whats the inverse
#help-36
mellow vale
merry quartz
final saddleBOT
@mellow vale Has your question been resolved?
thorny vault
Not sure what to do with the exponent in this problem
final saddleBOT
Not sure what to do with the exponent in this problem
faint locust
Not sure what to do with the exponent in this problem
What's the problem?
thorny vault
faint locust
Not sure what to do with the exponent in this problem
Where did you get the pi^7?
On the second to last line
faint locust
the term you wrote for g'(t) is correct
But then you tried to simplify and made a mistake
thorny vault
How would I simplify those terms?
thorny vault
I saw it in the video they gave me
thorny vault
Can I multiply 32 by -sinPIt?
faint locust
-32pi*cos(pi*t)^7*sin(pi*t) would probably already be simplified enough. You could simplify it more using trigonometry, since sin(x) * cos(x) = 1/2sin(2x), but perhaps that's not necessary
Yep, -32pi*cos(pi*t)^7*sin(pi*t) is correct
thorny vault
You were right no need I’ll try another example to master it thanks Kepe!
faint locust
np
thorny vault
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final saddleBOT
final saddleBOT
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tranquil pine
How do i find $\theta$
final saddleBOT
How do i find $\theta$
soft zealotBOT
please request a new nickname
tranquil pine
law of sines?
soft zealotBOT
tranquil pine
Yeah
bleak granite
that is that theta
tranquil pine
but i need to find the angle without calculator
tranquil pine
Don't have that in my brain
magic sparrow
skill issue
robust mulch
rad to deg is ×(180/pi)
bleak granite
there is the formula: $\arcsin(x)=-i\log\left(\sqrt{1-x^2}+ix\right)$
soft zealotBOT
FancyBredFries
fathom walrus
Yeah well the indians on Steve Harvey and Ellen can so you should be able to too
robust mulch
Oh you need to fin arcsin(2/3) without a calculator?
You either use some approximation series or leave it as arcsin(2/3)
bleak granite
You either use some approximation series or leave it as arcsin(2/3)
GarlicB our savior 🙏
tranquil pine
Okay
I will get a calculator
feels like cheating
My question was related to this problem btw
Thank you everyone
.close
final saddleBOT
robust mulch
You definitely need a calculator for this
Especially since the question asks you to round
final saddleBOT
Available help channel!
nimble quartz
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nimble quartz
so I proved my expression for when we have n as a power of 2
now I’m trying to prove it for all other numbers
I know that number is going to be between two powers of 2
and it needs to be more than the lower one’s minimum number of cuts since the maximum number of pieces you get with k cuts is 2^k
but how do I prove that k+1 cuts will work
scarlet sequoia
so when $n = 2^k$, the minimum number of cuts required is $k = log_2(n)$
soft zealotBOT
rafilou2003
scarlet sequoia
and if you want to extend it to any n, you would like to say that we round log_2(n) to the integer above
So show that for any n such that log_2(n) is not an integer, int(log_2(n)) is not enough cuts and int(log_2(n))+1 is enough
nimble quartz
**rafilou2003**
yes I proved that part
nimble quartz
So show that for any n such that log_2(n) is not an integer, int(log_2(n)) is no...
but I’m not sure about how to do this
how would I go about proving that when n isn’t a power of 2
@scarlet sequoia so I know that 2^k < n < 2^(k+1)
now I need to show that k cuts aren’t enough and k+1 cuts are
scarlet sequoia
now I need to show that k cuts aren’t enough and k+1 cuts are
by induction, show the property $P_k$ : "for any $2^k < n \leq 2^{k+1}$, $m(n) = k+1$"
nimble quartz
by induction, show the property $P_k$ : "for any $2^k < n \leq 2^{k+1}$, $m(n) =...
but that’s not true
scarlet sequoia
yep sorry
nimble quartz
the minimum number of cuts is k+1 when it isn’t a power of 2 right
soft zealotBOT
rafilou2003
nimble quartz
that’s exactly what I’m trying to do
I did it separately tho
so I proved that it’s always k for 2^k using induction
but I don’t know how to use induction for when it isn’t a power of 2
scarlet sequoia
distinguish two cases :
if n = 2p, then we can cut the original piece into... and by induction hypothesis...
if n = 2p+1, then we can cut the original piece into... and by induction hypothesis...
nimble quartz
distinguish two cases :
if n = 2p, then we can cut the original piece into... an...
honestly I’m really confused so I’d appreciate if you could elaborate
scarlet sequoia
ok let's do n = 2p
then we can cut the original piece into 2 pieces with 1 cut, making it p and p
If by hypothesis $2^{k+1} < n \leq 2^{k+2}$, then $2^{k} < p \leq 2^{k+1}$ and so the pieces of length p can be cut minimally with k+1 cuts
Since we can stack them, it just takes k+1 more cuts for the original piece to be cut completely
so the minimal number of cuts required is k+2
nimble quartz
If by hypothesis $2^{k+1} < n \leq 2^{k+2}$, then $2^{k} < p \leq 2^{k+1}$ and s...
wait what does our induction hypothesis even say
and why can p be cut in k cuts
it isn’t a power of 2 or smaller than 2^k?
