yes
#help-36
soft zealotBOT
▓hehe._.
grizzled crescent
yes
grizzled crescent
times what?
severe dagger
income
severe dagger
According to Kristin's observation, the tax is also equal to (p+0.25)% of her annual incoe
grizzled crescent
what?
severe dagger
ye
grizzled crescent
uhh ok...
grizzled crescent
ah yes
severe dagger
right
grizzled crescent
but whats different about those two you just said?
grizzled crescent
uhh yeah
severe dagger
and which one
severe dagger
oh, same information, expressed in different ways
grizzled crescent
ah ic
severe dagger
ye
anyway
where was i
lets see
p% × $28000 + (p+2)% × (I−$28000) = (p+0.25)% × I
soft zealotBOT
▓hehe._.
severe dagger
this bot man...
grizzled crescent
man
soft zealotBOT
▓hehe._.
severe dagger
ok
anyway
do u understand so far
becaues i gotta sleep soon
its 7:53 PM
i have tennis acadmedy tmr
6:30 am
lol
grizzled crescent
oh srry
severe dagger
very busy as u see
boreal yew
WHY DO I HAVE 17 PINGS FROM THIS SERVER
grizzled crescent
im srry lol uh
severe dagger
WHY DO I HAVE 17 PINGS FROM THIS SERVER
cuz u helper
severe dagger
srry uhh i pinged helpers because mine ditched
lol
tranquil pine
who pinged
severe dagger
who pinged
@boreal yew
boreal yew
i need help with my AP calc assignment
severe dagger
anyhow
its kinda nice to see people from around the world come to this channel
lol
grizzled crescent
moving onnn
severe dagger
im from canada
grizzled crescent
lol true
severe dagger
where y'all from rn
severe dagger
washington?
oh wait
i never mentioned which province im from
so which state u in
tranquil pine
i’m from New York
severe dagger
im british columbia
severe dagger
damn
grizzled crescent
someone save me
severe dagger
is it like midnight there
severe dagger
severe dagger
tranquil pine
severe dagger
anyway
grizzled crescent
aight so back to the question because i got like a few
😭
sooo why does the equation you gave me work
severe dagger
as much as i'd liket o stay and hep, my crazy mother is yelling at me to sleep
can i help u tmr
srry
it was last minute
😦
grizzled crescent
ok
lol
i might ask for some more help
i might have to ping again...
im gonna get cancelle
and warned
<@&286206848099549185>
😭
im sorry for pinging again but my second helper ditched me
severe dagger
im sorry for pinging again but my second helper ditched me
my bad man
severe dagger
*women
severe dagger
its ok go to sleep
its fine
my mom is boiling water
imw atching the fire for her
ok lets see
p% × $28000 + (p+2)% × (I−$28000) = (p+0.25)% × I
soft zealotBOT
▓hehe𓅭
severe dagger
we were there
@grizzled crescent
now, to make life easier, we can convert percent to decimals
0.01p × $28000 + 0.01(p+2) × (I−$28000)=0.0125 × I
soft zealotBOT
▓hehe𓅭
0.01p × $28000 + 0.01(p+2) × (I−$28000)=0.0125 × I
```Compilation error:```! LaTeX Error: Unicode character − (U+2212)
not set up for use with LaTeX.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.52 0.01p × $28000 + 0.01(p+2) × (I−
$28000)=0.0125 × I
You may provide a definition with
\DeclareUnicodeCharacter```
severe dagger
0.01p is used to represent
p% as a decimal.
severe dagger
and what is o?
bot stuff
severe dagger
ye
grizzled crescent
😭
severe dagger
what grade r u in
severe dagger
我困了
severe dagger
cya
supple nest
final saddleBOT
supple nest
why is this not right
supple nest
oh
fathom walrus
U need to sub back in
Yea do this
manic flame
also you forgot to divide by 2
supple nest
i did and it said i had the wrong answer
manic flame
du = 2dx
du/2 = dx
supple nest
why
manic flame
du = 2dx
du/2 = dx
this is why
fathom walrus
u = 2x - 5
fathom walrus
du = 2dx
du/2 = dx
therefore:
supple nest
why is du 2dx tho
manic flame
yes du would be 2xdx
tepid anvil
you are missing a term
manic flame
$\frac{d}{d\theta}\left(\frac{\sin^{3}\left(\theta\right)}{3}\right)=\sin^{2}\left(\theta\right)\cos\left(\theta\right)\ne\cos^{3}\left(\theta\right)$
soft zealotBOT
Combustion
manic flame
why is this wrong
$\int_{ }^{ }\cos^{3}\left(\theta\right)d\theta=\int_{ }^{ }\cos^{2}\left(\theta\right)\cos\left(\theta\right)d\theta$
soft zealotBOT
Combustion
manic flame
then use the hint that they gave you
final saddleBOT
@supple nest Has your question been resolved?
