idk i was tryna turn it into a radian to get the cos outta the unit circle like he did in the video but he already started off wit radians and got a perfect number outta the unit circle for cos
#help-26
topaz sinewBOT
@sonic bone Has your question been resolved?
sweet shard
idk i was tryna turn it into a radian to get the cos outta the unit circle like ...
You're supposed to multiply 630 by pi/180 to get 630 degrees into radians
Then take the cosine and sine of the resulting angle
sweet shard
Use period of cosine and sine to evaluate it
Do you know what period of a function is?
light raft
How did they get a -9x??
topaz sinewBOT
How did they get a -9x??
thorny flameBOT
Rahm Bow
lost laurel
$(2x -1)(x+5) = 2x^2 +10x -x -5)$
thorny flameBOT
Unquieterstew
light raft
$(2x -1)(x+5) = 2x^2 +10x -x -5)$
10x - 1x = 9x?
acoustic pecan
-x+10x
sonic dawn
sometimes you’re right and what you read is wrong
light raft
sometimes you’re right and what you read is wrong
so im right
lost laurel
seems so
light raft
Why does symbolab give me their answer
I ended up with 2x^2+12x+10 then factored to 2(x^2+6x+5)
Anyne know
@lost laurel
<@&286206848099549185>
anyone?
acoustic pecan
im just questioning my sanity
i have seen the issue with mine eyes
this denominator should be (2x-1)(x+5)
you get (2x+1)/(x+5)
multiply by (x-5)/(x-5)
[(2x+1)(x-5)]/[(x+5)(x-5)]=(2x^2-9x-5)/[(x+5)(x-5)]
weird how they just brush over it, carry on, then magically fix it
@light raft
topaz sinewBOT
@light raft Has your question been resolved?
light raft
this denominator should be (2x-1)(x+5)
DUDE SAME
I THOUGHT YOU CANT CANCEL WHEN ADDING OR SUBTRACTING
tired lagoon
why dont we multiply by rdrdtheta
topaz sinewBOT
why dont we multiply by rdrdtheta
tired lagoon
when we do this transformation
topaz sinewBOT
@tired lagoon Has your question been resolved?
spiral stream
How do you do this calculus related rates problem ?
topaz sinewBOT
How do you do this calculus related rates problem ?
young tinsel
A related Rates Problem
Okay so here is the general way to solve a Related Rates problem
- Draw a model/diagram of the scenario. Identify which variables are changing and which of them don't change. Varies according to Scenario.
- Identify the rates we are given and the rate we want to solve for. Ensure it makes Physical sense as a rate can be negative or positive. Depends according to the context of a question
- Get a starting formula that relates the two different rates together. You may have to sometimes rewrite it in terms of one variable, but it depends on the scenario.
- Implicitly differentiate both sides, alongside using the chain rule
- Once you have the rate you want to solve for isolated you can then plug in your knowns.
- Lastly ask yourself does this rate make physical sense according to my scenario (Ex. A tank is depleting water at a rate of 50 L / s. Find the rate in height wrt time when the water level reaches 4m. Mathematically expressing the depletion rate: dV/dt = - 50 L / s )
Have you done Optimization Problems?
topaz sinewBOT
@spiral stream Has your question been resolved?
spiral stream
Have you done Optimization Problems?
No
topaz sinewBOT
acoustic tangle
The e-s are basis vectors of the domain of whatever linear transformation is in question
Similarly e'-s form a basis for the image
topaz sinewBOT
@scarlet crown Has your question been resolved?
young tinsel
No
Uhhhh Optimization problems come before related rates.
Applied Maximum and Minimum problems?
clear knot
topaz sinewBOT
clear knot
how to solve with Laplace Transform?
sweet shard
how to solve with Laplace Transform?