scarlet sequoia
n = 2p
scarlet sequoia
**rafilou2003**
this is your induction
supposing Pk, we want to prove Pk+1
so let 2^(k+1) < n <= 2^(k+2) and show that m(n) = k+2
soft zealotBOT
rafilou2003
nimble quartz
ohh I was confused because you said k cuts
but how would you deal with odd numbers
scarlet sequoia
now try the same thing with the other case
scarlet sequoia
but how would you deal with odd numbers
yours to try at least before I give you more hints
nimble quartz
would it be two pieces (p and p+1)
and then p needs k + 1 cuts for the same reason
nimble quartz
now try the same thing with the other case
not sure about the p + 1 part tho
scarlet sequoia
if n is odd, then $n \leq 2^{k+2}-1$
soft zealotBOT
rafilou2003
scarlet sequoia
deduce what it means for p+1
nimble quartz
deduce what it means for p+1
oh I think I got it
just to confirm
this is simple induction right?
scarlet sequoia
yes
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@nimble quartz Has your question been resolved?
random chasm
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random chasm
Can someone explain how they got from step 1 to 2
final saddleBOT
@random chasm Has your question been resolved?
vital crag
,calc exp(-pi +log(2))
soft zealotBOT
Result:
0.086427836527545
,calc exp((1-i)*(log(2)+ i pi/2))
soft zealotBOT
Result:
6.147417534039 + 7.4008126711401i
You're leaving out context
random chasm
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@random chasm Has your question been resolved?
soft zealotBOT
random chasm
Sadge
heavy laurel
Can I walk thru my process and you can inform me if there's any gaps?
final saddleBOT
Can I walk thru my process and you can inform me if there's any gaps?
@heavy laurel Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
hard mist
Can someone explain this -proof- to me?
final saddleBOT
Can someone explain this -proof- to me?
desert mantle
which part of it do you not get
hard mist
From beginning till end
desert mantle
do you know that cos(x)=Re(e^(jx))
final tangle
have you worked with complex numbers before?
hard mist
yeah
final tangle
are you familiar with euler form / polar form / cis form?
hard mist
familiar with cartesian, trig and exp form
final tangle
and real and im components of a complex number
desert mantle
do you know e^(jx)=cos(x)+j sin(x)
hard mist
Yes
desert mantle
now take real part on both sides
desert mantle
e^(jx) is not real
hard mist
e^x is
desert mantle
the real part of it is equal to cos(x)
hard mist
or cant i split it
desert mantle
yes but why is e^x relevant here
desert mantle
that's the same thing
desert mantle
with 2pi+x instead of x
desert mantle
well cause that's what the proof uses
it proves the properties of cos using known properties of exp
cursive marlin
Guys, which one should I go over first, calculus or linear algebra? I'm learning math for ML and I just don't know that which topic should I be familiar with first? Or how would it make sense?
final saddleBOT
Guys, which one should I go over first, calculus or linear algebra? I'm learning...
plush merlin
its better to start with calculus
you can study LA with it at the same time if you want
if you cant then calculus first
worldly vale
They are pretty much independent until you need some linear algebra for multivariate calc
cursive marlin
its better to start with calculus
Okay
final saddleBOT
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rugged yoke
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rugged yoke
What is this symbol?
Context: elementary number theory
looking at the time complexity of prime factorization of n
grizzled tusk
it means equal or almost equal, like an approximation
grizzled tusk
he didn't calc the expected number of tries but ke knows it has to be around sqrt(n)/2 because of what you're trying to find (you didn't post what)
so he uses this symbol before the sqrt(n)/2 to say well, it's not necessarily that, but it's close enough
since his goal is to say it's O(sqrt(n)) anyway
he doesn't really need accuracy
he can be off by a bit and what he says is still true
final saddleBOT
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tranquil pine
question
Consider the rhombus $ABCD$ with centre $O$, with $\angle DAB < 60°$ and the equilateral triangle $ABE$ so that the points $E$ and $D$ are on either side of the line $AB$. The center circle $E$ and radius $AB$ intersect the line $AC$ at the points $F$ and $A$, and the line $BD$ at the points $G$ and $B$. Prove that the centres of the circles circumscribing triangles $EBA$, $FBD$, and $GCA$ form an equilateral triangle.
idea
We see that $\angle BGA*2=\angle BEA=60$, which means that $\angle BGA=30$
Because $ABCD$ is a rhombus, the diagonals are perpendicular $=> \angle GOA=90$
Using the 30-angle theorem we can simply show that $OA*2=GA=CA$
Because $OG$ is the perpendicular but also the median of the triangle $GCA =>CG=GA $
From the congruences, we can show that $CGA$ is an equilateral triangle.
WE can show that $B$ isn't the center of the circumscribing circle, because $OA^2=OB*OG$, which makes $BG=3k$ and $OK=k$
We also know that triangle $DFB$ is isosceles.
ALSO $BFAG$ is an writable quadrilateral
I don't know what to do forward. Hope one of you can help me! Thank you!
final saddleBOT
*question*
Consider the rhombus $ABCD$ with centre $O$, with $\angle DAB < 60°$...
soft zealotBOT
Ionela
tranquil pine
I just got stuck
I will also post my drawing
Hope on of you can help me
<@&286206848099549185>
?????
