartBOT
@real skiff Has your question been resolved?
frail walrus
lone heartBOT
buoyant saddle
x = (u + 2)/3
buoyant saddle
,rotate
ocean sealBOT
frail walrus
distribute?
frail walrus
ok
buoyant saddle
(a + b)c = ac + bc
exotic canopy
expand the brackets
buoyant saddle
exponent rules
buoyant saddle
x^a * x^b = x^{a+b}
frail walrus
what
exotic canopy
you should know these rules by heart if you are at calculus by now
silver plume
quick question on piecewise and how to connect them
frail walrus
thanks bro
ur good
bruh
i got the wrong answer
heres how i distributed
u^3/2 + 2u^1/2
all over 3
frail walrus
then i took out 1/3
so then the outside is 1/9
then i integrated
ill take a photo
,rccw
ocean sealBOT
frail walrus
i definitely integrated wrong cuz i got the wrong answer
buoyant saddle
dude forgot the 1/9 on the other term
frail walrus
bruh
buoyant saddle
bruh
frail walrus
i still got the wrong answer
buoyant saddle
😭
buoyant saddle
nah
frail walrus
what is wrong then
buoyant saddle
,calc (2^(7/2))/45 + (2^(7/2))/27 - 2/45 - 4/27
ocean sealBOT
Result:
0.47784939253243
man forgot how to do arithmetic
frail walrus
thats not the answer
frail walrus
answer is 2.415
buoyant saddle
the bounds
it’s not 1^2
that was for x
when you change to u you have to change the bounds
frail walrus
bro what
buoyant saddle
when you do a substitution the bounds of integration change
frail walrus
ive been doing all my questions without changing to u-bounds
and i got them all right
you can still use x-bounds
buoyant saddle
because you probably converted back to x
if you rewrote the anti derivative in terms of x then it’s fine
but you didn’t here
buoyant saddle
you can still use x-bounds
no
frail walrus
i just straight up replaced x with my bounds on previous questions and got my answer
when i change to u bounds i get the wrong answer
i dont get it
buoyant saddle
you can change your anti derivative which is in terms of u to be in terms of x then that’s fine
and you can keep the x bounds
frail walrus
im saying
i changed it into terms of u
but still used the x bounds
and got the right answers
buoyant saddle
you’re not communicating what you did properly then
frail walrus
im doing something weird
buoyant saddle
what you’ve done here is wrong
buoyant saddle
,w 1/9(2/5((4)^(5/2) - 1) + 4/3((4^(3/2) - 1))
ocean sealBOT
frail walrus
yes thats the answer
buoyant saddle
there you go
buoyant saddle
sure it did
frail walrus
how
buoyant saddle
your anti derivative was right you just plugged in the wrong bounds
i converted the u’s back to 3x-2
frail walrus
and what bounds did you plug in
buoyant saddle
and plugged in the bounds for x
buoyant saddle
nah
buoyant saddle
😭
frail walrus
whats the point of converting my x-bounds to u-bounds if i dont even use my u-bounds to calculate the solution?
its a useless step?
yeah what is the point
buoyant saddle
well you could convert them to u bounds
it does effectively the same thing
but it’s a matter of taste really
frail walrus
wdym
buoyant saddle
some people do
frail walrus
i got the right answer by keeping my bounds as x-bounds
buoyant saddle
i don’t tbh
frail walrus
i converted to u-bounds and my answer is wrong
buoyant saddle
i convert the all of the u terms back in terms of x
frail walrus
even though my integral is in terms of u
buoyant saddle
and then keep the x bounds
buoyant saddle
i converted to u-bounds and my answer is wrong
so when x = 1, u = 3x - 2 = 1
and when x = 2, u = 4
frail walrus
yes
buoyant saddle
so it’s from 1 to 4
frail walrus
i got those u bounds
buoyant saddle
right so judt plug them in
frail walrus
oh broooo
i was converting to u bounds then plugging the u bound inside of u = 3x - 2
you convert u bounds so you can just substitute the u
bro
im so cooked
buoyant saddle
yea
buoyant saddle
you’re welcome
frail walrus
.close
lone heartBOT
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vapid shuttle
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vapid shuttle
I am working on part (b). It has a typo, it is meant to say contains so that we are asked to prove
O(3) subseteq Isom(S^2)
I have proven this, its not bad. But, I am interested for my own sake now proving that
Isom(S^2) subseteq O(3)
cobalt monolith
hello i am Ivona Kornhauser.