elder girder
Help
elder girder
thin jasper
what's the question
west berry
Is RP a tangent?
elder girder
yes it says all line which apeear tangent are tangent '
final saddleBOT
@elder girder Has your question been resolved?
final saddleBOT
@elder girder Has your question been resolved?
final saddleBOT
@elder girder Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
mellow verge
@frail pebble
final saddleBOT
<@397085665923432448>
mellow verge
To prove ( (x + (1 - x))^n > \sum_{k=0}^{n} \binom{n}{k} \left(\frac{x}{1-x}\right)^k (1-x)^{n-k} > \sum_{k=0}^{n} \binom{n}{k} \left(\frac{x}{1-x}\right)^n (1-x)^{n-k} ), we can use the binomial inequality. The binomial inequality states that for every real number ( r > -1 ) and every positive integer ( n ):
[ (1 + r)^n > \sum_{k=0}^{n} \binom{n}{k} r^k. ]
Note that ( \frac{x}{1-x} ) is positive since ( 0 < x < 1 ). Therefore, we can apply the binomial inequality to each part of the given inequality.
For the left part:
[ (x + (1 - x))^n = 1^n = 1, ]
which is certainly greater than the binomial sum.
For the middle part:
[ \sum_{k=0}^{n} \binom{n}{k} \left(\frac{x}{1-x}\right)^k (1-x)^{n-k} ]
is guaranteed to be greater than ( (x + (1 - x))^n = 1 ) due to the binomial inequality.
For the right part:
[ \sum_{k=0}^{n} \binom{n}{k} \left(\frac{x}{1-x}\right)^n (1-x)^{n-k} ]
is equal to ( \left(\frac{x}{1-x} + (1-x)\right)^n ). Applying the binomial inequality, we get:
[ \left(\frac{x}{1-x} + (1-x)\right)^n > \sum_{k=0}^{n} \binom{n}{k} \left(\frac{x}{1-x}\right)^n (1-x)^{n-k}. ]
soft zealotBOT
⩩ 𓍢 ׅ 🎀⃞ꭑֹ𝗮̈𝗱ꫀ𝗹𝗂n͟𝗲̄ ♡゙ ˖ ݁ ˓ :
final saddleBOT
@mellow verge Has your question been resolved?
viscid nacelle
to find equatiopn of curve from gradient function do i just intergrate it?
viscid nacelle
say i have dy/dx = 3x^2 -20x +29
viscid nacelle
if you mean equation of the curve, then yes
cureve ofc sorry yeah
thanks
.close
final saddleBOT
random forge
final saddleBOT
Available help channel!
burnt stirrup
I need help to tackle this problem. I started by multiplying both sides with (1-z)^3 and I tried to manipulate the indexes of the sums, but I can't seem to get anywhere... It always leads to an absurdity or something similar.
final saddleBOT
I need help to tackle this problem. I started by multiplying both sides with (1-...
floral nova
The usual trick here is to notice that $\sum_{n=2}^{\infty} n(n-1)z^{n-2} = \frac{d^2}{dz^2} \sum_{n=0}^{\infty} z^{n}$
soft zealotBOT
JessicaK
final saddleBOT
@burnt stirrup Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
neon meteor
Please can someone walk me through Quantile Regression? I understand what a quantile is. What I don't understand is: how the loss function works (or is derived), and how a Y output variable can be quantile-regressed on an X-input variable.
final saddleBOT
Please can someone walk me through Quantile Regression? I understand what a quan...
neon meteor
Maybe if I just provide this slide from class and ask someone to hold my hand as I try to walk through this.
OK; here goes
q-hat is a value of random variable Y, which I assume we have a list of observed values for; i.e. we have n observations. Which particular value q-hat is depends on tau, the quantile level. q-hat(tau) is a function that takes a quantile level, sticks it into the Cumulative Distribution Function of Y, and returns a value of Y.
To return the value from the cumulative distribution of Y, the q-hat(tau) function minimizes the sum of many callings of the rho-sub-tau function, which takes as its input each observed value of Y, minus b, where b is the correct tau-th quantile value of Y.
(If I screw up at any point and you're reading this, just emoji-react with a red cross / the smiling poo face / the melty smile / etc.; whatever you feel like, it's up to you)
The rho-sub-tau function is a "loss function", i.e. it returns a value that describes the "loss" associated with a certain input value (right? pretty unsure here)
When a single Y-sub-i value in our array of observed Y-values is bigger than the true tau-th quantile value, the rho-sub-tau loss function takes a positive number as an input. Moreover, the bigger Y-sub-i is in comparison to b, the bigger the positive number input into the rho-sub-tau loss function. For example, if the tau-th quantile value was actually 3, and a Y-sub-i value was 9, then the rho-sub-tau loss function would take 9 – 3 = 6 as an input.