<@&286206848099549185>
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trail river
is my stupid sketch correct?
final saddleBOT
final saddleBOT
Available help channel!
modern wraith
Let p be a prime, suppose that an integer a satisfies $a^2 \equiv -2 \pmod p$ show that one of the equations $x^2+2y^2= {2p, p}$ has a solution
final saddleBOT
Let p be a prime, suppose that an integer a satisfies $a^2 \equiv -2 \pmod p$ sh...
soft zealotBOT
bigpufik
modern wraith
Well its obvious that their exists an integer $m$ such that $pm=a^2+2$, but I do not see why m has to be minimised to 2 or 1.
soft zealotBOT
bigpufik
modern wraith
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little python
what is the difference between-
final saddleBOT
what is the difference between-
little python
$\frac{\Delta \theta}{\Delta t}$ and $\frac{d\theta}{dt}$
soft zealotBOT
yajatk07
little python
does the delta one means-
theta final - theta initial/delta time
and the second is the differential one
final saddleBOT
@little python Has your question been resolved?
final saddleBOT
@little python Has your question been resolved?
cloud vigil
It depends on the context.
usually in physics --
$\frac{\Delta \theta}{\Delta t} = \frac{\theta_2 -\theta_1}{t_2 - t_1}$
soft zealotBOT
Feevo
final saddleBOT
final saddleBOT
Available help channel!
drifting sky
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drifting sky
i dont knve any idea not to do this can anyone explain
torpid meteor
What do you know about transversals?
drifting sky
almost everything
final saddleBOT
@drifting sky Has your question been resolved?
drifting sky
<@&286206848099549185>
tranquil pine
Y=9
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@drifting sky Has your question been resolved?
indigo plover
final saddleBOT
indigo plover
hi
So like here
I am trying to sketch
Is it best that i plug in a number in |x|
like |5| since is is lessthan or equal to 5
tranquil pine
hi
I am 12
People probably is smarter than me here
not probable everbody is
💀
indigo plover
lol
final saddleBOT
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indigo plover
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latent finch
I need help with factoring in algebra 2, factoring equations like the sum of cubes and the quadratic equations, i have problem with solving
stark lotus
What’s the equation ?
latent finch
i need help with
um
hold on
difference of squares
perfect square
difference of cubes
sum of cubes
and
this quadratic formula
..
lucid tree
send specific questions, if u want help with concepts, youtube them 💀
latent finch
lucid tree
whats the common factor there
latent finch
i dont get how im supposed to factorize it
lucid tree
what looks pretty similar
latent finch
a^2-1
lucid tree
no
latent finch
oh
lucid tree
its x^1/2
remove x^1/2
and u get x^1/2 (x^3 - 1)
nvm
u dont get that
actually i jus realized
im too lazy to do this and my life is meaningless
latent finch
im supposed to get x^1/2 (x-1) but it dont show how
latent finch
im too lazy to do this and my life is meaningless
pls broo i got test tmrw i will give smth in return someday trust
lucid tree
im supposed to get x^1/2 (x-1) but it dont show how
yes this is correct
multiply x^1/2 with x-1 and see what happens
lucid tree
remove x^1/2
lucid tree
but then we are adding the powers based on the laws of exponents
x^1/2 * x^1 = x^(1/2 +1) = x^3/2
latent finch
oh
i think i get the idea
ty
btw for the law of exponents
the negative power rule
is there anythin special we do if the power was norma
lucid tree
watchu sayin
slim magnet
final saddleBOT
slim magnet
The topic title says that these questions should be really simple and straightfoward with integration by parts
if I set u to cos^-1(x)
tiny gorge
did you try what they said
slim magnet
is there a smart way to do it?
tiny gorge
but instead of cos^-1(x) try u = cos(x)
slim magnet
no but Im supposed to use differentiation by parts'
not substitution
as in u=cos^-1(x)
tiny gorge
integration by parts for the second one i presume
tiny gorge
you don't need integration by parts for the integral of tan(x)
slim magnet
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cobalt bear
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cobalt bear
what do they mean by upper bound?
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tranquil pine
definition of family of functions?
final saddleBOT
definition of family of functions?
tranquil pine
sorry, this one'
I took a look at the answers and they were essentially just the zeros (i.e (x+3)(x-6)(x+4) ), but with a random number infront of them (i.e -4(x+3)(x-6)(x+4) )
Is it really just random?
what is the point of this question 😂
rotund citrus
just like a quadratic, when given a list of factors, you simply need the x values that make any of the factors 0. if there is a 0 at x = -3, that means (x + 3) must be a factor.
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@tranquil pine Has your question been resolved?
tranquil pine
just like a quadratic, when given a list of factors, you simply need the x value...
I know that
but what does it mean when it says family of functions
and is there a certain value you should place in the spot of k
for example k(x+3)(x-6)(x+4)
what can you replace k with
since (x+3)(x-6)(x+4) are essentially all in the "answer"
but the k is the only thing that changes
just wanted to know if there was a pattern or something im missing
<@&286206848099549185>
rotund citrus
k is simply another factor in your example. k could be anything, but if it's 0, then the x wouldn't matter since y = 0 for every x.
tranquil pine
so what it's asking for is just 3 random numbers with the three same zeroes for each question
rotund citrus
by family it just means cubic
as long as the highest degree of the polynomial is 3, its cubic and in the same family.