Take the Laplace transform of both sides
clear knot
Take the Laplace transform of both sides
Can you confirm RHS is
t*u(t)-t u(t-2) + 5u(t - 2) (step functions)
LHS is easy, i memorized it
and in that case if RHS is correct what is the LPT?
clear knot
Take the Laplace transform of both sides
What is LPT of t*u(t)-t u(t-2) + 5u(t - 2) ? don't need to check it
topaz sinewBOT
@clear knot Has your question been resolved?
topaz sinewBOT
@clear knot Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
topaz sinewBOT
Available help channel!
fluid belfry
topaz sinewBOT
fluid belfry
hi i was revising my notes and found this
this is box starting from A and going to O
i've written work done by weight is 0, shouldn't it be -mgR ?
topaz sinewBOT
@fluid belfry Has your question been resolved?
lucid junco
😭
topaz sinewBOT
@fluid belfry Has your question been resolved?
fair ruin
can i get helpp
topaz sinewBOT
can i get helpp
vernal matrix
<@&286206848099549185>
!15m
topaz sinewBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
vernal matrix
rain scroll
if I have a function f(x) = { x if x>_0 , 1/x if x <0}
Then if I want to find local maximum/minimum and global maximum/minimum.
Im having trouble understanding if 0 is considered a local min or nothing at all?
topaz sinewBOT
if I have a function f(x) = { x if x>_0 , 1/x if x <0}
Then if I want to find lo...
rain scroll
Since if we go towards zero from negative side its minus infinity. Or towards zero from positive its 0.
Its a local min if x is bigger than or equal to 0. But for the entire function, im having issues here thinking this one through
odd pagoda
local min means that f(x)>=f(0) for all nearby x (where "nearby" can be quite close). is that the case here?
rain scroll
"f(x_0) is a local minimum if there is an interval (a,b), x_0 belongs to (a,b) so f(x_0) <_ f(x) for all x which belongs to (a,b)differencnce Df" (sorry about bad translation of the definition)
rain scroll
Right
So, since for example f(-0.001) is lesser than f(0) then we dont have a local min then?
odd pagoda
basically, yes
more precisely, no matter how small we make that interval (a,b), you will always have some number a<x<0 such that f(x) < f(0)
neon iron
Is 0 included in the list of natural numbers?
topaz sinewBOT
Is 0 included in the list of natural numbers?
neon iron
internet searches suggest that it doesn't
marble gate
yes
sharp wyvern
its in whole numbers
sharp wyvern
some casses?
neon iron
yeah
marble gate
the peano axioms have 0 as a natural
like, it's axiom 1. 0 is a natural number
lol
sharp wyvern
damn
neon iron
hmmm....so I guess it is part of natural numbers then eh?
then I guess the whole distinction between whole numbers and natural numbers would be useless
marble gate
I believe that if you try to construct the natural numbers without 0, it will collapse
marble gate
then I guess the whole distinction between whole numbers and natural numbers wou...
no, because -1 is not a natural
sharp wyvern
-1 isnt a whole number either
acoustic tangle
I believe that if you try to construct the natural numbers without 0, it will co...
Why though?
odd pagoda
it depends on who you ask
odd pagoda
there is no correct answer
sharp wyvern
wait what
odd pagoda
sometimes 0 is included, sometimes it isnt
acoustic tangle
Yeah
neon iron
ahh I see
sharp wyvern
thats integer no?
marble gate
<:hmmCat:831508801646755850> Why though?
Peano's original formulation of the axioms used 1 instead of 0 as the "first" natural number,[9] while the axioms in Formulario mathematico include zero.[10]
oops my bad
but without 0 in the naturals you don't have an identity such that a+0=a
odd pagoda
it doesnt really matter in the end. you can always just rephrase your theorems for the other situation
marble gate
thats integer no?
...integers and whole numbers are the same
neon iron
well in this question
marble gate
the idea that whole numbers are only the naturals is bizarre
neon iron
what would the base case be in this question then?
odd pagoda
well this is a question about how your course defines the naturals
how should we answer that
acoustic tangle
but without 0 in the naturals you don't have an identity such that a+0=a
But you can still construct the integers from there and move on
marble gate
this just says that n is a natural, not that n is every natural
odd pagoda
n=0 would also work. just an empty sum on the left
thorny flameBOT
OFTA
Prove that
$$\sum^{n}_{r =1} (3r-1) = n^2(n + 1); n \in \N$$
```Compilation error:```! Undefined control sequence.
l.53 ...m^{n}_{r =1} (3r-1) = n^2(n + 1); n \in \N
$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.
Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l```
neon iron
$$\sum^{n}_{r =1} (3r-1) = n^2(n + 1); n \in N$$
thorny flameBOT
OFTA
neon iron
n=0 would also work. just an empty sum on the left
wait I don't get that
marble gate
the sum of no numbers is 0 lol
neon iron
AHh
odd pagoda
if $n=0$, then $\sum_{r=1}^0 (3r-1)=0$ is an empty sum
neon iron
smort
thorny flameBOT
Denascite
topaz sinewBOT
exotic carbon
log(a/b) = log a - log b
log(a^2) = 2 loga
log ab = log a + log b
that's all you need
topaz sinewBOT
topaz sinewBOT
Available help channel!
half field
topaz sinewBOT
half field
Hey there, can someone please teach me part b ?
turbid zealot
fluid belfry
show ur work
onyx yacht
I haven't checked your integration, but for the constant, set at t=0, s=0, since it has covered no distance at t=0
half field
I haven't checked your integration, but for the constant, set at t=0, s=0, since...
should i let s = 0 ?
onyx yacht
At t=0
onyx yacht
Did you plug in (0,0) for (t,s)
onyx yacht
So you should have gotten c=0
Yes
You can go ahead and calculate the displacements required now
Distance travelled 'in the third second' implies you need to find where it was at t=2 sec and t=3 sec
And deduce stuff from there
Notice the word 'distance' and not 'displacement' so you might have to look for where the velocity becomes 0 and a change of direction occurs
half field
to find distance travlled i should integrate something ?
onyx yacht
You don't need to integrate anything else.
You already have the position as a function of time
Use that, while taking care of when the the particles changes its direction
To get the distance
half field
Use that, while taking care of when the the particles changes its direction
plug in t = 0 in v ?
topaz sinewBOT
@half field Has your question been resolved?
fallow dagger
f(x)=(e^x)/(x-3) i need to find the derivative and i don t understand what formula to use here. i guess this is a composite function, what is f and what is g
topaz sinewBOT
f(x)=(e^x)/(x-3) i need to find the derivative and i don t understand what formu...
restive inlet
not really a composite function here
ionic oar
quotient rule
fallow dagger
f(x)/g(x)?
restive inlet
no
restive inlet
a fraction by itself is not a rule,
and you shouldn't be using f(x) there as its already being used
brazen ocean
f'g-g'f/g^2
junior jacinth
can I get some help with part b? thanks
topaz sinewBOT
can I get some help with part b? thanks
junior jacinth
this is the answer for a
ripe echo
this is the answer for a
A/B=1 => A=B
manic swan
-e^x(e^x +2) = (e^x - 2)³
junior jacinth
yea
and then I solve it
i get e^3x +7e^2x +14e^x+8
I put that in the calculator I got -4 -2 and -1
that's the ans for e^x right
if I want x i'm supposed to find ln(x)
but ln of any of those negative numbers isn't defined
what am I gonna do then
manic swan
@junior jacinth calc everything:
-e^(2x)-2e^x = e^(3x) - 6e^(2x) + 12e^x -8
manic swan
=
-e^(2x)-2e^x - [ e^(3x) - 6e^(2x) + 12e^x -8 ] = 0
=
5e^(2x) -14e^x - e^(3x) + 8 = 0
Put e^x = t
= +5t²-t³-14t+8=0
manic swan
can you check this rq
manic swan
but it's -3e^2x (-2)
No it's+3e^2x(-2)
fallow dagger
shouldn t it also be -8 at the end
fallow dagger
yeah and b is 2
junior jacinth
She made signal error
the +6e^2x ?
junior jacinth
yeah and b is 2
b is -2 no?
fallow dagger
no, if b is -2 the formula should ve been (a+b)^3
junior jacinth
ohhhh
manic swan
(e^x)³ + 3(e^x)²(-2) + 3(e^x)(-2)² +(-2)³
junior jacinth
I got it i got it
fallow dagger
(e^x)³ + 3(e^x)²(-2) + 3(e^x)(-2)² +(-2)³
yeah, i got the same
manic swan
(e^x)³ + 3(e^x)²(-2) + 3(e^x)(-2)² +(-2)³
Calc this
manic swan
=
-e^(2x)-2e^x - [ e^(3x) - 6e^(2x) + 12e^x -8 ] = 0
=
5e^(2x) -14e^x - e^(3...