Conversely, when a single Y-sub-i value in our array of observed Y-values is smaller than the true tau-th quantile value, the rho-sub-tau loss function takes a negative number as an input. Moreover, the further Y-sub-i is below b on the number line, the larger in absolute magnitude is the negative number input into the rho-sub-tau loss function. For example, if the tau-th quantile value was actually 3, and a Y-sub-i value was 1, then the rho-sub-tau loss function would take 1 – 3 = –2 as an input.
Only when Y-sub-i = b does the rho-sub-tau loss function take a 0 as input.
The rho-sub-tau loss function works like the following. Let's look at the parenthesized terms first.
tau is the quantile figure we're looking for; e.g. if we're looking for the 25%-quantile, AKA the 0.25 quantile, tau = 0.25.
Block-letter 1 is an indicator function that returns 1 if whatever the input to the rho-sub-tau function is negative, and returns 0 otherwise.
So, the parenthesized bit of the rho-sub-tau function is the quantile value if the input to the function is positive, and is the negative inverse of the quantile value if the input to the function is negative.
For example, if tau = 0.25, then if the input to the rho-sub-tau function is positive, the parenthesized bit of the rho-sub-tau function returns 0.25. If the input to the function is negative, the parenthesized bit returns –0.75.
The rho-sub-tau function takes the parenthesized bit, and multiplies it by the input value passed to it.
So, for example, let's say tau is 0.25. And let's say the tau-th quantile value, i.e. the 0.25 quantile value, AKA the 25% quantile, is actually 3. That is, b = 3.
While summing over the observed values of Y-sub-i, the sum takes a single observed value of Y, 9.
Y-sub-i – b = 9 – 3 = 6.
So we feed 6 into the rho-sub-tau function. 6 is larger than 0, so the indicator function inside the parentheses returns 0. That means the parentheses just contains tau = 0.25.
Then the rho-sub-tau function multiplies tau by the input to the function, which was 6.
0.25 * 6 = 1.5. So, the output of this particular calling of the rho-sub-tau function is 1.5.
1.5 gets passed back to the summation.
Every time a single observed value of Y is bigger than the actual 0.25-quantile value we're after, the rho-sub-tau function returns the quantile value (tau) multiplied by the distance between the single observed value of Y and the true tau-th quantile value of Y.
So, if tau is still 0.25 and the tau-th quantile value is still 3, and another single observed value of Y is 11, then, the distance between the true tau-th quantile and the observed value is 8, multiplied by the quantile value tau is 2.
But every time a single observed value of Y is smaller than the actual 0.25-quantile value we're after, the rho-sub-tau function returns the negative inverse quantile value (1 – tau) multiplied by the distance between the observed Y-value and the true tau-th quantile value.
But because that distance is negative (because [smaller than true value] minus [true value] produces a negative number), and negative times negative is positive, then the loss function returns a positive value.
It just returns a positive value for its "loss" that is the inverse value of the tau-value, multiplied by the absolute distance between the observed Y-value and the true tau-th value b.
So for example, b = 3, tau = 0.25. Y-sub-i = –2.
Y-sub-i – b = –2 – 3 = – 5.
The rho-sub-tau function takes –5 and multiples it by 1 – 0.25 = –0.75.
–0.75 * –5 = 0.75 * 5 = 3.75
Great, so I understand that the loss function returns loss values if the observed Y-value is not the true tau-th quantile b.
And, it weights loss values, so that if tau is small and Y-sub-i is bigger than b, the loss generated by a distance between Y-sub-i and b and is smaller than if tau was small and Y-sub-i was even smaller; in that latter case, the loss would be larger.
And vice versa, if tau is large (e.g. 0.8) and Y-sub-i is bigger than b, the loss generated by a distance between Y-sub-i and b and is larger than if tau was big and Y-sub-i was small; in that latter case, the loss would be smaller.
OK, that's where my understanding ends. I guess the questions are:
1) What's the point in weighting the losses according to where observed Y-values are in relation to some given tau?
and
2) What's the point in summing all those returned losses? The sigma-summation in the original image up there is just going to operate over every Y-value in our array of observations, right? How does that relate to a minimization of that sum?
final saddleBOT
@neon meteor Has your question been resolved?
final saddleBOT
neon meteor
.reopen
final saddleBOT
✅
neon meteor
<@&286206848099549185> ?
final saddleBOT
@neon meteor Has your question been resolved?
neon meteor
OK so I think I've answered my own questions, perhaps. If the tau-th value isn't b, then the loss function returns a higher value than the minimum.
For example, let's say that we have four observed Y-values: { –2, 3, 9, 15 }.
tau is 0.25; we want to find the 25% quantile. Now, we know that it's 3, but let's pretend we don't know it's 3 for the moment. Let's pretend we think it's 9. So we say b = 9.