(x+a)(x+b)(x+c) would satisfy that condition. a b c are determined by the numbers in each part of the problem.
tranquil pine
ohh okay
yeah I thought there was more to this
didn't want to believe that it was just that
rotund citrus
might be overthinking it. but from what i see, thats what its asking for.
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rotund citrus
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onyx sand
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quiet garden
How’s this wrong
final saddleBOT
How’s this wrong
warm ether
look at the domain
slow swan
1 < x < 5
olive bramble
The graph is right the domain isn’t respected
quiet garden
The graph is right the domain isn’t respected
No the graph is wrong too
I didn’t get my point for it
warm ether
your y intercept is wrong
olive bramble
Gradient is right tho
warm ether
oh wait thats a 9
slow swan
Deca look at the 1 <x < 5 . This is a finite line
quiet garden
Ok so I remove that last bottom dot?
slow swan
X cannot be greater than 5 so the last x equals 4
The last x value must be 2 since x is greater than one. I haven’t graphed in web assign in awhile so I’m not too how you would make this graph
slow swan
The 9 is the y intercept. Another way to write it is - 3x + 9. So move up a bit
quiet garden
But then that passes the 1 in the equation
warm ether
it seems okay to me
slow swan
Yea I just checked sorry
warm ether
the domain is (1,5)
if you can have hollow dots then you should extend it to the 5 and 1 points
since i assume x is real
and then the range would be (-6,6)
slow swan
For web assign for some questions they give you the option to practice another before you guess wrong too many times on the one that’s graded as well. Use that to your advantage
It’s only for some questions
quiet garden
For web assign for some questions they give you the option to practice another b...
I have 3 more tries
quiet garden
the domain is (1,5)
How u get those? Also my graph still wrong
warm ether
i assume its the 3rd button on the tool list
slow swan
The domain is stated in the 1 < x <5
quiet garden
i assume its the 3rd button on the tool list
I mean ur domain and range cus it’s not on my graph
quiet garden
The domain is stated in the 1 < x <5
My graph is still wrong
slow swan
Is it the same graph as the picture you took earlier?
warm ether
if you can have hollow dots then you should extend it to the 5 and 1 points
because of this
the graph still reaches to the points of 1 and 5 its just not defined exactly at them
so you need a hollow point
warm ether
seems better yes
quiet garden
I entered it like that but it was wrong and when I went to check previous it doesn’t save the hole
warm ether
the only graphical thing left i can think of is the dots but i doubt it
also does that second tool under the select one draw solid lines or do you only have the faint ones
quiet garden
Faint ones
slow swan
Can you remove the dots in the middle? Webassign might recognize them as points
quiet garden
Yeah I did that and it worked
slow swan
Shift the entire line +1 right
X must be between 2-4, however, the empty circle points start at 1,6 and end at 5,-6
final saddleBOT
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bitter umbra
final saddleBOT
bitter umbra
can someone help me solve this differential equation
this is a logistic problem
i have the integral
1/4ln(x)-1/4ln(4-x)=1/20t+C
loud sundial
Do partial fractions on the left hand side
loud sundial
1/4ln(x)-1/4ln(4-x)=1/20t+C
this isn't correct
bitter umbra
is it correct now
loud sundial
is it correct now
yeah
bitter umbra
this is an answer to a similar problem
i need to get to something liek this
im just not sure where the x0 came from
because i can solve for x
but i get something liek this
loud sundial
im just not sure where the x0 came from
probably just represents some constant that arises from the constant of integration
maybe the initial value of x
if the question had context
loud sundial
But this isn't right, idk where the t went
bitter umbra
But this isn't right, idk where the t went
yeah i forgot to do that
im doing it rn
yea?
loud sundial
seems good to me
bitter umbra
yeah just
loud sundial
because they somehow got x0
x_0 denotes the initial value of x when t=0
basically switching out one way of representing the constant for another
bitter umbra
yeah
i checked
its not it
idk what it is
it inital value
but ur supposed to find C somehow
only problem is idk how to if i am given no point
loud sundial
just send the original question
bitter umbra
its not really a question thats why but i will ig
u basically had to make your own
i did a already
i integrated already
bitter umbra
initial value selected from where
is my question
is it from the graph
this is the solution curves
loud sundial
initial value selected from where
selected from "let it be whatever the hell you want"
loud sundial
basically for some arbitrary value x_0
hence why I said this
I gtg, but it is just another way of representing the constant (you're basically replacing one unknown with another)
that is the constant of integration with x_0
final saddleBOT
@bitter umbra Has your question been resolved?
final saddleBOT
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keen hedge
i forgot how 3b works
final saddleBOT
i forgot how 3b works
keen hedge
O
the derriative of 3a, is 2(4x+3)
and answer of 3b is 12
how come...
if x = 0, then dydx = 6
<@&286206848099549185>
keen hedge
HUH
opps my bad, lol
however, what about the 9?