So you will end with this
Now solve for t
And replace t value when you done
junior jacinth
=
-e^(2x)-2e^x - [ e^(3x) - 6e^(2x) + 12e^x -8 ] = 0
=
5e^(2x) -14e^x - e^(3...
but this thing, I got t=0.737
if I solve for x, that would be -0.305
right?
manic swan
(e^x)³ + 3(e^x)²(-2) + 3(e^x)(-2)² +(-2)³
(e^x)³-6(e^x)²+12e^x +8
e^x = 0.737
x= ln(0.737)
fallow dagger
did u get the answer ?
if u did, send a pic how did u solve the equation here, ping me and close it, cus i can t figure it out
topaz sinewBOT
@junior jacinth Has your question been resolved?
junior jacinth
e^x = 0.737
x= ln(0.737)
now screw that ans key imma go with that
fallow dagger
can u send a pic
junior jacinth
can you check this rq
um this the same
but that's not correct
you said
imma correct it now
thanks so much
fallow dagger
aight
junior jacinth
.close
solemn jolt
Can someone help me with this question? I don't quite understand the meaning of symmetric group.
topaz sinewBOT
Can someone help me with this question? I don't quite understand the meaning of ...
solemn jolt
this is the english translation of the question from chat gpt
and apart from the messed up notation it's accurate
strange whale
Can someone help me with this question? I don't quite understand the meaning of ...
the set of all bijections G -> G, and the operation is function composition : that's what S(G) is
it's like S_n the permutation group, except you're permuting elements of another group G now
solemn jolt
what are bijections
strange whale
invertible functions
solemn jolt
i know what what a bijective function is
but so a set of all the functions that are bijective?
strange whale
yes
solemn jolt
can a set have functions instead of elements?
strange whale
why not
strange whale
all the functions from G to G that are bijective
solemn jolt
all the functions that have G as domain and G as codomain as well
do we care what these functions are exactly?
strange whale
not really
we're only looking at specific examples here
left translations as they call it
"multiplying on the left by a" if you wanna be less fancy
solemn jolt
ok ok
lemme tell what I understand from the notation
and you tell me if it's right
strange whale
ok
solemn jolt
so first the function _atau is defined as a function that takes element g from the G set and multiplies is by a which is also in the G set
and the second function (.)tau is a function that takes element a from the G set and gives out a function that is Basically a bijective function of G from set of functions S(G)
and we wanna see if the homomorphism criteria applies to the function (.)tau
that right?
strange whale
sounds good
if you're not convinced, you should try and show that _a tau is indeed a bijection G->G first
solemn jolt
oh yeah
we wanna see if _a tau is both surjective and injective
so we wanna make sure first that no 2 unequal elements from G, going through the function _a tau yields the same element
so _at(g_1) =/= _at(g_2)
and that every element from G is reached by the Function _at
strange whale
yeah
strange whale
so we wanna make sure first that no 2 unequal elements from G, going through the...
working with the contrapositive is usually easier tbf
i.e. 'if ag_1 = ag_2 then g_1 = g_2'
that's what it boils down to here
solemn jolt
i.e. 'if ag_1 = ag_2 then g_1 = g_2'
how can I show that this is true?
solemn jolt
what does invertible mean?
strange whale
has an inverse
solemn jolt
oh
strange whale
group inverses
solemn jolt
has an image?
strange whale
yes
strange whale
right
solemn jolt
ok how does every element being invertible help
and do we know that the element a exists in set G?
