youre overthinking it
#help-0
vale wigeon
$\int_a^b f(x) \dd{x}$ gives the area under the graph of $y=f(x)$ (whatever $f(x)$ may be) between $x=a$ and $x=b$
ocean sealBOT
Ann
vale wigeon
and in this case you are integrating the constant function 4
tropic oasis
so it would be a straight line going through y=4?
lone heartBOT
@tropic oasis Has your question been resolved?
vale wigeon
so it would be a straight line going through y=4?
it should be the straight line y=4
the horizontal line going through (0,4) if you will
tropic oasis
it should be _the_ straight line y=4
because width is 4 and height is 4
4*4=16
does that sound correct?
vale wigeon
the width is what?
tropic oasis
well like the shape
vale wigeon
the shape goes from 0 to 3 on the x-axis
tropic oasis
of the line on x=0 and x=3
vale wigeon
and how does that give a width of 4
vale wigeon
yes
lunar pendant
lone heartBOT
lunar pendant
can someone help
lone heartBOT
@lunar pendant Has your question been resolved?
lunar pendant
<@&286206848099549185>
waxen flame
yw
mighty arrow
I need help finding a probability of a system in a video game.
I have had an average of 73 (pity) across 8 trials (rolls)
i have a data set here, column D is what i'm mostly intrested in.
I have been told that the mean is ~69.4 and the standard deviation is ~14.5 (im assuming this is correct)
i want to know what the probability of getting an average of 73 across 8 trials.
currently i've gotten a chance of 681.495041708 our of 1 000 000 but I dont believe that thats correct.
mighty arrow
ive been using this website to find the Z-score https://www.calculator.net/z-score-calculator.html?c1raw=73&c1mean=69.4&c1sd=14.5&calctype=zscore&x=0&y=0
here is the work for my result of 681/1000000
0.40196 is the result for X>73
this may seem simple but i have zero experience with standard deviations
also i want to know how to find the probability of this for any number of trials
placid zinc
What is a pity? What is a roll?
mighty arrow
so
placid zinc
Note that the normal distribution is just an approximation. It may be a little weak if you only have 8 trials
Also may not matter if you are just trying to get ideas
mighty arrow
Note that the normal distribution is just an approximation. It may be a little w...
i have a complete data set, i want to know the probability of getting a certain number with n amomunt of trials
okay the complete context is
genshin impact is a gacha game
in this game you can "roll"
a roll in an attempt to get a valuable item
every unsucessful roll adds to a "pity counter"
your pity is the roll number where you got the valuable and can be between 1 and 90
placid zinc
Okay so the chances you're successful change, based on how unlucky you've previously been?
mighty arrow
there is a data set for the sucsessfull roll pity and looks something like this
the data that matters is distibution of sucessfull pulls
pull = roll
https://www.hoyolab.com/article/497840 source of the chart above is here + provides additional context
mighty arrow
your pity is the roll number where you got the valuable and can be between 1 and...
continuinfg from here
the mean average pity is 69.4 (from what ive been told)
placid zinc
Ok I see. Your odds increase if you've gone ~70 without a success
mighty arrow
my average pity is 73 (from getting 8 valuables)
placid zinc
Okay. So, the bottom right is pretty important. However, it looks nothing like a normal distribution.
So, normal distribution calculations won't work well on it
Luckily, they've done that calculation for you, and put it into that top chart
mighty arrow
Ok I see. Your odds increase if you've gone ~70 without a success
yeah here are the probabilitys, the number decreases until 74 (due to geometric distributon)
mighty arrow
Okay. So, the bottom right is pretty important. However, it looks nothing like a...
that is probably the problem here lmao
placid zinc
The probability that you'll get it in less than 73 pulls looks to be approx 35%?