vapid shuttle
This I think is harder. I started,
Let $\varphi:S\to S^{2}$ be an isometry of $S^2$ then for all $p\in S, v,w\in T_pS$ we have $$\langle d\varphi_p(v), d\varphi_p(w)\rangle =\langle v,w \rangle$$
ocean sealBOT
Austin
vapid shuttle
Now, first I even have to show that varphi is a linear map to have hope it is in O(3). I don't know how to do this
Please ping me if you have any ideas.
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@vapid shuttle Has your question been resolved?
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@vapid shuttle Has your question been resolved?
vapid shuttle
<@&286206848099549185>
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@vapid shuttle Has your question been resolved?
violet urchin
This I think is harder. I started,
Let $\varphi:S\to S^{2}$ be an isometry of $S...
You may want to consider that isometries of S^2 can be extended to R^3
vapid shuttle
You may want to consider that isometries of S^2 can be extended to R^3
In what way?
violet urchin
In what way?
Take your point, shrink it to S^2, apply the iso, then unshrink it
vapid shuttle
clever
vapid shuttle
You may want to consider that isometries of S^2 can be extended to R^3
Extended in what way, because R^3 is not a surface
and if you mean extended as distance-preserving maps, I don't see how this is true
say phi is the isometry, phi:S^2 -> S^2
we can define phi*:R^3 -> R^3
by phi*(x)=phi(x/||x||)
i dont know how to show this is distance preserving if it is at all
violet urchin
we can define phi*:R^3 -> R^3
by phi\*(x)=phi(x/\||x|\|)
Not quite the right choice of map.
This will leave us with something on the unit sphere
violet urchin
Extended in what way, because R^3 is not a surface
and if you mean extended as d...
The broad idea is that we can extend it to an isometry, and that isometry will be orthogonal
The construction of the isometry is pretty natural, you got very close to it above
vapid shuttle
Did we not want something on the unit sphere
Phi we know is from S^2 to S^2 so I assumed thats what we would want
violet urchin
Did we not want something on the unit sphere
Well no, we want a transformation on R^3 which will be our candidate for the orthogonal map that phi is a restriction of
The natural candidate is the isometry R^3 to R^3 which phi is a restriction of, which we're trying to construct
vapid shuttle
Okay
Yes
When you say isometry R^3 to R^3 do you mean just distance preserving map
because in my course isometry is for regular surfaces
like maps between them
violet urchin
When you say isometry R^3 to R^3 do you mean just distance preserving map
Isometries in general are (often bijective but it depends on your source) distance preserving maps between metric spaces
vapid shuttle
Okay
When I say isometry of S^2 I mean a map that preserves inner products on the tangent space
but not necessarily distances
I think you know this though just wanted to clarify
vapid shuttle
When I say isometry of S^2 I mean a map that preserves inner products on the tan...
So we probably want to alter the phi*(x)=(x/||x||) I proposed earlier so that it does this
violet urchin
When I say isometry of S^2 I mean a map that preserves inner products on the tan...
Riemannian isometries are equivalent to metric isometries given bijectivity
vapid shuttle
oh ok I see
violet urchin
So we probably want to alter the phi*(x)=(x/||x|\|) I proposed earlier so that i...