oh
strange whale
betrachte fur a in G
solemn jolt
it literally says there
strange whale
yea
solemn jolt
nevermind
i still dk how to prove its surjectivity
how can I show that a*g covers all the elements in G
can I maybe use the fact that It's a group
strange whale
it boils down to the fact that a has an inverse also
strange whale
yea
solemn jolt
and a' g is also in group cuz of closure clause
solemn jolt
now for the real deal
right
I'm still a bit confused with the whole function going from a set full of elements to a set full of functions
solemn jolt
is there like an example I can see to better understand it
solemn jolt
you'll get used to it as von neumann said
D'x
strange whale
i don't know what you know so idk what example to cook up which will be insightful for you
solemn jolt
wait so what we are tryinbg to prove is that (.)t(xy)=(.)t(x)(.)t(y)
strange whale
no
strange whale
the argument is the a here
solemn jolt
a is just a random element from the set G right?
strange whale
you're trying to show $_ {ab}\tau = _a\tau \circ _b\tau$
thorny flameBOT
aPlatypus
solemn jolt
yooo
strange whale
i.e. stated in an easier way, multiplying by ab is the same thing as multiplying by b then multiplying by a
solemn jolt
hmmm
when I did an example of group homomorphism, we had two groups G and H for example like so (G, o) and (H, #)
and we'd have to show that f(aob) = f(a) # f(b)
for a certain function f
strange whale
sure that's the same thing
it's just that the notation for the translation is a bit weird
$\tau(a \cdot b) = \tau(a) \circ \tau(b)$
thorny flameBOT
aPlatypus
strange whale
that's essentially what we have here
strange whale
if you unfuck the notation
solemn jolt
and instead of elements, it has functions
and it also has some operation just like any group
strange whale
yep
solemn jolt
**aPlatypus**
in what you wrote here, we describe the operation of S(G) as o
since it's the codomain and on the other side of the equal sign
strange whale
yes
solemn jolt
ok I understand it apart from the whole element to function thing
so how do we actually show that?
strange whale
each of these tau(a) tau(b) tau(ab) is a function yes
multiplying on the left by a
multiplying on the left by b
multiplying on the left by ab
solemn jolt
wait would this be valid to say: We have a set G and in this set there are a bunch of elements. and each of these elements map to a function from the set S(G) and those function are denoted as _at
solemn jolt
multiplying on the left by a
multiplying on the left by b
multiplying on the lef...
yes
strange whale
i.e. stated in an easier way, multiplying by ab is the same thing as multiplying...
as I showed here, intuitively it's quite obvious what that equality says
solemn jolt
hmm
strange whale
if you pierce through all the layers of notation, that's what you get
solemn jolt
yes
i get that
i wish I knew how to use this math thing
so I could write it out with their indexes behind them
strange whale
I mean you're pretty much using it already
solemn jolt
**aPlatypus**
but basically, we wanna show this
strange whale
$_a \tau$
thorny flameBOT
aPlatypus
solemn jolt
$_ {ab}\tau = _a\tau \circ _b\tau$
strange whale
but let's stick with $\tau(a)$ it's more readable
solemn jolt
**AzerimA**
ok
strange whale
I mean do what you want
if you want to use the cursed notation no problem
I'll use it also
strange whale
$\tau(a \cdot b) = \tau(a) \circ \tau(b)$ right so
thorny flameBOT
aPlatypus
strange whale
we want so show these two functions are equal, no matter what a and b in G are
solemn jolt
yes
strange whale
how do you show 2 functions are equal generally ?
solemn jolt
we show that their outputs given equal inputs are the same?
