cool
#help-0
lone heartBOT
icy sierra
thanks dude
no probs
lone heartBOT
Available help channel!
drifting stump
lone heartBOT
drifting stump
I would like to ask how do i solve this question. Thank you
gray isle
using the definition of continuity
drifting stump
using the definition of continuity
How does it work ?
icy sierra
How does it work ?
if a function has breaks or holes in between it is discontinuous
drifting stump
What i have to do it prove lim X>2- is qual to lim X<2+?
If the results are same, it is continuous
frail grove
do u mean the epsilon delta definition or $\lim_{x\to a}f(x)=f(a)$ ?
ocean sealBOT
Adam Chebil
civic flame
anyone could help me think how to make f(x) formula from this? assuming x is Refill, and f(x) is Cumulative Price
lone heartBOT
anyone could help me think how to make ``f(x)`` formula from this? assuming ``x`...
@civic flame Has your question been resolved?
timber turtle
its been 15 min so you can do <@&286206848099549185> now
pale kestrel
-
Compute the number of integer paths from (0, 0) to (n, n) that only go right or up
-
How many of those don't go below y = x
-
2n choose n
-
Looking for a hint
pale kestrel
It probably helps if I recall what the answer to 2 was supposed to be, but I cant atm zzz
royal meadow
a hint? ok consider sorta reflecting all the things that do go below y=x upwards
and then how much does that cut down on possibilities
pale kestrel
but what about the things that go both above and below
royal meadow
just reflect the bits that go below
pale kestrel
k will try
pale kestrel
I mean like...
its not clear to me without having a really good go how this allows me to proceed
Maybe i should try a small n
n = 3
royal meadow
give it a shot
junior blade
i wonder if you can write down an induction
pale kestrel
And then you want me to reflect
junior blade
eh, probably not
pale kestrel
So that will become U R U U R R
junior blade
you have to figure out how many paths get smushed into the same path
that seems hard
pale kestrel
yeah...
junior blade
count how many paths hit y = x k times, and then weight those by 2^(1-k)
pale kestrel
So the answer relates to the catalan numbers for whatever reason, idk anything about those
But yeah i wanted to try get there from first principles
keen plinth
the answer to 2. is the catalan numbers exactly
pale kestrel
Does understanding how to do 2 essentially boil down to understanding these numbers
however theyre constructed, whatever they are
like thats their definition you mean?
maybe i should go lookit up 
pale kestrel
count how many paths hit y = x k times, and then weight those by 2^(1-k)
Whats your thinking behind this, not sure I follow
junior blade
Whats your thinking behind this, not sure I follow
if you have k-1 traversals away from y=x, you can flip each of those below the diagonal independently
keen plinth
if you reflect across y=x-1 after the first time the path dips below y=x, you will always reach (n+1,n-1)
pale kestrel
hmm. Ok i think ive got enough hints to play around with for now - ty
pale kestrel
if you reflect across y=x-1 after the first time the path dips below y=x, you wi...
ah ok, thats like smart
and that leads to exactly the answer i remember now
Will have a go writing it down before i close
hmm hmm think im almost there. tys
.close
grizzled geode
How to solve?
lone heartBOT
How to solve?
icy sierra
Do you know long division
left roost
How to solve?
did you learn about l'hopital's rule?
grizzled geode
did you learn about l'hopital's rule?
Nope
grizzled geode
Do you know long division
I know but that would a lot of time
pale kestrel
So the usual approach to limits that arent -> 0
is to do a substitution to make them -> 0
That's not always necessary, but is often helpful when you're stuck
So the substitution y = x - 1 will do the trick here.
lone heartBOT
@grizzled geode Has your question been resolved?
fallen rain
For this question why is 4-2gsin(alpha)?
lone heartBOT
For this question why is 4-2gsin(alpha)?
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.
worn fox
you decompose the force of gravity into components parallel to the slope and perpendicular to the slope
fallen rain
Is there a formula for calculating acceleration
I think is the formual F=ma
rigth?
*right
worn fox
yes thats what they mean when they say "use newtons second law"
but its really "sum of the forces = ma"
hence the 4-2gsin(alpha)
4 is going up the slope (in direction of accelertion) and the force of gravity going down the slope (opposing acceleration) is 2gsin(alpha)
lone heartBOT
@fallen rain Has your question been resolved?
fallen rain
@worn fox Why they didn't add R (the reaction force)
fallen rain
When we need to resolving perpendicular or parallel to the slope?
fallen rain
@worn fox
worn fox
well here youre trying to find the acceleration
and the direction of acceleration is parallel to the slope
so you resolve parallel to slope
worn fox
if you're trying to solve for something that is acting in a direction perpendicular to the slope
or sometimes you might need to do both
lone heartBOT
@fallen rain Has your question been resolved?
polar rover
What/Is there is a non-trigonometric function where f(0) = 0, f(1) = 1, f(2) = -1, f(3) = -1, f(4) = 1, and for all x in Natural Number set, f(x) = f(x+4)?
polar rover
Z
vale wigeon
wait hang on
polar rover
Z+ i should say
vale wigeon
f(0) = 0
f(4) = 1
f(x) = f(x+4)
the third of these contradicts the first two
so im gonna ask for the original context.
alpine sable
Can anyone plz help me why is this wrong ?
vale wigeon
Can anyone plz help me why is this wrong ?