Given this #help-0 message, we just need to alter it so that it preserves distances
And we can assume that phi preserves distances
vapid shuttle
Why can we assume that
violet urchin
Why can we assume that
vapid shuttle
sorry if I'm misunderstanding but phi is not given to be bijective
violet urchin
Is it not an element of the isometry group?
vapid shuttle
Oh right its a diffeomorphism
I forgot
Wait so
would not then all riemannian isometries be equivalent to metric isometries
but I swear that they need not preserve distances
violet urchin
but I swear that they need not preserve distances
Ok so I've screwed up a little but the broad approach still works. I'm just going to give you that we want phi* to be |x|phi(x/|x|). This is not necessarily a metric isometry of R^n but it is a very natural extension of phi and it will be orthogonal. It's just not quite as nice to show orthogonality as I thought.
The screwing up was 3 am brain confusing metric isometry as a subset of R^n to metric isometry as a Riemannian manifold.
violet urchin
Ok so I've screwed up a little but the broad approach still works. I'm just goin...
Anyway, the real content of the proof is in showing that this phi* is orthogonal.
vapid shuttle
so we want to show that $$||\varphi\left(\frac{x}{||x||}\right)\cdot ||x||-\varphi\left(\frac{y}{||y||}\right)\cdot ||y||||=||x-y||$$
ocean sealBOT
Austin
so we want to show that $$||\varphi\left(\frac{x}{||x||}\right)\cdot ||x||-\varphi\left(\frac{y}{||y||}\right)\cdot ||y||||=||x-y||$$
vapid shuttle
and we can use that varphi is an isometry S2->S2
violet urchin
and we can use that varphi is an isometry S2->S2
Yes.
violet urchin
The screwing up was 3 am brain confusing metric isometry as a subset of R^n to m...
Actually, 3 am brain was right, specifically for S^n.
Wow, I'm a mess.
I'm so sorry about this lol.
violet urchin
so we want to show that $$||\varphi\left(\frac{x}{||x||}\right)\cdot ||x||-\varp...
So yes, we're showing this, and we can use that phi is distance-preserving in R^3.
vapid shuttle
Why is phi distance-preserving? this I have not seen
violet urchin
Why is phi distance-preserving? this I have not seen
Showing that for S^2 preserving the riemannian metric is the same as preserving the euclidean metric is just a little euclidean geometry
You should go through this though
lone heartBOT
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echo totem
hello
vale wigeon
what kind of integral convergence tests do you know of
keen idol
hm reminds me of dirichlet test
echo totem
what kind of integral convergence tests do you know of
DCT and LCT only
echo totem
so ik sinx is between -1 and 1
vale wigeon
there's two points where bullshit happens
there is x=1 and there is x=+∞
you will have to consider both
you need to tell whether or not the fraction has a finite limit as x -> 1
and if it doesn't, what power of x does it behave like
grizzled mauve
it should be x going to 1^+?
thats a more precise notation, the way its written now has this implicit. but same integral
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chrome bloom
lone heartBOT
chrome bloom
What would the LCD for number one be?
zinc bolt
Factor $m^2 + 3m - 4$
ocean sealBOT
@zinc bolt
zinc bolt
What do you get?
chrome bloom
(m-1)(m+4)!
zinc bolt
Well not the factorial but yes/j
chrome bloom
These are the same as the other sides' denominators
zinc bolt
mhm
chrome bloom
so the lcd would be (m-1)(m+4)?
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chrome bloom
.close
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forest marsh
ocean sealBOT
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gleaming valley
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gleaming valley
Yes, but i didn't understand and i need to send this homework today
kind glade
!xy
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
gleaming valley
!xy
Exerc´ıcio 10. Encontre a soma dos vetores indicados na figura,
nos seguintes casos:
or in English
Exercise 10. Find the sum of the vectors shown in the figure,
in the following cases:
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twilit dagger
Its asking me to prove why AOH and COE are congruent. I have no idea if they are or not.