Find our (Y-sub-i – b) values:
–2 – 9 = –11
3 – 9 = –6
9 – 9 = 0
15 – 9 = 6
Pass them into the rho-sub-tau function:
–11 * –0.75 = 8.25
–6 * –0.75 = 4.5
0 * 0.25 = 0
6 * 0.25 = 1.5
Sum the returned values from the rho-sub-tau function:
8.25 + 4.5 + 0 + 1.5 = 14.25
OK, now let's say we now guess (correctly) that b = 3.
Find our (Y-sub-i – b) values:
–2 – 3 = –5
3 – 3 = 0
9 – 3 = 6
15 – 3 = 12
Pass them into the rho-sub-tau function:
–5 * –0.75 = 3.75
0 * 0.25 = 0
6 * 0.25 = 1.5
12 * 0.25 = 3
Sum the returned values from the rho-sub-tau function:
3.75 + 0 + 1.5 + 3 = 8.25
And then if we guess (incorrectly) that b = –2:
Find our (Y-sub-i – b) values:
–2 – (–2) = 0
3 – (–2) = 5
9 – (–2) = 11
15 – (–2) = 17
Pass them into the rho-sub-tau function:
0 * 0.25 = 0
5 * 0.25 = 1.25
11 * 0.25 = 2.75
17 * 0.25 = 4.25
Sum the returned values from the rho-sub-tau function:
0 + 1.25 + 2.75 + 4.25 = 8.25 also?
So I guess the 0.25 quantile could be either –2 or 3
But what's happening here is: when our guess of b is the correct tau-th quantile value we're after (in our example, 3), the loss function returns larger losses for quantiles below the tau-th value, and smaller losses above the tau-th value, such that the losses are proportional; i.e. they cancel each other other. E.g. in the rho-sub-tau loss function, in the parentheses, the absolute value of that parenthesized value when a single observed Y-value is below b is 0.75. But for the three observed Y-values above b, the absolute value of the parenthesized value is 0.25. And those three 0.25s summed balance out the single 0.75
So the weighted losses balance out when our guess of b is correct
OK, thanks me
.close
tranquil pine
If the number of calls received per hour by a telephone answering service is a Poisson random variable with parameter $\lambda = 6$. What is the probability that the next 3 calls will be received within the next 30 minutes?
final saddleBOT
If the number of calls received per hour by a telephone answering service is a P...
soft zealotBOT
tranquil pine
So i was thinking of an Erlang distribution where [
\m fx =\f{x^{n-1}\m\exp{-\f x\beta}}{\beta^n (n-1)!}
]
soft zealotBOT
tranquil pine
but i dont see how to apply this? i dont think we know what beta is
final saddleBOT
@tranquil pine Has your question been resolved?
candid hull
the arrival time of 3 calls is a sum of 3 exponentials, so yeah it follows an erlang distribution (n=3)
seems like beta is just the mean time between calls here
so beta=lambda I guess
@tranquil pine
tranquil pine
so beta=lambda I guess
wouldnt it be beta = 1/lambda in that case?
candid hull
no
lambda is already the mean time of your poisson
we all thank notation overloading
final saddleBOT
candid hull
.reopen
final saddleBOT
✅
candid hull
wait crap you're right, confused poisson for exponential for a second @tranquil pine
yeah lambda for a poisson distribution is the rate of arrival
tranquil pine
oh okay LMAO
yeah i had to go back to the table and double check because i got confused 😵💫
candid hull
so indeed lambda = 6 calls per hour means that beta = 10 mins between calls in average
candid hull
yus
final saddleBOT
final saddleBOT
Available help channel!
cold torrent
I’m trying to solve for variable g with the the differentiable and continuous equation (right side notes labeled 3). The worksheet says the answer should a number over pi but I keep getting 0. Pls help
final saddleBOT
I’m trying to solve for variable g with the the differentiable and continuous eq...
@cold torrent Has your question been resolved?
final saddleBOT
@cold torrent Has your question been resolved?
final saddleBOT
@cold torrent Has your question been resolved?
final saddleBOT
@cold torrent Has your question been resolved?
final saddleBOT
@cold torrent Has your question been resolved?
true topaz
I’m trying to solve for variable g with the the differentiable and continuous eq...
Have you mistakenly said cos(0) is 0 here
On the right hand side of your equation
Cos 0 is 1
surreal reef
$\cos (\theta) = \frac{1 \pm \sqrt 5} 4$
final saddleBOT
$\cos (\theta) = \frac{1 \pm \sqrt 5} 4$
soft zealotBOT
ξ ∈ 龘
strange rune
you want to solve for theta?
rustic wedge
hmm
rustic wedge
Won't there be two diff solutions?
there'll be inf many solutions
west berry
Ye ik but
rustic wedge
cus cos is periodic
surreal reef
Yes, just find the basic ones
west berry
Yeah ik
surreal reef
One theta for +, another for -
west berry
But for + and - it'll be different (you won't get the same ans on addition of 2npi)
surreal reef
Okay... We knew that
rustic wedge
btw have u tried anything @surreal reef
surreal reef
Tried triangles
But couldn't find any that works
What do u even start with to solve this?
surreal reef
Only noticeable thing is that it's cosθ = half of golden/silver ratio
rustic wedge
construction could be involved too
rustic wedge
Only noticeable thing is that it's cosθ = half of golden/silver ratio
doesnt help tho
surreal reef
Which identities
rustic wedge
dunno perhaps inverse function identities
west berry
I just have a feeling that cos5(theta) will give us smth
rustic wedge
stuff like this ig
rustic wedge
I just have a feeling that cos5(theta) will give us smth
root of unity method?
west berry
No coz
surreal reef
root of unity method?