What's that
and when I use that
storm karma
Its just the point on the func
final saddleBOT
keen hedge
thx for ur help btw
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Available help channel!
harsh spoke
<@&286206848099549185> hello sorry i just joined this as a last resort im having alot of trouble with implicit relations
final saddleBOT
<@&286206848099549185> hello sorry i just joined this as a last resort im having...
harsh spoke
sorry if this wasnt the discord that i should be on
keen hedge
differate that twice
harsh spoke
i missed my classes so im unsure on how to do that
is it possible in this discord for people to show how it is done so i get can my other questions done
.close
final saddleBOT
final saddleBOT
<@&286206848099549185> hello sorry i just joined this as a last resort im having...
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.
Available help channel!
heavy laurel
could someone help me understand this?
final saddleBOT
could someone help me understand this?
heavy laurel
specifically 1 and 2
I have an idea of how to do them, I just would like to check with others to see if my logic is correct
vital crag
I have an idea of how to do them, I just would like to check with others to see ...
show your work here
heavy laurel
show your work here
I think I got 1 and 2 down. 35 and true, although I'll double check.
heavy laurel
show your work here
For the open ended response, I've said that after finding the GCD of two numbers a and b using the Euclidean algorithm, back substitution helps us find specific numbers x and y so that ax+by equals the GCD. This shows how the GCD relates to the original numbers...
final saddleBOT
@heavy laurel Has your question been resolved?
soft zealotBOT
Yustiban
buoyant linden
first time dealing with such a problem. As such I have no ideas
trail mango
maybe the first thing you should notice is {u_n} must not converge uniformly to u
then you can try modifying classical examples that show pointwise convergence isn't enough to interchange limits and integrals
buoyant linden
maybe the first thing you should notice is {u_n} must not converge uniformly to ...
that is true! However, I still don't see the implication nor the approach from here
hmm
buoyant linden
then you can try modifying classical examples that show pointwise convergence is...
Would you be able to guide me a little. I am on rly deep waters with this one haha
trail mango
sorry i am too busy with smth else
buoyant linden
well RIP
civic ether
hey, does anyone know two complicated functions such that one function is greater than the other for x< 0
final saddleBOT
hey, does anyone know two complicated functions such that one function is greate...
civic ether
i wanted to test something so i wanted two complicated function which retains above property for that
i tried the elementary ones like x^3 and x^2
mint orbit
hey, does anyone know two complicated functions such that one function is greate...
x and xsinx maybe
they both have to be complicated?
civic ether
they both have to be complicated?
i have to consider two functions (which i do not know the relationship of)
and then i want to apply a decreasing function to it to see if the answer will just be the inverse of what i should normally be getting
so for x^2 and x^3
if i don’t know their relationship and i consider dividing by x then i’ll have x and x^2 to compare
and i know x> x^2 for x< 0
but then i’d have to switch again to then say x^2> x^3 for x<0
now i want to try that with something more complicated
mint orbit
and i know x> x^2 for x< 0
this isnt true
civic ether
this isnt true
i know, i’ve given my own bounds for x<0
civic ether
oh also typo
x^2 > x for x<0
but yes i’ve given my own bounds of x<0 for the entire question
mint orbit
and x^2 < x for 0 < x < 1
civic ether
i know
mint orbit
okay
mint orbit
well idk what you mean complicated
but just latching on sinx or so works well for testing stuff
civic ether
i want to see if my “trick” works for more complicated functions rather than just elementary polynomials
civic ether
but just latching on sinx or so works well for testing stuff
but x not greater than xsin(x) for x < 0 though
civic ether
hey, does anyone know two complicated functions such that one function is greate...
i wanted the bound condition to be met too^^
mint orbit
then use xsinx and -x
mint orbit
they are equal in some places
infinitely many places
but you could just add 1 to the line or whatever
deft sandal
Someone explain the 3rd part for me
final saddleBOT
Someone explain the 3rd part for me
tired walrus
as in the third line?
deft sandal
I dont remember being able to do that
tired walrus
im asking to confirm if that's what you want explained
deft sandal
Ye
tired walrus
x * x^-1 = 1, yes
deft sandal
If you multiply x^-2 by x does it become x^-1 too?
tired walrus
yes of course, exponent laws
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
Is this true or false, or cannot be said?
final saddleBOT
Is this true or false, or cannot be said?
keen nacelle
I'd say true? It's a bit confusing since personell cost isn't really defined here. Assuming it is baked into the manufacturing cost, it is true
it's hard to give a good answer here since I don't know how personell cost is defined
tranquil pine
What’s personnel cost?
keen nacelle
That's what I'm asking you
tranquil pine
Maybe it can’t be said?
keen nacelle
maybe? Depends what they've taught you personel cost is in whatever course that is
tranquil pine
That’s not a learning course
keen nacelle
It seems to be some kind of test or exercise so it's probably connected to or part of some course though
In which course they probably define and explain all terms
tranquil pine
It’s a test which determines if the candidates are eligible for the apprenticeship or not
keen nacelle
Look at it this way then;
material cost is fixed
Manufacturing cost is cost of the processes + labor required
Maybe making a battery requires very little work but very expensive processes, or the other way around
You don't have enough info
I'd choose cannot say
tranquil pine
Since labor cost is not defined in the here “cannot say” would be the right answer
keen nacelle
agreed
tranquil pine
It was correct
keen nacelle
nice
final saddleBOT
final saddleBOT
Available help channel!