Just looking at that chart anyway
You probably have the raw data already
mighty arrow
yeah
the columns for the chart are
C = IF(B90<74,0.6/100, C89+6/100)
D = (1-SUM(D$1:D89))*C90
E = D90*B90```the pity count is shifted by +1 from the row number
the functions are taken from pity number 89
mighty arrow
The probability that you'll get it in less than 73 pulls looks to be approx 35%?
yeah, but i want to know the probability of my average pity of getting a valuable being equal to or greater than x with n valuables being obtained
lone heartBOT
@mighty arrow Has your question been resolved?
mighty arrow
i assume the probability would go down with increased trials
like the probability of getting 90 is ~1% but the probability of geting 90 twice is 1%^2
but i dont think thats the right method
because 73 isnt far from 69 and i dont think the average would be 0.075/1000000 to get a 74 average across 18 trials
imma try to better phrase my question.
given the data set / graph (distribution of sucessful pulls)
ive detemined the average mean to be ~69.4.
with this, i want to find the probability of getting a mean average of X or higher, given a sample size of Y samples (from the data set)
for example, i know the probability of getting N>69.4 being 50%
what is the probability of the mean average being > 69.4 given 15 trials
<@&286206848099549185>
is it just 0.5^15?
and is there a way to find this for anu data set and with any values of X & Y, because i have been unable ti find one.
ngl this channel is prolbably gonna get timed out
mighty arrow
mean average is the mean of all the samples plots in the graph
sample is a random selection of a data point
placid zinc
Mean of a plot?
mighty arrow
Mean of a plot?
like the mean of all the points in the graph
so you would have a 50% chance to get higher / lower when taking a sample
placid zinc
What is getting "higher" or "lower"?
mighty arrow
the mean average i want to test the probability of is the average of Y random samples being greater than a value X
mighty arrow
What is getting "higher" or "lower"?
for a random sample or mean of random samples to be greater than or less than a given value X
mighty arrow
Getting N > 69.4? What's N?
N would be the average of my samples
placid zinc
You're trying to make it as vague as possible but that's going the wrong way. This made a bit more sense when it was a game
placid zinc
yeah, but i want to know the probability of my average pity of getting a valuable being equal to or greater than x with n valuables being obtained
- That one seemed important
mighty arrow
yeah
placid zinc
But my problem is that I don't think I understand the pity system
Actually, that "per pull probability" chart might be the correct thing to use
mighty arrow
the pity system is just based on this graph, the details arent important, just know the chance of getting a valueable on a certain pity is exactly the percentage on the graph
mighty arrow
Actually, that "per pull probability" chart might be the correct thing to use
the per pull probability is just at a certain pity the chance of getting a valueable
the important one is ,for every valuable gotten, what is the pity it was obtained at
which is the sucsessful pull one
placid zinc
Right. That's what you want to know more about
One sec I'll read the site
I don't see where they give pity a number?
Like, what's the pity at if you fail pull 75?
placid zinc
OH
mighty arrow
so if i got a valuable at pull 60, i got it at 60 pity
yeah sorry i shouldve made that way more clear
placid zinc
I think they're using "pity" as the sharp incline on the bottom left graph
mighty arrow
thats "soft pity"
placid zinc
But regardless. Okay. So you want to know "what's the probability that you get n items in less than x pulls"?
mighty arrow
no, kinda the opposite
if i get n items, whats the probability that the average pity is greater than x
placid zinc
Oh I see.
n items being your sample, you want to know the mean "difficulty" in attaining them
mighty arrow
yeah basically
placid zinc
I have good news and bad news
mighty arrow
huh
placid zinc
If n is somewhat large (like n = 30) then the central limit theorem kicks in, and the thing you are asking for is well approximated by a normal distribution
For the bad news,
if n is fairly small, then this will be so messed up, I doubt it has a closed form
mighty arrow
Oooh. so thats why i was told to find the standard deviation
placid zinc
You are better off using a programming solution for small n
mighty arrow
For the bad news,
if n is fairly small, then this will be so messed up, I doubt ...
yeah, there is a calculator for the easier question (probablity of n valuables in x pulls) but not my question.
yeah a programming soution would probably work...
ill see what i can come up with...