!occupied
lone heartBOT
Can anyone plz help me why is this wrong ?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
polar rover
mmhmm that's why i said for all N
original function is trigonometric and i have to find the non-trig version for a power series
This specifically has just been frustrating me for like an hour
polar rover
I don't know if I can show the original problem, but I'll try to catch you up to speed:
f(x) = sin(x) + cos(x) - 1
f(0) = 0
f^1(0) = 1
f^2(0) = -1
f^3(0) = -1
f^4(0) = 1
vale wigeon
I don't know if I can show the original problem,
why not
polar rover
Give me one second i'll see if i can find it
Yeah i'm just gonna give up on this one thanks though
vale wigeon
why can't you show me the original problem?
polar rover
I can't find the sheet I have my work on
Been trying to solve this one specific thing in notability
vale wigeon
notability?
lone heartBOT
@polar rover Has your question been resolved?
tacit arch
notability?
Just a note app
fervent timber
no
sly mantle
.close
dapper bluff
hello
stark crater
i tried cross product and it didnt work
show work?
should have worked as long as you remembered to make magnitude 1 after
dapper bluff
should have worked as long as you remembered to make magnitude 1 after
so take the unit vector?
and the just do a*b = 0 right?
stark crater
so take the unit vector?
Nah, you do the cross product first, this gives you a perpendicular vector. The problem asks for a unit vector so you need to normalize it
maybe thats what u meant
idk what u meant by a*b=0 though
stark crater
I believe you should have gotten -1 for j component
1(5)-3(2)=-1
Nvm I forgot how determinants work
You right
Now find magnitude, then divide (3, 1, -2) by it
stark crater
Should be done after that
stark crater
np
dapper bluff
.close
knotty kernel
Hi, please help me with this homework
Eng: 6) In the unitary circumference a point P of the circumference whose angle of the center is
glacial patrol
Hi, please help me with this homework
Eng: 6) In the unitary circumference a po...
,rotate
ocean sealBOT
glacial patrol
Pues simplemente búscalo en Google entonces :p
knotty kernel
okey, muchas gracias
glacial patrol
no problema
knotty kernel
.close
serene vault
hello
serene vault
how can i relate PPV to baye theorem
this being bayes theorm
say I have a population in which 0.2% have the disease
and the test has a 90% sensitivty and specificity rate
it is easy to construct this using PPV... but when it comes to using bayes theorem it confuses me
what would be p(b) in bayes theorem...
delicate acorn
do you have a picture of the question?
glacial patrol
P(B) = P(B|true)P(true) + P(B|false)P(false)
serene vault
.9 being the 90% sensitivity
0.002 being the .2% incidence rate of disease found
and the .1 being the 10% of false positives
i guess im failing to understand the context of P(B|true) etc
B given true?
glacial patrol
OK so 10% false positive refers to the case where virus or whatever is not there but is detected anyways if I'm interpreting it correctly?
serene vault
correct
where someone who does not have the disease is marked positive
the sensitivity
the specificity is also 90%
glacial patrol
OK lemme give them better labels them
glacial patrol
B = "marked positive"
- = "marker not there"
- = "marker there"
P(B|-) = 0.1
P(B|+) = 1 - P(B|-) = 0.9
Then P(-) = 0.998
P(+) = 1 - 0.998 = 0.002
P(B) = P(B|-)P(-) + P(B|+)P(+)
wait just to check
Sensitivity is detect when it is there right?
serene vault
yep
glacial patrol
OK yeah
plucky void
Have you tried your calculator yet?
serene vault
this isnt about using a calculator
i could easily divide it all out using PPV
but i am trying to better understand baye theorem
just wana bump this down
glacial patrol
cus you start off with $P(B) = P((B \cap (+ \cup -)))$, since + and - are complementary events
ocean sealBOT
992qqoloy
serene vault
so what is P(A) and does this essentially mean the probability of A
denoted by the "P"?
glacial patrol
Then that's $P(B \cap +) + P(B \cap -)$
ocean sealBOT
992qqoloy
glacial patrol
Yeah
And then if you have two events like $X$, $Y$, it's also the case from another statement of bayes' rule that$P(X \cap Y) = P(X| Y) P(Y)$, so $P(B \cap +) = P(B| +) P(+)$, similar for the other term
ocean sealBOT
992qqoloy
glacial patrol
just wana bump this down
The full statement is like $P(A|B) P(B) = P(A \cap B) = P(B|A) P(A)$
ocean sealBOT
992qqoloy
serene vault
could i write P(A|B) as: (Probability person has X disease given a positive result)
or would it need to be more specific
like Probability person has X disease given 90% sensitivity on positive result
serene vault
so P(A) is (probability person has X disease)
which is defined as 0.2%
due to the rate of incidence?