azure trellis
got an interesting question
final saddleBOT
got an interesting question
azure trellis
prove 4^n +5^n will never equal 9^n for integers n >= 2
I'm having a gut feeling that it is a proof by contradiction
void valley
just counterexample
azure trellis
and the condition is that n is greater than or equal to 2
lol
yeah otherwise the thing would break
azure trellis
integer greater than or equal to 2
versed crater
,w 4^12 + 5^12 - 9^12
soft zealotBOT
azure trellis
huh I thought you had to prove for all integers greater than or equal to 2
versed crater
Prove that it does not equal for all n > 1?
versed crater
Well…
$a^n + b^n = c^n$ has no integer solutions for $a,b,c$ for $n>2$
That’s Fermat’s last theorem
azure trellis
bro no way they want us to prove that
soft zealotBOT
Frosst
soft zealotBOT
versed crater
Mhmm I just thought it was a cool use of the theorem, which has now been proven to be true
versed crater
prove 4^n +5^n will never equal 9^n for integers n >= 2
So if you were trying to prove something like this you could just use a result from somewhere else
azure trellis
as in like use the proof for fermats that already been done?
versed crater
Well yeah
versed crater
prove 4^n +5^n will never equal 9^n for integers n >= 2
I can tell you that statement is true because of Fermat’s last theorem
azure trellis
isnt the proof for that 109 pages or something like that 😭
versed crater
I might (definitely) not understand the proof but I am told it is a correct and complete proof of the theorem
azure trellis
very cool
one of my friends just proved it using the binomial expansion
pretty interesting
versed crater
Ah this works
azure trellis
I dunno how he saw that
azure trellis
better than memorising the theorem lol
versed crater
Now that you’ve seen it you’ll know to apply it in similar circumstances
And same for me
azure trellis
yea for sure
the grind never stops
thanks for your help btw
really appreciate it
.close
lunar forum
doing seperation of variables for heat equation
final saddleBOT
doing seperation of variables for heat equation
lunar forum
why is the case when lambda is greater than zero result in a sqrt of lambda?
nevermind
i see it
.close
orchid crystal
i got my reasoning
orchid crystal
i'm wrong, i got the ans key
lethal estuary
looks like you might need Bayes' theorem, or something to do w/ conditional probability
orchid crystal
that is to be known for proceeding further
the answer's 360/391 if anyone's solving
perhaps not
.close
heavy laurel
Could someone help me with this problem?
final saddleBOT
Could someone help me with this problem?
fickle crater
Could someone help me with this problem?
riddles are not math problems broski
worldly vale
This is literally a logic problem
craggy plume
unsure if the logic of this one depends on the technicality of the 3rd statement or if i'm making a mistake lol
craggy plume
because Athos is not, and porthos is not
can you not tell that porthos must be a spy
and then that'd be aramis technically can't be a kanve because porthos is a spy
unless aramis' statement hinges on it being an opinion and not to be taken as a fact to be understood as true/false under the pretenses
sturdy cypress
i can tell porthos is a spy, from that point
but yeah, you could tell immediately too
craggy plume
is both porthos being a spy and aramis being a knave possible
because if so i think the question's a little silly lol
scarlet sequoia
Well technically you didn't ask Aramis about Porthos
So when you ask him about porthos he could be like "he is not the spy"
cosmic estuary
Could someone help me with this problem?
this is a 'brilliant' riddle, just look up Ted-ed alien riddle, the whole reasoning is there i believe
sturdy cypress
it makes perfect sense
aramis wouldn't say he's the spy
so he's lying
there's no tension
heavy laurel
This is my answer thusfar everyone: If Athos is the Knight, then Porthos must be the Spy as a knight cannot lie and Porthos has claimed to be a knave, which would be a lie. However, this makes Aramis' statement true as well, but there can only be one knight, so this scenario is invalid. If Porthos is the Knight, this is impossible as it contradicts his own statement of being a knave. if Aramis is the Knight, then his statement about Porthos must be true, making Porthos the Spy. This would mean Athos is the Knave, which aligns with his statement of not being a spy (as he lied). Therefore, Athos is the Knave, Porthos is the Spy, and Aramis is the Knight.
heavy laurel
riddles are not math problems broski
I said the same thing but I'm getting these sorts of problems wrong on my mathematical structures exam...not sure how to approach these things
heavy laurel
oh
sturdy cypress
he would have to say porthos is knave or knight, that's the truth
he's denying it, it's a lie
he's like, making a statement about a statement, and you're collapsing into "he's a spy"
heavy laurel
he's like, making a statement about a statement, and you're collapsing into "he'...
So Athos is the knight instead?
sturdy cypress
yeah
heavy laurel
Porthos is the spy?
sturdy cypress
yes
heavy laurel
Aramis is the knave?
sturdy cypress
and aramis is lying, and tricking you
the truth is that if you asked him, he would say Porthos is the knight or some bullshit like that
heavy laurel
the truth is that if you asked him, he would say Porthos is the knight or some b...