.close
lone heartBOT
placid zinc
I'll think on it too. Neat question though!
mighty arrow
ty
lone heartBOT
Available help channel!
desert elbow
Hey good sir of mathematics
lone heartBOT
Hey good sir of mathematics
desert elbow
Im in an exam and I know nothing can you help with the questions
mortal trellis
we don't help with cheating
wheat crystal
gl on your exam!!
desert elbow
Already failing that shit
lone heartBOT
@desert elbow Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
median leaf
hey in my class tmrw, we are going to go over the FTC and i am just trying to read a bit ahead so i wont be lost, can someone explain how this works?
median leaf
yes
i like
dont really know whats going on
how is it useful?
i dont get how a function can be an area of another function
when that should mean it should be a horizontal line
vale wigeon
a function is just a thing that takes in a number and returns a number (in the simplest case)
vale wigeon
this means integral of f(t) over the interval [a,x]
vale wigeon
the interval of integration depends on the input to g
median leaf
so its saying that the integral function(?) of a given function is also continuous and differentiable on the same interval as the given function and its derivative is the same as the given function
idk if "integral function" is the right word
karmic rapids
idk if "integral function" is the right word
integrand, is that what you mean?
median leaf
oh is that the term
vale wigeon
yeah integrand
also you don't need f to be differentiable
just continuity will suffice
median leaf
this just means integral of f(t)
so g(x) is the integrand of this
okay
i think it kinda clicks
the FTC really just shows the relationship between derivatives and integrals
bc the 2nd part is much much more intuitive to me
cuz i kinda figured it out in my head already
where the integral of f(x) from an interval [a,b] is the same as the difference of the antiderivatives
on the end points
karmic rapids
the FTC really just shows the relationship between derivatives and integrals
$\int f(x)dx = \frac{d^{-1}f}{dx^{-1}}$
ocean sealBOT
illuminator3
karmic rapids
median leaf
oh yeah yeah
its like a staircase
if you go up the staircase of 2x
it goes like 2x-> x^2 -> x^3 /3 ... etc
which is integration?
and down the staircase is like
differentiation
this is mindblowing NGL LMAO
.close
lone heartBOT
lone heartBOT
Available help channel!
native tartan
can anyone help me prove
A-(A-B) = A cap B
lone heartBOT
can anyone help me prove
A-(A-B) = A cap B
native tartan
<@&286206848099549185>
lone heartBOT
@native tartan Has your question been resolved?
alpine sable
lone heartBOT
tawny schooner
lone heartBOT
Available help channel!
alpine sable
Isn't $2x+dx^2$ ?
lone heartBOT
Isn't $2x+dx^2$ ?
ocean sealBOT
Shihab
alpine sable
ah you mean, $x^{2}+2x.dx/{dx} + dx^{2}-x^{2}/dx$
ocean sealBOT
Shihab
alpine sable
Thanks.
lean depot
Ok I need you to be a bit more precise with this
alpine sable
I thought i can just replace that dx with 1 because there is dx.
lean depot
**Shihab**
This is not correct, or at least I don't see what you mean by this
Let's try from the top
alpine sable
Just as a first thing
Does that affect ?
vale junco
Doesn't everything cancel?
alpine sable
Ah
vale junco
I'm confused
alpine sable
Thank you.
lean depot
$\frac{x^2 + 2x\cdot\mathrm dx + (\mathrm dx)^2 - x^2}{\mathrm d x}$
ocean sealBOT
Boytjie
lean depot
What I notice first is that on the numerator, the $x^2$s cancel
ocean sealBOT
Boytjie
lean depot
so in fact this is equal to
lean depot
$\frac{ 2x\cdot\mathrm dx + (\mathrm dx)^2 }{\mathrm d x}$
ocean sealBOT
Boytjie
lean depot
Not everything cancels, I disagree with that
vale junco
Why
alpine sable
**Boytjie**
Yes
lean depot
But now this is much simpler right?
alpine sable
Yes
lean depot
Now this is where the confusion seems to be
Because I say that
$\frac{ 2x\cdot\mathrm dx + (\mathrm dx)^2 }{\mathrm d x} = 2x + \mathrm dx$
ocean sealBOT
Boytjie
lean depot
Do you agree with that?
vale junco
I do but when u multiply by dx everything cancels
lean depot
I'm sorry mope, I still don't see what you mean by that, but this is shihab's question so I'm going to continue
alpine sable
Do you agree with that?