glacial patrol
yeah
glacial patrol
Nah P(B|A) is .90
serene vault
so what is P(B)
serene vault
maybe theres more to the bayes theorem i am missing
serene vault
can we take a step back
to P(B|A)
why would A change the outcome of (B|A)
it is already established that there is 90% sensitivity
without the need for the incidence rate of 0.2%
glacial patrol
Well Hopefully whether the disease is there or not affects the probability that it gives a positive
Otherwise it'd be a really bad test
serene vault
maybe its the outline of the question im being asked
cause it first says the sensitivity is 90%
then later says the incidence rate
glacial patrol
yeah incidence rate is just P(A)
glacial patrol
Yup
serene vault
but so is P(A|B)
glacial patrol
You can calculate P(B) in terms of the knowns tho
P(B) is the denominator in the PPV expression
Cus $P(A)$ gives you $P(A^C)$
ocean sealBOT
992qqoloy
glacial patrol
That's just $1 - P(A)$
ocean sealBOT
992qqoloy
glacial patrol
And $P(B|A^C) = 1 - P(B|A)$
ocean sealBOT
992qqoloy
glacial patrol
serene vault
hmm ok this is where im missing
glacial patrol
Proof of a more general formula where E_i partition the whole sample space (this is basically that formula but E_1 = A and E_2 = A^C)
And this is the total probability theorem proof
lone heartBOT
@serene vault Has your question been resolved?
olive cypress
I’m trying to use lagrange multipliers to solve this
lone heartBOT
I’m trying to use lagrange multipliers to solve this
olive cypress
The function f(x, y) = x^2 + y^2 is maximized on the circle x^2 + y^2 <= 1 at what values?
the options are (0, 0), (0, 1), (1, 0), (1, 1), and (1/sqrt2, -1/sqrt2)
I think it’s all of them except (0, 0) and (1, 1) but I’m not sure
<@&286206848099549185>
plush sundial
The function f(x, y) = x^2 + y^2 is maximized on the circle x^2 + y^2 <= 1 at the point (1, 0).
olive cypress
The function f(x, y) = x^2 + y^2 is maximized on the circle x^2 + y^2 <= 1 at th...
why not the other 2?
plush sundial
which other 2
plush sundial
why not the other 2?
which other 2
olive cypress
which other 2
(0, 1) and (1/sqrt2, -1/sqrt2)
plush sundial
(0, 1) and (1/sqrt2, -1/sqrt2)
oh sorry
(0, 0), (0, 1), (1, 0), (1, 1), and (1/sqrt2, -1/sqrt2) are all correct values where the function f(x, y) = x^2 + y^2 is maximized on the circle x^2 + y^2 <= 1.
i dont really get this stuff
olive cypress
.reopen
lone heartBOT
✅
olive cypress
bruh did you just ask chatgpt or something
olive cypress
The function f(x, y) = x^2 + y^2 is maximized on the circle x^2 + y^2 <= 1 at wh...
<@&286206848099549185>
pallid scarab
I think it’s all of them except (0, 0) and (1, 1) but I’m not sure
it is
(1,1) is not on the circle
and so since you're solving on x^2 + y^2 <= 1
the highest value you can ever hope to get is x^2 + y^2 = 1
which is indeed the max
olive cypress
can you please explain how you would solve it with lagrange multipliers tho because I want to make sure I understand it
olive cypress
which is indeed the max
so I got 2x = lambda * 2x and 2y = lambda * 2y
lone heartBOT
@olive cypress Has your question been resolved?
wintry sun
I dont want a full solution with proofs. I just scribbled a bit and want to ask you if my expectations are right:
Let f: X->Y be a mapping from X to Y for any two sets. Refute or prove:
(a) For all subsets 𝐴, 𝐵 ⊂ 𝑋 we have 𝑓 (𝐴 ∩ 𝐵) = 𝑓 (𝐴) ∩ 𝑓 (𝐵).
(b) For all subsets 𝐴, 𝐵 ⊂ 𝑋 we have 𝑓 (𝐴 ∪ 𝐵) = 𝑓 (𝐴) ∪ 𝑓 (𝐵).
(c) For every subset 𝐴 ⊂ 𝑋 we have 𝑓 (𝑋 \ 𝐴) = 𝑌 \ 𝑓 (𝐴).
(d) For all subsets 𝐴, 𝐵 ⊂ 𝑌 we have 𝑓^(−1) (𝐴 ∩ 𝐵) = 𝑓^(−1) (𝐴) ∩ 𝑓^(−1) (𝐵).
(e) For all subsets 𝐴, 𝐵 ⊂ 𝑌 we have 𝑓^(−1) (𝐴 ∪ 𝐵) = 𝑓^(-1) (𝐴) ∪ 𝑓^(-1) (𝐵).