The answers aren't roots of unity
west berry
I had to find cos18 once
rustic wedge
The answers aren't roots of unity
i never said that. oh wait this isnt a root of unity 🤦♂️ nvm
west berry
And I used a similar method to get a similar ans
I'm not entirely sure it would work for this tho
rustic wedge
what did u do exactly, lorentz
west berry
Let 18=x
So cos(5x)=0
And then I split 5x to 2x and 3x
rustic wedge
hmm
west berry
Lemme think of smth else
rustic wedge
u would need to know an integer such that i * (1+/-root(5))/4 = a rational multiple of pi
surreal reef
Answer is ||1/5 pi and 3/5 pi||, does that help to work backwards?
rustic wedge
hmm let me think
1/5 pi..do we have an identity for theta/n?
i know for n theta
not the other way around tho
i suppose i could reciprocal
west berry
**ξ ∈ 龘**
Ok here's what I got
|| If cos theta is taken when + is taken from ±, then cos(3 theta)= it's conjugate||
rustic wedge
its too much work
rustic wedge
Ok here's what I got
|| If cos theta is taken when + is taken from ±, then cos(3...
how does that help?
rustic wedge
oh
west berry
Hmm
rustic wedge
cos(3x) = cos^3 x - 4cos x iirc
west berry
Ye
rustic wedge
no wait
west berry
4 cos^3 x -3 cos x
west berry
No wait
rustic wedge
how did u get that lorentz
west berry
how did u get that lorentz
I just found cos 3x using that formula
And it came to be it's conjugate
They're not equal
But
rustic wedge
You can find out cosx + cos 3x and cosx*cos3x
cos x + cos 3x = is just 1/2
west berry
Yes
rustic wedge
this is wrong
west berry
Why
rustic wedge
because cos x + cos 3y = 1/2 imples 4cos^3 y - 3cos y + cos x = 1/2
oh
me isstupid
west berry
It's alr
west berry
And find cosx-cos3x
.
west berry
Why didn't I see that bruh
I have cosx and cos3x and I use the longer method to find their difference
rustic wedge
how do we get theta from this again?
west berry
x = (1+root(5))
How did you get that
rustic wedge
alr enough of this
first
lets assume
4x = 1+root(5) and 4y = 1-root5
correct?
west berry
Why so?
rustic wedge
then u said cos(3x) = cos y, right?
west berry
No
rustic wedge
then?
west berry
I just found cos3x and found it to be the conjugate of cosx
rustic wedge
I just found cos3x and found it to be the conjugate of cosx
what is x tho??
rustic wedge
so u assume theta to be something like a+root(b)?
west berry
x=θ
rustic wedge
cus conjugate doesnt make sense else
west berry
cus conjugate doesnt make sense else
No look
I took cos(theta) as( 1+sqrt(5))/4
And I found cos(3theta) which was (1-sqrt(5))/4
I thought we could get smth but
final saddleBOT
@surreal reef Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
restive valley
Is a 4.355% of difference large in general, or does it depend on the sample size and overall size/units of measurement?
I calculated an average slope of 5.45, with 4.355% deviation. Measurements are in hours, and lets say, y is distance in meters. Statistics ain't as accurate as calculus/analysis, but it's a lot easier. (in this scenario)
final saddleBOT
Is a 4.355% of difference large in general, or does it depend on the sample size...
restive valley
.close
midnight sparrow
what is the difference between a definite function and a continuous function?
midnight sparrow
like sometimes we say we need that function to be definite on an interval for instance but not necessarily continuous what's the difference
desert mantle
well a function is for example positive definite if f(x)>0 for all x. but is that what you mean?
can you give a concrete example?
strange rune
definite = the function is defined on all points inside the interval (or set more generally)
like for example
desert mantle
is the original language english?
midnight sparrow
no sry I'm french maybe my traduction is not good
strange rune
une fonction est définie sur un ensemble si pour n'importe quel element x de l'ensemble f(x) existe
midnight sparrow
maybe the term is defined
strange rune
another example: f(x) = 0 if x =/=0
midnight sparrow
une fonction est définie sur un ensemble si pour n'importe quel element x de l'e...