thorny flameBOT
aPlatypus
strange whale
$\tau(a\cdot b)$ is a function and we're applying that to $x$
thorny flameBOT
aPlatypus
solemn jolt
ok ok
strange whale
that's what we're trying to show
sure it's not too hard but let's take it step by step shall we
solemn jolt
oh ok
strange whale
just use the definition of tau(a.b)
solemn jolt
I just see _at as a single function
strange whale
yeah fine
solemn jolt
and treat it like one letter f
strange whale
$_{a\cdot b}\tau (x)$
thorny flameBOT
aPlatypus
strange whale
I'm just taking it slow cause you're not used to all that stuff
so it's better to do it one time very formally
solemn jolt
please do. it's very helpful
strange whale
and then you'll be fine for the rest of your life
so
so $_{a\cdot b}\tau(x)$ is $(a\cdot b)\cdot x$
thorny flameBOT
aPlatypus
strange whale
now if you recall your group axioms
you should be able to work a little bit with that expression on the right
solemn jolt
a.b is an element of the group G
yes
huh
$_{a}\tau \cdot\ _b\tau$
how do i make cdot to an actual dot
thorny flameBOT
AzerimA
random zealot
Yea
solemn jolt
so is ${a\cdot b}\tau(x)$ the same as $({a}\tau \cdot\ _b\tau)(x)$
thorny flameBOT
AzerimA
random zealot
Can someone help me with this question? I don't quite understand the meaning of ...
Solving this problem not only requires deep knowledge across multiple disciplines, but also requires the synthesis of highly complex concepts and interaction between various fields of science and technology. This task is impressive in its versatility, the need for an integrated approach to the solution and the scale of knowledge coverage. To begin with, it is necessary to call into teams experts in such disciplines as quantum physics, neurobiology, graph theory, artificial intelligence, information theory and many others. Experts in these fields will provide a deep understanding of the fundamental concepts that are associated with the task. In addition, outstanding computer scientists and computer scientists are needed to develop state-of-the-art algorithms and computing platforms that can effectively implement a solution to the problem. Additionally, ecologists and economists could contribute to understanding the environmental and economic implications of this challenge, taking into account its impact on the environment and society. It cannot be overlooked that such a task will also require a deep understanding of the ethical and legal aspects involved in its solution. Thus, solving this problem is a colossal undertaking, combining many areas of scientific knowledge and technology, and requiring extraordinary synthesis and coordination.
strange whale
**AzerimA**
what does that even mean (on the right) ?
thorny flameBOT
AzerimA
strange whale
you have to prove this equality of function is true
like yes it is true
otherwise your profs wouldn't have told you to show it
but just saying the equality over and over won't prove anything
solemn jolt
I thought what I was showing wasn't the equality
i thought it was a step going towards it
now I realize that I'm tripping
thorny flameBOT
aPlatypus
strange whale
are you fine with that equality
I just used how tau is defined
multiplying on the left by a.b, that's what _(a.b) tau is
solemn jolt
but instead of multiplying the argument by just a, you multiplied it by a.b because we are workign with _a.btau instead of _atau
strange whale
yes
strange whale
now we know that (a.b).x is also in set G
well sure we've already shown this function goes from G to G, it's true but not very useful
well now you want to have _a tau ° _b tau somehow
strange whale
now if you recall your group axioms
as I hinted at here
solemn jolt
can we use the fact that _at is surjective?
strange whale
applying 1 group axiom is enough here
solemn jolt
the inverse identitiy right? like how we did to show surjectivity of _at?
solemn jolt
fuck
putting me on the spot out here
ok ok
so there were 5 axioms
one about closure
u said it's useless already
and the inverse identity also no go
so we have associativity and the thing with neutral element
wait actually there were only 4 axioms nevermind
strange whale
yea
solemn jolt
so we have shown that _a.bt(x) = _at(b.x)
and
from there
umm
well we are triying to get to _bt(x) . _at(x)
strange whale
well what's b.x ?
strange whale
so we have shown that _a.bt(x) = _at(b.x)
here
solemn jolt
b.x is an element of G
strange whale
sure
solemn jolt
💀
strange whale
_b tau(x) = what?
solemn jolt
left multiplication, yada yada...
wdym by left multiplication?
solemn jolt
_b tau(x) = what?
a.x
strange whale
wdym by left multiplication?
that's what the tau_a, tau_b does
multiplying on the left
strange whale
so we have shown that _a.bt(x) = _at(b.x)
^
replace that b.x
by its tau expression
solemn jolt
a.b.x right?