I expect:
wrong, right, wrong, right, right
lone heartBOT
I dont want a full solution with proofs. I just scribbled a bit and want to ask ...
@wintry sun Has your question been resolved?
wintry sun
<@&286206848099549185>
pallid scarab
you're correct in your intuition
solemn dagger
- The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers revealed that at the freezing point of water, some give readings below 0°C and some give readings above 0°C. Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. If 1.1% of the thermometers are rejected because they have readings that are too high and another 1.1% are rejected because they have readings that are too low, find the two readings that are the cutoff values separating the rejected thermometers from the others. Round to 2 decimal places. [8 points]
I can’t really understand this question and how to do it. I’ve tried using videos, chegg, and none of it makes sense. Someone please help ♥️
stray socket
Apply the normal distribution with mean 0 and s.d of 1. And look for the value x such that P(X <= x) = 0.011
solemn dagger
Ah, I knew I messed up a step. I did 1.1 instead of 0.011
stray socket
According to my cg 50 it should be -2.29 and 2.29
stray socket
Ah, I knew I messed up a step. I did 1.1 instead of 0.011
ah
solemn dagger
I did this problem twice and both times I knew I messed up
So the highest would be 0.011 and the lowest would be -0.011?
stray socket
No, 0.011 is the probability it cant be negative
solemn dagger
Does this look correct? I’m sorry for asking so many questions
stray socket
the 0.011 should be after the = sign
solemn dagger
How would I write down the answer and steps? I know I have to write down the equations
stray socket
hmm
solemn dagger
Sorry, lemme rephrase that lol
Do we get -2.9 from the p(x < or equal to) equals 0.011?
stray socket
yep you're finding a value such that only 1.1% of values are equal to that value of less than it
solemn dagger
Is there anything else I have to write for the problem
stray socket
are you allowed a calculator?
solemn dagger
We can’t use technology to help us with this
stray socket
just formulae?
solemn dagger
Yeah and our own papers
stray socket
I haven't been taught any methods to find the inverse normal without a calculator, we get given a table. Even then it only has specific values like 1%, 5%, 10% so not values like 1.1%
solemn dagger
Yeah that is what’s so weird about this assignment
stray socket
Yeah that is what’s so weird about this assignment
yh sorry i have no idea then
solemn dagger
Nah you’re okay:). Thanks for the help
sour dove
which part?
lone heartBOT
@alpine sable Has your question been resolved?
subtle blade
is it possible for magnitude to be a negative number?
lone heartBOT
is it possible for magnitude to be a negative number?
subtle blade
because for this problem i got a negative magnitude
heres what i did
acceleration of block a being -3.12 doesnt seem right to me because it's going up the incline in the problem right
tardy stag
is it possible for magnitude to be a negative number?
yes if it's going the opposite way to how you drew it
subtle blade
i did something wrong then because isnt it going up in the problem?
tardy stag
acceleration of block a being -3.12 doesnt seem right to me because it's going ...
yeah the hanging block should win that fight
subtle blade
right
do you know where i went wrong?
oh wait nvm i forgot weight for summing y forces
thank you for the help though
.close
unborn geyser
lone heartBOT
unborn geyser
Help
ocean sealBOT
AℤØ
unborn geyser
you need help with the dropdown?
So answer to it is x?
jagged cobalt
yeah
unborn geyser
@jagged cobalt bruh
jagged cobalt
youve just written the values of x
ocean sealBOT
AℤØ
unborn geyser
3
jagged cobalt
yeah
unborn geyser
Is 10^0 answer 0
jagged cobalt
yeah
unborn geyser
How about this
ocean sealBOT
AℤØ
unborn geyser
$log_{16}(x)=y \implies 16^y=x$
But it only gives me x
unborn geyser
So I just plug in the numbers to x and then 16^x
lone heartBOT
@unborn geyser Has your question been resolved?
toxic geyser
hii, so i was wondering how to find the basis of a subspace in R5 but that satisfies an equation thats equal to another equation
toxic geyser
for example
3a-3b+12c=12d+0e=-3b-6d+6e
like its the double equal
thats kinda confusing me
i tried to do the rref
assuming that they were each individual vectors
but i didnt get the right answer
i also tried once in rref, putting it in parametric form
to identify the leading
and use the leading variables' equation
but that would be finding the basis for a nullspace
im a little lost
something like this
lone heartBOT
@toxic geyser Has your question been resolved?
toxic geyser
<@&286206848099549185>
toxic geyser
<@&286206848099549185>
lone heartBOT
@toxic geyser Has your question been resolved?
grand umbra
scenic wing
$\frac{x^2}{\frac{1}{x}}$
lone heartBOT
$\frac{x^2}{\frac{1}{x}}$
ocean sealBOT
putridplanet
scenic wing
how do i turn this into x^3
sour verge
x^2 / (1/x) = x^2 / (x^-1) = x^(2-(-1)) = x^3
scenic wing
$$x^2 / (1/x) = x^2 / (x^-1) = x^(2-(-1)) = x^3$
ocean sealBOT
putridplanet
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sour verge
$$x^2 / (1/x) = x^2 / (x^{-1}) = x^{(2-(-1))} = x^3$$
scenic wing
i thought you add the exponents not subtract
ocean sealBOT
Azyrashacorki
opaque vigil
How would I simplify and combine like terms for the following?