quelle est la différence avec continu
strange rune
f(0)=1
this is defined
on R
but not continuous
at 0
all x s admit an output through f
so its defined
but its not continuous clearly
tranquil pine
Sorry not about the question but what is ur pfp phoestaclies
midnight sparrow
because I have a text that say f : R --> K is defined on I an interval. Say that F is a primitive of f on I . But we need that f to be continuous to have a primitive no ?
pfp ? what is it
not just defined but also continuous so I don't really understand the difference
oh ok I see I think
desert mantle
we dont actually need that f is continuous. the integral $\int_0^x f(x) dx$ can exist without $f$ being continuous
soft zealotBOT
Denascite
desert mantle
continuity is sufficient, but not necessary
midnight sparrow
like floor function is defined on R but not continuous
but the fondamental theorem say that f has to be continuous no ?
desert mantle
pfp ? what is it
profile picture
it doesnt have to be
if it is, then ftc applies
midnight sparrow
ok cause our teacher say that it need to be continuous
desert mantle
if f is continuous then the integral is guaranteed to exist
midnight sparrow
the condition is that it's on an interval
desert mantle
if not then you might run into problems
midnight sparrow
ok I see
desert mantle
but it can still exist as long as your function is not too bad
midnight sparrow
ok so it can exist without being continous but if it's continuous we know for sure that it exists
ty a lot 👍
desert mantle
yes
ancient plank
I would like to have some help how to tackle these problems and solving them
final saddleBOT
I would like to have some help how to tackle these problems and solving them
@ancient plank Has your question been resolved?
final saddleBOT
Available help channel!
tranquil pine
I have a question regarding verifying that [
0.\overline 9 = 1
]
final saddleBOT
I have a question regarding verifying that \[
0.\overline 9 = 1
\]
soft zealotBOT
tranquil pine
I thought about it, but the most common way of showing it through some algebraic manipulation is not valid at all is it
low gull
in this notation is the overline just repeating 9's?
green ibex
ye
tranquil pine
yes exactly moosey
granite bay
ye
tranquil pine
so what is a more rigorous approach?
green ibex
sequences :)
amber holly
Just use calculus and verify that $\sum_{i=1}^{\infty}\frac{9}{10^i} = 1$
soft zealotBOT
A Lonely Bean
green ibex
^ you can define the above as a partial sum (sequence) that converges yes
ocean lintel
Which is natural since that's how we define the decimal expression of a number
tranquil pine
oh yeah we did cover this in my calc 2 class
I just remembered
it's been so long
but yeah thanks
.close
hot patrol
how did they go from step 2 to 3?
final saddleBOT
how did they go from step 2 to 3?
void valley
just integration
$$\dv{x} \sqrt{x}=\frac{1}{2\sqrt{x}}$$
Using chain rule:
$$\dv{t} \sqrt{3+t^2}=\frac{1}{2\sqrt{3+t^2}} \cdot \dv{t} (3+t^2)=\frac{\cancel{2}t}{\cancel{2} \sqrt{3+t^2}}=$$
$$=\frac{t}{\sqrt{3+t^2}}$$
soft zealotBOT
Modus
hot patrol
.close
final saddleBOT
final saddleBOT
Available help channel!
vivid walrus
final saddleBOT
vivid walrus
!status
final saddleBOT
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
$P(t)=210\left(\frac{1}{2}\right)^{\frac{t}{138}}$
like this?
oh right \left and \right moment
soft zealotBOT
Akira (fumo)
hard rampart
looks good to me
vivid walrus
I don't think so
vivid walrus
do i need to plug 200 into the p(200)?
hard rampart
**Akira (fumo)**
u should have 200 instead of 210
ohh LOL
210 is the name of the substance 💀
like carbon-14
it's not an actual number for the problem lol
vivid walrus
yeah?
how i can make it correct then
ill try another attempt
$P(t)=200\left(\frac{1}{2}\right)^{\frac{t}{138}}$
soft zealotBOT
Akira (fumo)
vivid walrus
now plug 200 into the equation?
hard rampart
yes
vivid walrus
for p(t)
hard rampart
**Akira (fumo)**
this is part
a
u did part(a) correctly
now part b
asks u to calculator for 5 years
hard rampart
u just did part a
vivid walrus
do you mean like it's already done?
hard rampart
yes
vivid walrus
oh okay
hard rampart
that is the answer
vivid walrus
$P(5)=200\left(\frac{1}{2}\right)^{\frac{5}{138}}$
soft zealotBOT
Akira (fumo)
vivid walrus
like this?
vivid walrus
hmm
hard rampart
ur equation only works because t is in days
don't overcomplicate it
how many days are in 5 years
lol
hard rampart
I hope u know how many days are in a year
vivid walrus
60 months
60 months for 5 years
but we're looking for days
is there a way i can find for days
hard rampart
ok just tell me how many days are in a year
hard rampart
I think it's 365
vivid walrus
,w how many days are in a year
soft zealotBOT
vivid walrus
oh okay
hard rampart
ok
soft zealotBOT
Result:
1825
this?