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snow berry
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snow berry
Why is this reversed?
like, it is 0 1 and 1 0 initially and now it is 1 0 and 0 1 in the second part
<@&286206848099549185>
god
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brave field
Can someone help why did volume increase as the ambient temperature goes down (Im pretty sure gas expands when heated)....
Is the encircled formula an actual formula? (the 35 and 15.6 are the ambient temp in C)
brave field
<@261414614296690688>
equals.. ive used it and it gave the correct answer... im not sure if the textbook is wrong
half onyx
V1/V2=S1/S2?
brave field
yeah volume and specific gravity, its my 1st time hearing about it
half onyx
it is taught to me differently so idk
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thick holly
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thick holly
It asks the area of “?”
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foggy lake
can someone explain this to me?
lone heartBOT
can someone explain this to me?
foggy lake
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upbeat torrent
I need help on understanding how to set up equations to solve for trusses. I understand it has something to do with trigonometry (sin, cos, and tan) but I don't get how it all comes into finding the members
dusky steeple
I need help on understanding how to set up equations to solve for trusses. I und...
RAx=0
RAy=500
RCy=700
AD=-833 (Compression)
AB=667 (Tension)
CD=-1167 (Compression)
BC=933 (Tension)
BD=1500 (Tension)
upbeat torrent
Tysm
dusky steeple
if you hire me, I will solve your every problems.
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arctic cosmos
Hi, I am in a debate with my maths teacher about a probability related question.
The question goes as follows: A computer program scrambles the word 'creations' so that all the latter's positions are random, what is the probability that the letter A and T are next to each other in the result.
My teachers solved the question as follows: 9 positions for A or T, 2 positions for A or T next to the other A or T, making 19 combinations, then - 2 if the A or T is on the edge, so 16 combinations. Then, there are 9! ways that the letters could be arranged, giving 16/9! or 1/22680 chance of A and T appearing adjacent to each other. This probability seemed way to low to me, so I used a website to generate a set of 100 random scrambles of the word 'creations', and tallied the times that A and T were adjacent. I got 17/100. My question is, how do I calculate the actual probability. Thankyou!
rustic coral
Hi, I am in a debate with my maths teacher about a probability related question....
Your teacher forgot to order the other 7 letters besides A and T
,w (16*7!)/9!
ocean sealBOT
rustic coral
arctic cosmos
thankyou, I will try to wrap my head around this I don't quite understand haha, but that result lines up with my trial
oh
I get it
thankyou so much
empty mason
Hi, I am in a debate with my maths teacher about a probability related question....
Think of it like this. We group the AT together and think of it as one letter. Now we have total of 8 letters, of which there are 8 ways of rearranging the AT around clearly. Multiply this by 2 because there are 2 ways of rearranging the AT within itself. But don’t forget to multiply by the 7! ways of rearranging the other 7 letters. So we get the numerator to be 167!. The total number of ways of rearranging the letters is 9!, our denominator. So the probability becomes 16 * 7! / 9! = 16/(89) = 2/9
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solemn vigil
how does [ ] this bracket come in the formula and how does the - in -3cosθ come?
vale wigeon
$(a - b)(c-d) = a(c-d) - b(c-d)$, but you could also write that as $$a(c-d) + (-b(c-d))$$ if you wanted.
ocean sealBOT
Ann
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lucid aurora
can someone help me find the turning point of this
lone heartBOT
can someone help me find the turning point of this
lucid aurora
i know it has to be done via completing the square but i'm a liiiitle bit lost
lavish cave
i know it has to be done via completing the square but i'm a liiiitle bit lost
you don't actually have to complete the square
lucid aurora
oh!
lavish cave
you can use the fact that x-coordinate of vertex = -b/(2a)
lucid aurora
yeah i did it like that before and it was really messy
i got like a bunch of fractions
lavish cave
i got like a bunch of fractions
those fractions should simplify
$x = \frac{-(4)}{2(-2)}$
ocean sealBOT
south
lucid aurora
uhh
omg i was thinking the messy one was a different one
haha sorry thanks 😅
.close
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lavish cave
no worries!