(1 - x)^3
tardy stag
$(1-x)³ = (1-x)\cdot(1-x)²$
ocean sealBOT
Haylsune Miku
tardy stag
so do the squared part first and then multiply it again
opaque vigil
Thank you! It might be too late and I've been doing math for hours now, the simplest answer eluded me 
.close
celest oak
What’s the fastest way to compute this partial derivative ?
lone heartBOT
What’s the fastest way to compute this partial derivative ?
tardy stag
three part product rule i think
(fgh)' = f'gh + fg'h + fgh'
quotient rule is a trap
dry kelp
does a congrunce still have a solution if theres no modular inverse?
dry kelp
?
lone heartBOT
@dry kelp Has your question been resolved?
lone heartBOT
@dry kelp Has your question been resolved?
tacit arch
does a congrunce still have a solution if theres no modular inverse?
depends
lone heartBOT
lone heartBOT
Available help channel!
eager iron
lone heartBOT
eager iron
I’m looking at 100 derivatives video and just got a quick question
The professor said that the notation for the second derivative is d^2y/dx^2
Because you’re d/dx ’ing (dy/dx)
But in that case.. why isn’t the notation d^2y/d^2x^2?
In the upper right corner
Because it’s not the same right? I mean if you multiply xy with xy you don’t get xy^2.. you get x^2y^2 no?
Or (xy)^2 But that’s not What we wrote here..
Last question - What does it mean if a function is not differentiable?
Thank you and sorry if these were stupid questions :(
lone heartBOT
@eager iron Has your question been resolved?
lone heartBOT
@eager iron Has your question been resolved?
placid zinc
But in that case.. why isn’t the notation d^2y/d^2x^2?
It basically is. But we quite it as d²y/(dx)², except writing the parenthesis every time would be a pain
So we write d²y/dx²
eager iron
ok, good to know
But then i wasn’t entirely wrong, that’s What i was afraid of haha
Cheers
.close
limpid spade
limpid spade
.close
lone heartBOT
lone heartBOT
Available help channel!
hollow island
How do I solve for this algebraically:
lone heartBOT
How do I solve for this algebraically:
hollow island
yea ik
vale wigeon
ok i guess you could just treat this as a system of linear equations
hollow island
its for an assingment
hollow island
wdym
i just need this to be done algebraically like simultaneous equations or sum
the start point is (200,10) and end point is (270,40)
the derivative of the start point is the ugly number, the derivative of the end point is 0
hollow island
therefore, the first equation is the start point, second is end point, 3rd is start derivative, fourth is end derivative
kinda?
im just connecting this polynomial
from one point to another
but i just need to be able to show algebraically
vale wigeon
yeah, you fix the value and derivative at two points
hollow island
what
vale wigeon
you have an unknown polynomial function for which the values at two points are fixed and the derivatives at the same points are fixed
vale wigeon
what im saying is that i think you're setting yourself up for a nightmare of work doing it THAT way specifically.
and i think there's a better way
hollow island
algebraically?
vale wigeon
yes, it'll be algebraic still
vale wigeon
i'll call the x values you've got $x_1$ and $x_2$ if you don't mind.
ocean sealBOT
Ann
vale wigeon
so $x_1 = 200$ and $x_2 = 270$ but im deliberately abstracting those away
ocean sealBOT
Ann
hollow island
ok
vale wigeon
ok now
we have our four endpoint data: $\begin{cases} y_1 = f(x_1) = 10 \ y_2 = f(x_2) = 40 \ y'_1 = f'(x_1) = -0.073... \ y'_2 = f'(x_2) = 0 \end{cases}$
ocean sealBOT
Ann
hollow island
yes
vale wigeon
these data have the nice property of being linear, meaning that if we computed these data for two polynomials and added them together, the result would be the same as if we had computed them for the sum
this lets us do the following pro gamer move:
create 4 polynomials in which exactly one of these 4 values is 1 and all the others are 0
and then add them up with the coefficients 10, 40, (ugly -0.073) and 0
hollow island
example?
i dont quite understand
visually thinking abt it doenst make sens
sense
vale wigeon
for example, i'll make $g_1$ be the polynomial with the following data: $$\begin{cases} g_1(x_1) = 1 \ g_1(x_2) = 0 \ g'_1(x_1) = 0 \ g'_1(x_2) = 0 \end{cases}$$
ocean sealBOT
Ann
hollow island
how come?