hard rampart
yes
vivid walrus
ok then i need to plug this into the formula now?
i mean the equation mb
alright got the right answer
thank you mate
🫡
.close
tranquil pine
Use a half-angle formula to find sin(11π/12).
final saddleBOT
Use a half-angle formula to find sin(11π/12).
tranquil pine
.close
final saddleBOT
final saddleBOT
Available help channel!
unique aspen
help idk how to continue this
final saddleBOT
help idk how to continue this
unique aspen
white tiger
cos/cos = 1 not 0
final saddleBOT
@unique aspen Has your question been resolved?
dull swift
Dont know how exactly to condense it. if someone can walk me through it that would help
Condense to a single logarithm
4log(x)-1/3log(x^3+1)+3log(x-1)
final saddleBOT
Dont know how exactly to condense it. if someone can walk me through it that wou...
random forge
,tex .log rules
soft zealotBOT
random forge
you need the first 3 rules here, show what you tried and where you are stuck
dull swift
im sorry but i dont know where to start here
im not trying to ask for the answer
just asking if you can walk me through the problem
dull swift
oh wait
dull swift
it would be logx^4 right?
warm forge
Yep. May or may not be useful, but it's an option.
What about the three terms (log term1) - (log term2) +(log term3)
Can we see anything in that big part?
OK, what about the third term. It sort of looks the same sort as the first one
Can you see any way to change it?
dull swift
im not getting it sorry
warm forge
$log(x^4) - 1/3+log(x^3+1) + 3log(x-1)$
You got the first term. Try the third term?
$log(x^4) - 1/3log(x^3+1) + 3log(x-1)$
soft zealotBOT
G. Spark
austere crystal
final saddleBOT
hybrid heath
,rotate
soft zealotBOT
hybrid heath
!status
final saddleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
tbh i just need help with one and i should be good on the rest
not rly sure hwo to lay it out
im p sure the down one unit is just -1 at the end
soft zealotBOT
SWR
hybrid heath
Let's add
- a vertical vertical scale a
- a horizontal scale b
- a vertical displacement h
- a horizontal displacement k
austere crystal
uh
hybrid heath
The transformed function will look like $y=a\cdot f\left(\frac{x}{b}-k\right)+h$
soft zealotBOT
SWR
austere crystal
oh ok
jus tso i dont ahve to scroll
ok ok
so
y = 5 x IDK (4/pi - 1) + 5
yeah i havf no clue lol
hybrid heath
y = 5 x IDK (4/pi - 1) + 5
You got the vertical stretch correct. 5 x ....
hybrid heath
That would be a horizontal displacement of +1. You want a vertical displacement of -1.
hybrid heath
yes. H is your horizontal displacement
austere crystal
y = 5 x _ (x x) - 1
hybrid heath
Let my try getting us there another way
austere crystal
ok
hybrid heath
Let's start at the original function: y=tan x
austere crystal
yes
hybrid heath
How do we add a vertical stretch of a factor of 5?
hybrid heath
5tan(4pi) is just a number
hybrid heath
im just trying to add on piece by piece
This is the goal, yes, but you keep dropping your x variable, which you need to make this a function.
hybrid heath
vertical stretch would turn it into y=5tan x
👆
hybrid heath
Do you know what a function is?
austere crystal
yes
hybrid heath
In your words, tell me what a function is
hybrid heath
sorta.
There's nothing particularly wrong with your way of saying it, but it doesn't capture the whole idea
austere crystal
if i just see the answer i can translate it on to the other porblems 😭
hybrid heath
Simply put a function is where you provide some input, and you get an output.
hybrid heath
if i just see the answer i can translate it on to the other porblems 😭
Yes but then you're not learning the why of the solution. There's more value to education than just parroting the bare minimum of information
hybrid heath
if i just see the answer i can translate it on to the other porblems 😭
Ironically, this is you trying to act like a function. You want to know what output to provide for the input you are being given.
hybrid heath
Sure
austere crystal
hybrid heath
Okay, so a function is where you have some input, and you are trying to get an output from it.
austere crystal
yes
hybrid heath
Generally, your input is a variable that you can plug in, and is designated, usually, as x
hybrid heath
If f is the function, the operation of the function on your input x is usually written as f(x). This output is usually assigned to the variable y, so the most generic equation of a function is y=f(x)
hybrid heath
So the idea of vertical stretch is that, say I want to scale the output by a scale of 5, that's just saying I want my output to be 5 times whatever the output used to be.
So if f(x) was my output, then what is 5 times my output?
hybrid heath
No. That's the output of your function when the input, x, is 5.
That is, f(5) is just evaluating f(x) at x=5
hybrid heath
Let me say it like this, what is 5 times some variable n?
austere crystal
5n
austere crystal
10x
soft zealotBOT
SWR
austere crystal
ok
hybrid heath
So, what is 5 times f(x)?
austere crystal
oh
hybrid heath
so what is 5 times tan x?
austere crystal
5tanx
austere crystal
yes
hybrid heath
Your original output used to be tan x, but now you want your output to be 5 times your original output.