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wicked gazelle
Uhhh I still need help in this one. Idk how to do this or what to do in this
lone heartBOT
Uhhh I still need help in this one. Idk how to do this or what to do in this
@wicked gazelle Has your question been resolved?
lone heartBOT
@wicked gazelle Has your question been resolved?
lavish cave
Uhhh I still need help in this one. Idk how to do this or what to do in this
Let the amount put into the 3 investments be x, y, z respectively
Can you write one equation that relates x, y, z?
(you need three equations in total for this question)
lavish cave
idk what to do in this bro....
what must x + y + z be equal to?
wicked gazelle
bro the 3 investmetn rate is 10% 12% and 15%
so
x=10
y=12
z=15
now x+y+z= 1310 (given in question itself)
glad iron
bro the 3 investmetn rate is 10% 12% and 15%
so
x=10
y=12
z=15
now x+y+z= 1310...
You don't know how much you invested in the 10%, 12% and 15% investments
wicked gazelle
nope
glad iron
Those are the variables then
lavish cave
bro the 3 investmetn rate is 10% 12% and 15%
so
x=10
y=12
z=15
now x+y+z= 1310...
you've misunderstood the question
glad iron
Let x be the amount invested in 10% investment and similarly for y and z
glad iron
Then try forming equations and using matrices to solve them
lavish cave
so the total profit from the investments is 1310
wicked gazelle
Let x be the amount invested in 10% investment and similarly for y and z
so for y the invested amount is 12%?
lavish cave
then my profit is 3000 * 10% = 300
the actual amount you invest, before you multiply by 10% or 12% or 15%, is just x, y, and z
wicked gazelle
so the total profit from the investments is 1310
yeah but how do i write in matrices method
glad iron
so for y the invested amount is 12%?
Yes
lavish cave
yeah but how do i write in matrices method
write the 3 equations in x, y, z first
glad iron
yeah but how do i write in matrices method
First convert the given stuff in english to equations in x, y and z
lavish cave
then?
write them first then it's easy
so I'm telling you that x + y + z = 1310 is wrong
but one of the equations is indeed x + y + z = something
wicked gazelle
10% of 10000 is 1000 right?
lavish cave
10% of 10000 is 1000 right?
yes
well you don't know that you put 10,000 into the 10% investment
wicked gazelle
so it could be 1000+1200+1500= 1310....
okai that sounds so wrong
so the question is complete
lavish cave
yes, 3 equations and 3 variables x, y, z
lone heartBOT
wicked gazelle
.reopen
lone heartBOT
✅
wicked gazelle
If your kind enough pls do both 😔🙏 or any one is enough
glad iron
Oh dang are you also a JEE aspirant?
glad iron
Lol
wicked gazelle
can barely pass boards
glad iron
If your kind enough pls do both 😔🙏 or any one is enough
Isn't there a straight up formula for this in NCERT?
wicked gazelle
Isn't there a straight up formula for this in NCERT?
idk is there any?
glad iron
Yes there is
wicked gazelle
all i need is step by step answers
wicked gazelle
Yes there is
lemme check (by any chance do you know what chapter this question is from?)
knotty grotto
Uhhh I still need help in this one. Idk how to do this or what to do in this
solve with either a super simple system of linear equations
or like college level matrices manipulations for transposing and computing cofactors of an inverse matrix (unsure what else "use matrix method" could rever to)
glad iron
lemme check (by any chance do you know what chapter this question is from?)
3d geometry IG
wicked gazelle
solve with either a super simple system of linear equations
or like college leve...
line eqn as in AX+BY=C?
wicked gazelle
3d geometry IG
okai okai
wicked gazelle
Isn't there a straight up formula for this in NCERT?
bro there are alot of formulas which one do i even use?
glad iron
There's one specifically for the foot of a perpendicular
glad iron
That's for 2d dude, 3d formula is different
wicked gazelle
x1-x2-x3/X???