solemn jolt
oh
strange whale
stop undoing _a tau
strange whale
$_{a\cdot b}\tau(x) = _a\tau(_b\tau(x))$
thorny flameBOT
aPlatypus
strange whale
yeah
solemn jolt
YAHH BABBYYY
fuck yeah
good shit
I know it felt like walking a paraplegic accross the street
but thanks a lot man
I actually understand it
strange whale
so much crap to unfold to just use associativity lol
solemn jolt
ahahaha
strange whale
there's still one more question in your exercise
strange whale
$\tau_a(x) = x \cdot a$
thorny flameBOT
aPlatypus
strange whale
multiplying on the right by a
solemn jolt
this is just the same thing except the a is on the right
strange whale
yea
solemn jolt
it must be homomorphic right?
strange whale
try it out
topaz sinewBOT
@solemn jolt Has your question been resolved?
strange whale
@solemn jolt got it?
solemn jolt
working on it
strange whale
aight
solemn jolt
wait
i think the right translation is not homomorphic
unless it is an abelean group
unless the group is also commutative which i don't think it is
strange whale
yea you're right
solemn jolt
no it's not homomorphic
as the question hasn't stated that the G group is an abelean group
strange whale
yup
topaz sinewBOT
@solemn jolt Has your question been resolved?
gusty patio
Hello, can someone help me with an exercise in continuous differentiable functions?
topaz sinewBOT
Hello, can someone help me with an exercise in continuous differentiable functio...
gusty patio
ionic oar
neckbreaker
gusty patio
hello
gusty patio
Determine the real parameters a and b, so that the function is differentiable on R
I solved it, but at the end, it tells me that b= -1
gusty patio
oh
ionic oar
oh wait theres a command
ionic oar
I solved it, but at the end, it tells me that b= -1
,rccw
thorny flameBOT
ionic oar
what you did is fine then
topaz sinewBOT
@gusty patio Has your question been resolved?
ancient dagger
What is the goal?
gusty patio
I have to solve the limit
ancient dagger
Is it to find valid a, b, and c?
gusty patio
I know how to find out, but the limit stops me, I don't know how to find out
ancient dagger
Like to find the limit as f goes to infinity?
ancient dagger
Ah okay, well you wrote down that c = 1 if the limit exists
ancient dagger
Ohhhp
I see
What kind of background do you have? Do you know about L’Hopitals Rule?
gusty patio
nope
ancient dagger
Well here’s one thing you could do: split the fraction in the limit
gusty patio
how??
ancient dagger
$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$
thorny flameBOT
Karl
gusty patio
aaa
gusty patio
how? 😅
ancient dagger
$\lim (a + b) = \lim a + \lim b$
thorny flameBOT
Karl
gusty patio
and then?
ancient dagger
oh shucks
yeah one of those is bad
Okay wait
we dont really have to do any of this
e^x grows much faster than x right?
gusty patio
I think
ancient dagger
gusty patio
e is 2,7
ancient dagger
gusty patio
how to solve this one
ancient dagger
Yeah and 1 is a constant
gusty patio
1
drowsy bluff
l'hopital?
gusty patio
I didn't learn yet
gusty patio
Sorry Hanee
no worries
drowsy bluff
you could write the x over to ln x I think
drowsy bluff
I think I have an idea
gusty patio
hello?
drowsy bluff
Im looking at my books
gusty patio
ooo
drowsy bluff
Really hard without l'hopital XD
drowsy bluff
alright
gusty patio
drowsy bluff
It's hard to read sorry XD
drowsy bluff
What's the question?
drowsy bluff
so the function is xe^x and -x^2 + ax + b?
gusty patio
yep
drowsy bluff
and we need to find an a and b where it's differentiable on R
and R is real number line?
gusty patio
R are the real numbers, i.e. all the numbers
gusty patio
me too
gusty patio
yep
drowsy bluff
gusty patio
drowsy bluff
derivative of second function is -2x + a
Yes then you put them equal to each other at the x-point 1
gusty patio
how did you find the derivative of xe^x?
drowsy bluff
product rule
gusty patio
didn't learn about that as well 🤓
drowsy bluff
How else are you supposed to do this question??
Well the darivative of basically taking the limit
drowsy bluff
I'll try to work the first limit out for you!