Ok, so I went back and modified the reasoning: If Porthos is the Spy, then Aramis must be the Knave (as he's lying about what he would say regarding Porthos), and Athos must be the Knight (telling the truth about not being a spy). If Porthos is the Knave (lying about being a knave), then either Athos or Aramis could be the Spy, with the remaining one being the Knight. However, in this scenario, Aramis's statement becomes ambiguous as it could be a lie or truth depending on his identity. Therefore, we get this: Athos is the Knight, Porthos is the Spy, and Aramis is the Knave?
sturdy cypress
i don't like it because it's not like mine, can't be objective soory
final saddleBOT
@heavy laurel Has your question been resolved?
heavy laurel
i don't like it because it's not like mine, can't be objective soory
Could we do a recap?
Sorry, it's tricky.
heavy laurel
i don't like it because it's not like mine, can't be objective soory
So to recap, all I have is this: If we take Athos to be the knight, then the knave can either be Porthos or Aramis...." Porthos says "I am a knave", and Aramis says "if you asked me about Porthos, I would say he is the spy", but Porthos cannot be a knave because him being one would be a contradiction since Knaves cannot tell the truth, and he'd be doing that if his statement is true. Therefore, he is a spy. This follows that Aramis is a knave, because he is lying due to the fact that he said Porthos is a spy, and knaves always lie. Therefore, in this first case: Athos is the knight. Porthos is the spy. Aramis is the knave.
wait ignore the above I'm stupid, Aramis is clearly telling the truth
heavy laurel
and aramis is lying, and tricking you
Wait so did you extrapolate here that Aramis is the knave? That wouldn't make sense because he correctly identifies Porthos as the spy...so he'd be telling the truth.
heavy laurel
is both porthos being a spy and aramis being a knave possible
Do you understand the problem yourself?
craggy plume
my understanding is it functions off of the third statement being a kind of 'trick'
aramis isn't saying 'Porthis is the spy'
he's saying something which essentially means nothing
so disregard his statement
then it works
heavy laurel
so disregard his statement
But I'd still have to assign him an identity, no?
craggy plume
yes, he's the knave by elimination
heavy laurel
yes, he's the knave by elimination
And it's all because his identity hinges on the phrasing of his response?"If you asked me..", "I would..."
craggy plume
the logic in order is
- porthos must be the spy, as "i am a knave" => he cant be a knave as knaves must lie, and he cant be a knight because knights cant lie
- athos is the knight, as if he was a knave his statement would be a contradiction
- aramis is the knave by elimination
craggy plume
And it's all because his identity hinges on the phrasing of his response?"If you...
yes
i think it's a little silly but 🤷
actually i think it works better w/ how it was explained above, i missed that angle
aramis' statement is weird and finnicky though so i like my method more
which just disregards his statement entirely because it doesnt matter
sturdy cypress
the proof doesn't have to explain what the person you assigned by elimination means with his statement
but your interpretation is wrong, aramis is lying
heavy laurel
but your interpretation is wrong, aramis is lying
How though? Aramis correctly identified Porthos as the spy..
sturdy cypress
he didn't do that
heavy laurel
he didn't do that
oh
sturdy cypress
you assumed that's what he said
heavy laurel
How else should we interpret what he said? Sorry if i assumed
sturdy cypress
that's not the precise meaning, he incorrectly told you what he would say
heavy laurel
that's not the precise meaning, he incorrectly told you what he would say
makes sense
sturdy cypress
since he's a knave, if you asked him this, he would tell you "Porthos is a knight"
that's the truth
which he denies
heavy laurel
wait
heavy laurel
which he denies
So he isn't actually making a definitive statement, he's just leading us on to what he wants us to think he'd say?
sturdy cypress
well since you fell for it, it makes sense to frame it like that, that he's being tricky
but it's not ambiguous actually
it's precise, he's lying, he could be telling the truth in a weird way too
like if he was a knight
he could tell you the truth in a super weird way that would mislead you, doesn;t make him a knave
heavy laurel
he could tell you the truth in a super weird way that would mislead you, doesn;t...
So he's the spy, not the knave?
sturdy cypress
he's the knave
heavy laurel
lmao maybe math isn't for me 💀
sturdy cypress
you can't really tell if you're having an unusually hard time, maybe you're in fact learning faster than average
but even if you;re not, it's still worth the time 🤷♂️
final saddleBOT
@heavy laurel Has your question been resolved?
terse parcel
Hello I need help with this problem , I gotta demonstrate that for any n>= 5 ; 2^n > n^2 using the recurrence method
final saddleBOT
Hello I need help with this problem , I gotta demonstrate that for any n>= 5 ; 2...
lethal estuary
is that different than induction?
lethal estuary
well start with the base case. then assume that if it is true for n=k, it is true for n=k+1
lethal estuary
well if $2^n > n^2$, how can you get that to "look like" the statement for n=k+1
soft zealotBOT
cwatson
lethal estuary
you ultimately want to show that $2^{n+1} > (n+1)^2 = n^2 + 2n + 1$
soft zealotBOT
cwatson
terse parcel
**cwatson**
I wanna show this
lethal estuary
yeah, it's a bit tricky. you can see the logic behind it here: https://math.stackexchange.com/a/497102/993372
terse parcel
yeah, it's a bit tricky. you can see the logic behind it here: https://math.stac...