vale wigeon
and another polynomial $g_2$ with these: $$\begin{cases} g_2(x_1) = 0 \ g_2(x_2) = 1 \ g'_2(x_1) = 0 \ g'_2(x_2) = 0 \end{cases}$$
hollow island
oh so on so forth
ocean sealBOT
Ann
vale wigeon
yes
hollow island
ok
vale wigeon
and then we will build up your polynomial from these pieces
hollow island
what is this method called btw?
vale wigeon
polynomial interpolation
vale wigeon
i guess hermite interpolation more specifically?
idk, i'm just sort of winging it here not sticking to any particular named method.
vale wigeon
alright so execution might not be as smooth as we could have hoped
hollow island
oh sorry thank you
vale wigeon
almost done
hollow island
no worries
hollow island
what the
vale wigeon
it's got sliders and shit so you can play around w different values
and i've explained where everything comes from as best i can
vale wigeon
is what all in order
hollow island
like the steps u provided
cuz i see u got it right
but its kinda all over the place and idk where to start
vale wigeon
yeah it is in order
vale wigeon
yes
hollow island
how did u get the h(x) function
vale wigeon
i integrated $(x - x_1)(x - x_2)$
ocean sealBOT
Ann
vale wigeon
this is because i wanted a function whose derivative vanishes at x = x_1 and x = x_2
hollow island
so u subbed x1 for 200 and x2 for 270?
vale wigeon
yes
hollow island
then the intergral of that?
vale wigeon
well, yeaeh
hollow island
ic
vale wigeon
but you can also just treat x_1 and x_2 as constants
which i did
and it's just a polynomial function so it is not hard to integrate
i used h as a raw ingredient for g1 and g2
hollow island
and how did u come to get the functions of g1 and g2
like can u justify why u did what u did?
vale wigeon
hollow island
and where did k and l functions come from
vale wigeon
this is the main idea
vale wigeon
and where did k and l functions come from
again, raw ingredients.
so you know that a polynomial is zero at x = x_1 if and only if it has (x - x_1) as a factor right
hollow island
do u think i can just say that if im justifying it in my assignment
vale wigeon
i don't see why not.
hollow island
fair enuf
vale wigeon
you're working with derivatives anyway
hollow island
yea
vale wigeon
say, how much linear algebra do you know
hollow island
nah
vale wigeon
dang
vale wigeon
yeah cause like i kind of had those in mind when making this entire thing?
hollow island
its just advanced maths but not like higher yfm?
vale wigeon
but dont worry
vale wigeon
yes
vale wigeon
i'd say that like. this formula is the meat of it all
vale wigeon
this one?
hollow island
yea
vale wigeon
yeah what about it
hollow island
wdym the division by 2 and 6
vale wigeon
main pine
My dumbass needs some help. I'm thinking of buying a new phone soon paying by installments ofc.
$110 per month. But I need to pay it for 24 months total. How much is the overall total? $110 x 24 Months =?
main pine
Yes. I'm that ridiculously stupid.
ocean sealBOT
Result:
2640
amber nymph
Open calculator on your phone/pc i guess
runic aurora
It's just matter of using calculator
runic aurora
Which calculator does that 💀
amber nymph
Yeah but it shows me weird symbols and shi 💀
glacial patrol
this is like some enxt level dumbassery ngl 
but at least you're polite about it 👍
worn fox
Christ people leave them alone
main pine
Sorry
lone heartBOT
@main pine Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
blazing yew
yooo can someone help me with the problem
lone heartBOT
yooo can someone help me with the problem
blazing yew
(5a - 6b + 3c - 5c) + (2 - 7c + 5b + 3a) = 8a - b + _c + 5
what's the blank because i'm trying it over and over and keep getting different answers
tiny cipher
what's 3c - 5c ?
tiny cipher
should be +2
blazing yew
how so
wait
nvm i get it
did they put the problem in wrong or something
dont worry about it, i'll take it up with my teacher gang
thanks
.close
strange fractal
Hello
noble frost
if you used v = v0 + at then it should be correct
lone heartBOT
@strange fractal Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
boreal dove
Can i get some help for finding the range (without calc or graphing) of the following:
boreal dove
What I tried was:
finding the domain of the inverse
finding the derivative (to find turning point)
finding the limits at infinity, -infinity, and at the ends of the domain
coral flower
domain of inverse of function is the range of the function
boreal dove
hmm
I couldn't work it out
finding the limits at infinity, -infinity(horizontal asymptote), and at the ends of the domain
would this be valid
seems to be the quickest way
thick lynx
Can i get some help for finding the range (without calc or graphing) of the foll...
I would rationalize the numerator
boreal dove
of the inverse?
thick lynx
No, of f
That would give us $\frac{1}{\sqrt{x + 4} + 2}$.
Note that x can't be 0 (taken from f).
As x -> infty, this will go to 0.
The denominator will be the smallest at x = -4. Thus, we'll have the greatest value there, 1/2.
So our range is (0, 1/2], but we need to take into account the x \neq 0 restriction
At 0, y is 1/4.