I believe its possible without l'hopital
gusty patio
really?
gusty patio
ooo
gusty patio
who knows, maybe you will invent a new theorem😂😂
topaz sinewBOT
mental remnant
because its created by var
cunning yarrow
or if this is GML try a GML discord
hallow garden
A bag contains 7 green balls and 3 yellow balls.
Sani takes three balls out of the bag, without replacement.
(i)Find the probability that all three balls he chooses are yellow.
(ii)Find the probability that at least one of the three balls he chooses is green.
topaz sinewBOT
A bag contains 7 green balls and 3 yellow balls.
Sani takes three balls out of t...
hallow garden
Can someone explain
topaz sinewBOT
@hallow garden Has your question been resolved?
marble gate
!status
topaz sinewBOT
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
@hallow garden
marble gate
okay so, what's the probability that he pulls 1 ball and it is yellow
violet hornet
Hi
violet hornet
Can I ask here ?
marble gate
Can I ask here ?
no.
violet hornet
Where ?
hallow garden
and now what's the chance the 2nd ball will also be yellow
Second 7/10
marble gate
well there's only 9 balls in the bag
hallow garden
So 7/9
marble gate
the chance of getting a green ball on the second pull if you get a yellow in the first is 7/9
but we want a second yellow ball
marble gate
great
and now we can work out...if we've now pulled 2 yellow balls, what's the chance of getting the 3rd yellow ball on the last pull
marble gate
excellent - so now we have our 3 probabilities, we can work out the probability of all 3 of these happening
hallow garden
How?
marble gate
remember the chance of A and B happening (if they are independent) is P(A)*P(B)
marble gate
well....yes, but the way we worked it out was with conditional probabilities 😛
so we can treat them as independent
marble gate
yep!
marble gate
sure, go for it
marble gate
okay this question has a lot of words but at least it gives you the tree diagram
hallow garden
Ye
I got six possible out comes
F F
F NF F
F NF NF
NF F F
NF F NF
NF NF
dunno if correct
marble gate
which part is this for
hallow garden
I wanted to understand the question so I combined the possibilities it’s not the answer for any part 😝
Idk if I’m doing correct
marble gate
I /think/ there are 2 you're missing
hallow garden
Which ones
marble gate
I think the diagram left out the top and bottommost branches of the 3rd calculator for space
hallow garden
Ye so the diagram is wrong or the question is tricky?
hallow garden
The question is values of p and q
marble gate
I misread the questgion
hallow garden
I misread the questgion
Oh ok
hallow garden
If that’s 1/20 then NF is 19/20?
hallow garden
not all events are equally likely
Oh
hallow garden
But wait NF, F, F
marble gate
for a and b we are only testing 2 calculators
hallow garden
This is counted?
hallow garden
for a and b we are only testing 2 calculators
Ohh
marble gate
hallow garden
Gotcha
Now exactly 1 faulty
P(FNF OR FNF OR NF OR NF)
So add these
OR add right
marble gate
we're still only testing 2 calculators
hallow garden
F F
F NF F
F NF NF
NF F F
NF F NF
NF NF
hallow garden
we're still only testing 2 calculators
k one sec let me see again
marble gate
but yes, it's P(faulty then not faulty) + P(not faulty then faulty)
hallow garden
damn I counted twice
Thanks I’m getting it
I’ll attempt all here, you are fine?
With that
marble gate
sure
hallow garden
K thanks 🙏
hallow garden
C probability is 0
Because there is no FFF
not possible
1/20 * 1/20 * 0/20
That’s 0/20
Not possible
Right?
Oh wait I misunderstood
marble gate
no? C is asking for one of the first two faulty and then the 3rd one faulty
marble gate
ye
marble gate
ye
marble gate
P(FF) + P(NF, F, F) + P(F, NF, F)
hallow garden
For e
1000 * 0.00725
Which is 7.25
marble gate
hallow garden
I really appreciate your help 🙏. Wish you very best in your life
I’m going to close this channel 👍👍👍
.close
slow tundra
I don’t understand the first question
topaz sinewBOT
I don’t understand the first question
odd jacinth
what's written besides the question is the formula you could use to answer