5 times "original output" = 5f(x) because "original output" = f(x)
Now you want a vertical shift down of 1
this requires graph knowledge.
graphs of functions are every point (x, y) that satisfies y=f(x), where x is the horizontal displacement from the origin, and y is the vertical displacement
hybrid heath
y is also your output variable, so if you want a vertical shift down of 1, that's saying you want your new output to be 1 less of your original output
hybrid heath
so wouldn tthat go at the end
It doesn't need to go at the end, but I see what you are saying
moving down by 1 would just be y=f(x)-1
hybrid heath
But you could also write it as $y=-1+f(x)$ if you so wanted to
soft zealotBOT
SWR
hybrid heath
Anyway..
hybrid heath
These are important things to know when you do these kinds of problems
austere crystal
i know but its been 40 minutes
hybrid heath
Yeah but it's time spent learning things you should know.
hybrid heath
anyway, what do you have so far? We've add a vertical streatch by factor of 5, and vertical displacement downward by 1, so what does that new function look like?
austere crystal
i have
5tanx
and to make it move down
i would od
5tan - 1 ?
or 5tanx - 1?
austere crystal
which one
hybrid heath
Last thing we need to do is the new period of the function
hybrid heath
Do you know the period of just regular y=tan x?
hybrid heath
The second. You can't just drop the x
hybrid heath
tan(x) is a function, tan by itself is just nonsense
austere crystal
yep
austere crystal
isnt there no period for tan?
?
hybrid heath
There is a period for tan
Period is just the distance before the function starts to repeat
,w plot y=tan(x)
soft zealotBOT
hybrid heath
isnt there no period for tan?
This made me believe you thought there was no period for tan
austere crystal
5tanx -1 (pi - 4pi)
austere crystal
This made me believe you thought there was no period for tan
my bad
hybrid heath
5tanx -1 (pi - 4pi)
I can't parse what this saying
austere crystal
me neither
i pulled it out my ass
ignroe that
lets move on
so
5tanx -1
and now we have the period
which is pi
how should i place pi into my equation?
@hybrid heath
hybrid heath
A period of pi means the function repeats every pi distance
austere crystal
so should period be at the end
hybrid heath
We want a period of 4pi, which means it needs to take 4 times as long to repeat
hybrid heath
If it takes 4 times as long to repeat, that's basically saying you need a horizontal stretch factor of 4
austere crystal
ok
so
5tanx - 1 (4 ?
starting the parenthesis cuz i know there is mroe tha tneeds to go in there right
hybrid heath
5tanx - 1 (4 ?
Not quite.
austere crystal
hybrid heath
and for you, f is just tan
austere crystal
5tanx -1 (pi/4 ?
hybrid heath
so it would be $y=a\cdot\tan\left(\frac{x}{b}-k\right)+h$
soft zealotBOT
SWR
austere crystal
5tanx -1 (pi/4 ?
hybrid heath
not quite
I understand you are desperate to be done, but your impatience is making this harder.
Either try to work on this tomorrow, or take a minute to be ready to figure this out.
austere crystal
can we finish in 10 min?
austere crystal
I understand you are desperate to be done, but your impatience is making this ha...
i was expecting this to take 5 min not an hour and 10 min
i really do appreciate ur help though
hybrid heath
I don't make promises on times
austere crystal
im just not a big math person, i learn it, test, move on yk
hybrid heath
It depends on your abilities.
It's fine to not care about math, but I will not feed you answers nor make you do rote memorization to survive tests.
You learn nothing from that.
Unfortunately, you're getting help from someone who cares that you actually learn the material
austere crystal
ik
hybrid heath
You'd probably like math more if your teachers were like that, tbh
austere crystal
i wish i was more in to math tbh
yeah my teacher def not like that
what grade ru in
hybrid heath
It's easy to not like things you never understood. It's hard to give it a chance once you've disliked it for so long.
hybrid heath
what grade ru in
I graduated a long time ago. I'm a full ass adult yo
austere crystal
where at
hybrid heath
engineer
hybrid heath
you don't need math, but you need to have analytical skills
austere crystal
yeah ive heard that
its kinda like a alternative route for me
just cuz idrk what i want to do yet
still in highschool
hybrid heath
I switched a lot in high school
trying to decide between math, physics, and comp sci
My majors were physics and math, but I did comp sci
college is just a stepping stone. Where you end up depends on your desires and work ethic
austere crystal
comp sci prob best for money and freedom tbh
austere crystal
college is just a stepping stone. Where you end up depends on your desires and w...
fr
hybrid heath
great for money (in USA), can be rough for freedom
Really depends on your skill set and work ethic
austere crystal
some ppl go into college thinking they will get a garunteed job
austere crystal
yeah