Thus, we need to take out that value from (0, 1/2].
Thus we obtain that the range is (0, 1/4) u (1/4, 1/2].
@boreal dove
boreal dove
I see
thick lynx
WA agrees
boreal dove
WA?
thick lynx
WolframAlpha (a sort of graphing calculator)
thick lynx
np
More specifically, we need to take out 1/4 because our function only ever takes it on once (you can notice this by imagining how 1/x looks like for x > 0, as this is similar to that)
But yeah, I think rationalizing the numerator is common for finding the range, it was suggested here too, for example https://math.stackexchange.com/questions/2798275/how-do-i-find-range-of-this-function?noredirect=1
boreal dove
.close
honest vigil
can any1 help me with this?
lone heartBOT
can any1 help me with this?
thick cipher
is there a free math calculator website that doesnt have a paywall?
unreal violet
can any1 help me with this?
take the terms as a-d,a and a+d
honest vigil
take the terms as a-d,a and a+d
mind explaining further?
not sure what I did wrong here
unreal violet
uh you have to take terms as a-d, a and a+d
so that when you add the "d" gets eliminated
and you get 3a = 111
so a = 37
and then just substitute a = 37 in (a+d)^2-(a-d)^2=1776
honest vigil
uh you have to take terms as a-d, a and a+d
as in t1 t2 t3?
livid flame
How do I do the following problem? The container says it evaporates water at the rate of area of the surface of the water which would pi*f(y)^2; however, this is only constant if the shape is a cylinder as f(y) would be constant
livid flame
How do I do the following problem? The container says it evaporates water at the...
the area of the surface area of the water would be pi*f(y)^2
lone heartBOT
@livid flame Has your question been resolved?
livid flame
<@&286206848099549185>
high cargo
How do I do the following problem? The container says it evaporates water at the...
Why would it need to be a cylinder? If it gets narrower at the top then it loses less water at the same time, but the water level drops faster for the same water loss. They cancel each other out, so it’s constant
livid flame
Why would it need to be a cylinder? If it gets narrower at the top then it loses...
how would you show that mathematically?
high cargo
how would you show that mathematically?
Probably using integrals
livid flame
Probably using integrals
Can you give me more of a hint
high cargo
Can you give me more of a hint
Weil i don’t know the solution. But I’d probably try to define the water loss with an integral (relative to the time t) and then show that y is proportional to t or something. But that’s just some approach off the top of my head, i can’t guarantee it works
Might be complete bollocks but it would be what I’d look into
livid flame
I mean if the surface area is proportional to the water loss, and taking into account that the water level drops faster for the same water loss, isn't it almost obvious that the water would drop at a constant rate?
high cargo
Yes
alpine sable
Can i give you a hint too?
high cargo
Id much prefer you giving a hint than me
alpine sable
I don't want to make a mistake when giving hint 😭😭😭
high cargo
Just do it like me
Tell them straight up you don’t know
Then they can’t be mad if it’s wrong
alpine sable
Okay okay thx for confident wait
I hope its right Lol
To show that the water level drops at a constant rate, you need to demonstrate that the rate at which the water evaporates is constant. In this problem, you're given that the container is filled with water, and the water evaporates at a rate proportional to the area of the water's surface.
You correctly mentioned that the area of the surface of the water is given by πf(y)^2. To show that the water level drops at a constant rate, you should consider the rate of change of this area with respect to y. This is equivalent to finding d/dy [πf(y)^2].
Start by differentiating this expression with respect to y and see if it simplifies to a constant. If it does, it means that the rate of change of the water's surface area, and consequently the rate at which it evaporates, is constant, which is what you need to show.
Nah i am to shy now
Bye
Nvm my chat
blazing yew
Nah i am to shy now
no fr
i get too nervous to ask questions
cuz half of them r so stupid
alpine sable
My teachers shames me if I make a mistake
alpine sable
I hope my hint can give you little help
livid flame
but the surface area is already proportional proportional to the rate of evaporation
so taking the derivative wouldn't make much sense
alpine sable
Wait let me think WHAHAHAHA
alpine sable
but the surface area is already proportional proportional to the rate of evapora...
You're right, and I apologize for any confusion. You are correct that the surface area of the water is already directly proportional to the rate of evaporation. Therefore, taking the derivative of the surface area with respect to y wouldn't provide further insight into the constancy of the rate of water level drop.
The key point here is that the surface area itself is directly proportional to the rate of evaporation, and this relationship remains constant regardless of the shape of the container. Therefore, you don't need to take a derivative in this context to show the constancy of the rate of water level drop. Thank you for pointing this out.