What do these mean
What does the dollar sign mean
And end align
I think that link is meant for pc users
terse parcel
Hello I need help with this problem , I gotta demonstrate that for any n>= 5 ; 2...
<@&286206848099549185>
lethal estuary
lethal estuary
yeah the second part is the tricky one
lethal estuary
$2 \times 2^n > 2 \times n^2$ is just using the induction hypothesis. The second inequality completes the induction proof, and uses what he does in the second half of his answer
soft zealotBOT
cwatson
final saddleBOT
final saddleBOT
Available help channel!
empty leaf
hi
finite vale
b. X - ~ (,)
honest mirage
I haven't learned this idk how to help
worthy shale
what is part b asking
final saddleBOT
@finite vale Has your question been resolved?
finite vale
what is part b asking
X - ~ ()
I'll double check when I'm back from the gym
It like won't let me send it before it auto goes to that discord doesn't let you put underscores
finite vale
what is part b asking
: Yoonie is a personnel manager in a large corporation. Each
month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately
four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time
it takes her to complete one review. Assume Χ is normally distributed. Let X
¯
be the random variable representing the mean
time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.
finite vale
<@&286206848099549185> can someone help me please im beggigng it's been hours
empty schooner
can someone please help with this one
Find two vectors v1 and v2 whose sum is <5,-1>, where v1 is parallel to <-5,3> and v2 is perpendicular to <-5,3>. what is v1 and v2
hard plover
<@&286206848099549185> can someone help me please im beggigng it's been hours
Use Chat-GPT, it'll explain everything for you.
twin adder
final saddleBOT
twin adder
I need to find the critical points of the surface $f(x, y) = y\sqrt{x} - y^2 - x + 3y$ for $0 \le x \le 9$, $0 \le y \le 5$
soft zealotBOT
o.O
twin adder
I have the gradient, but I have no idea how to solve the gradient to be 0
I was also wondering if I was supposed to use lagrange multiplier since this is optimization
I have $\triangledown{f} = \left(\frac{y}{2\sqrt{x}} - 1, \sqrt{x} - 2y + 3\right)$
soft zealotBOT
o.O
twin adder
Not sure how to solve for the x partial or y partial at 0
$$\frac{y}{2\sqrt{x}} - 1 = 0$$
$$\sqrt{x} - 2y + 3 = 0$$
soft zealotBOT
o.O
twin adder
actually do we just use Extreme Value Theorem
final saddleBOT
@twin adder Has your question been resolved?
twin adder
.close
sonic crescent
Hi, does anyone know how to do this?
final saddleBOT
Hi, does anyone know how to do this?
sonic crescent
Do we do a u sub?
royal gust
Ye. x = 4tan(u)
If you're new to trig subs, take a quick look for a video to see a problem done. It's a bit more involved than usual subs
sonic crescent
How did you recognize this needed trig?
I guess you recognized this
nevermind, i don't think that applies here
royal gust
Because tan²(x) + 1 = sec²(x)
Which allows us to transform the denominator
1 + t²
1 - t²
t² - 1
All get their own sub
sonic crescent
i am confused
i do not know how tan got involved in this integral
or how the formula for sec^2(x) affects the denominator of 1/(x^2 + 16)
royal gust
Have you tried the sub yet?
final saddleBOT
@sonic crescent Has your question been resolved?
sonic crescent
Have you tried the sub yet?
I tried u substitution and got
u = x^2 + 16
du = (x^3/3) + 16x dx
dx = du / ((x^3/3) + 16x)
so our integral becomes
(du / ((x^3/3) + 16x)) / u
which is harder to integrate i think
royal gust
Ye. x = 4tan(u)
I meant the sub I suggested lol
Remember that when you u-sub, you're taking the derivative of both sides
sonic crescent
idk how to use that tho because the integral has no tan in it
royal gust
If you DID do
u = x² + 16
Then du = 2x dx
sonic crescent
oh i took the integral instead of the derivative lol
so using x = 4tan(u)
we get dx/(4tan(u)^2 + 16) ?
royal gust
x = 4tan(u)
dx = 4sec²(u) du
And x² = 16tan²(u)
We get
∫ 4sec²(u) / (16tan²(u) + 16) du
And of course don't forget to change the bounds to u
final saddleBOT
@sonic crescent Has your question been resolved?
storm orchid
final saddleBOT
storm orchid
Work is Force*displacement
The acceleration here would be zero though, so wouldn't the work be zero?
Or, how is that not the case I guess is a better question since that can't be the case.
nvm force of gravity.
.close
gusty pond
Can you find the problem with this proof, I saw it on the internet a few days ago and it took me 5 minutes to figure it out
final saddleBOT
Can you find the problem with this proof, I saw it on the internet a few days ag...
gusty pond
Find the mistake with this proof
i^0 = 1
i^4 = 1
i^0 = i^4
0 = 4