I think i am the one learning not you WHAHAHAHAH
Tell me if you still confused about my hint or have a problem with my hint lol WHAHAHAHA
lone heartBOT
@livid flame Has your question been resolved?
rancid narwhal
lone heartBOT
rancid narwhal
in number b? won't the A = Area of rectangle + Area of semicircle?
but if I do that my answer doesn't match
why's that so?
alpine sable
Algebraic error maybe?
rancid narwhal
no
alpine sable
Can you show your progress?
rancid narwhal
i fully did that correctly
alpine sable
Send a picture
rancid narwhal
i don't have my phone right now but i do can type it
alpine sable
Alright
alpine sable
Maybe try ignoring what you got in A?
Try something simpler
Just do area of the rectangle TPQS + Area of the semisircle
Remember that it's a semicircle, not a full one
alpine sable
See that was the error
rancid narwhal
oh yea
alpine sable
I forget to do that as well sometimes too lol
rancid narwhal
been under a lot of stress u know 😅
alpine sable
Yeah dw
unborn geyser
Help
unborn geyser
Is -log_5^(x)
tacit arch
Is -log_5^(x)
What's your question
unborn geyser
Yes I see your image
Is new question
tacit arch
Try to finish a question before asking a new one
lone heartBOT
@unborn geyser Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
rapid notch
rigid pike
lone heartBOT
lone heartBOT
Available help channel!
candid lance
gcd being a function that finds the greatest common divisor between the two
lone heartBOT
gcd being a function that finds the greatest common divisor between the two
@candid lance Has your question been resolved?
velvet veldt
gcd being a function that finds the greatest common divisor between the two
still working?
candid lance
still working?
yeah still working on it, I have no clue how to write a proof for this
velvet veldt
i forget the exact theorem but there is something like gcd(x, y) = gcd(x , y - x)
this is basically the same thing
candid lance
oki ty I shall look into that
candid lance
I would love some help
velvet veldt
So let’s make a variable z, x is divisible by z and y is divisible by z
next chasm
gcd being a function that finds the greatest common divisor between the two
use eulers theorem
velvet veldt
use eulers theorem
that’s what we’re proving
next chasm
take two number, a and b
yeah ok
WLOG a <= b
if b >= a then b = k*a + p
k, p belong to N
then b mod a = p
candid lance
what does WLOG stand for?
velvet veldt
without loss of generality
slow stratus
lone heartBOT
slow stratus
I get to lim(17^k/(17^k-2^k)) and then I'm not sure what to do from there
tacit arch
use 17^k - 2^k > -2^k for all k >= 1
lone heartBOT
@slow stratus Has your question been resolved?
ocean whale
Gets canceled out
velvet veldt
tan^2 = sin^2/cos^2 which cancels out with cos^2
ocean whale
Because you distribute
velvet veldt
becoming sin^2
velvet veldt
the denominator is distributing cos^2 to 1 - tan^2
lone heartBOT
fringe sleet
the parenthesis explains it
solemn birch
i am getting help from a math solver website and it says that 15 should be multiplied with each side but it only gets multiplied on the right side?
tacit arch
15 / 3 = 5
solemn birch
why 15 / 3?
solemn birch
okay and also, why does 15 multiply with each side?
tacit arch
3 * 5 = 15
solemn birch
is that a rule?
tacit arch
is what a rule?
solemn birch
i'm very dumb with equations
tacit arch
something like this?
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-gcf/v/greatest-common-divisor-factor-exercise
alpine valve
am I doing this right
lone heartBOT
am I doing this right
stark yew
,w factorize 2x^3 + x^2 - x
ocean sealBOT
stark yew
am I doing this right
So far so good. Go ahead and compute A, B, and C.
lone heartBOT
@alpine valve Has your question been resolved?
stark yew
,w partial fractions 1/(x(2x-1)(x+1))
ocean sealBOT
stark yew
,w int 1/(2x-1) dx
ocean sealBOT
stark yew
Almost
It would be
$$ -\ln\mid x\mid + \frac13\ln\mid x+1\mid + \frac23\ln \mid 2x - 1\mid $$
alpine valve
wait why
ocean sealBOT
waris
alpine valve
oh mb
bc u sub
so 1/6 du = dx
4/6 is 2/3
and 1/u is ln|u|
so 2/3 ln|6x-3|
and u=3x+3
du=3dx so 1/3du = dx
stark yew
Sincere apologies. I made a mistake too
It would be
$$ -\ln\mid x\mid + \frac13\ln\mid x+1\mid + 2\ln \mid 2x - 1\mid $$
ocean sealBOT
waris
ocean sealBOT
stark yew
u = 6x - 3
du = 6 dx
4/(6x - 3) dx
= 4/u du/6
= (4/6)du / u
Hmmmm..
It's 3am and i really don't wanna go and get a notebook : |
stark yew
I don't see why 2/3 ln(6x-3) is wrong
I don't see it either
alpine valve
maybe bot wrong
stark yew
But 2/3 ln|2x - 1| doesn't appear to be wrong either
stark yew
maybe bot wrong
Oh no the bot is definitely not wrong
alpine valve
lol
stark yew
,w plot (2/3)ln|2x-1| and (2/3)ln|6x-3|
ocean sealBOT