Not so much, i think that the bottom dx will cancel the top dx and the 2x and (dx)^2 will be the result.
lean depot
No worries
OK so I think there's some confusion here regarding how fractions work
Let's ignore the dxs for a bit
alpine sable
yes
ocean sealBOT
Boytjie
lean depot
Do you think you can simplify this expression into something nicer?
alpine sable
yes
lean depot
What do you reckon it is?
alpine sable
$\frac{a\cdot x}{x}+\frac{b\cdot x}{x}$
ocean sealBOT
Shihab
ocean sealBOT
Shihab
lean depot
OK, so you seem to be struggling with fractions
alpine sable
i forgot
lean depot
Oh do you want to give it another shot?
ocean sealBOT
Shihab
lean depot
Yes, this is right
alpine sable
yeah
lean depot
Now there's a really great simplification you can do here. I'll wait for you to spot it.
Tip: What is x/x?
lean depot
Great
alpine sable
$a\cdot1+b\cdot1$
ocean sealBOT
Shihab
lean depot
And....
vale junco
So everything does cancel
lean depot
mope, I don't think this is helpful right now
You had this: $\frac{a\cdot x}{x}+\frac{b\cdot x}{x}$
vale junco
Fine
ocean sealBOT
Boytjie
lean depot
Now shihab, I just want you to appreciate that when you have the fraction symbol, what it means is that you divide the thing on top by the thing on the bottom
So let's just focus in on a.x/x
$\frac{ax}{x}$
ocean sealBOT
Boytjie
alpine sable
yeah
lean depot
So it's just a!
alpine sable
yes
ocean sealBOT
Boytjie
lean depot
We're clear on that?
alpine sable
x cancels x it will result 1
alpine sable
We're clear on that?
yes
lean depot
Yeah that's another way of seeing it
OK so let's go back to our problem
$\frac{ 2x\cdot\mathrm dx + (\mathrm dx)^2 }{\mathrm d x} = 2x + \mathrm dx$
ocean sealBOT
Boytjie
ocean sealBOT
Boytjie
lean depot
So can you use this rule to show why it's 2x + dx?
alpine sable
yes
lean depot
Can you give it a shot?
alpine sable
yes
lean depot
Go ahead!
alpine sable
$2x\cdot\frac{\mathrm dx}{\mathrm d x}+\mathrm dx \cdot \frac{\mathrm dx}{\mathrm dx}= 2x + \mathrm dx$
ocean sealBOT
Shihab
alpine sable
So it is 2x + dx and not 2x + dx^2
alpine sable
Yes because the + in fraction can collect multiple numbers i mean the bottom one so when we cancel some numbers we should know that bottom number is not just one number.
- and -
alpine sable
Yeah, i know now thank you!
lean depot
No problem
alpine sable
.close
lone heartBOT
alpine sable
.reopen
lone heartBOT
✅
lone heartBOT
lone heartBOT
Available help channel!
lost coral
whats the problem
lone heartBOT
whats the problem
lost coral
echo socket
64(1 - (0.75)^4) =/= 64 - (0.75)^4
echo socket
Yeah now it's fine
worldly kernel
Tal ves alguien tiene conocimientos de ecuaciones diferenciales parciales ?
lilac nest
You should only use English on the server
I don't speak Spanish(?) anyways so I have no idea what you're talking about
tender dew
partial differential equations
lilac nest
What's the question?
languid bolt
he's asking if anyone knows partial differential equations
lilac nest
That's not a question though, @worldly kernel ask a question and we will be able to help you
lone heartBOT
@worldly kernel Has your question been resolved?
clear tendon
I need a general type to to write a function from N0->N0 that follow the condition below for every n
clear tendon
function that is not like f(x)=x+a when a is constant
oak perch
f(3n) can be anything
clear tendon
f cant be f(x)=x^2
I can't sent the question because of it not in English
and translator don't work good for Discrete mathematics
oak perch
$f(n)=\frac{(w^{n}-w)(w^{n}-w^{2})}{(1-w)(1-w^{2})}g([\frac{n}{3}])+\frac{(w^{n}-1)(w^{n}-w^{2})}{(w-1)(w-w^{2})}(g([\frac{n}{3}])+1)+\frac{(w^{n}-1)(w^{n}-w)}{(w^{2}-1)(w^{2}-w)}(g([\frac{n}{3})])+2)$ for any g from $N_{0}$ to $N_{0}$, where $w=\frac{-1}{2}+\frac{\sqrt{-3}}{2}$
ocean sealBOT
Cogwheels of the mind
clear tendon
I don't this that what they meant, i need to say the size of the set of the funcion is bigger then א0
alef zero
oak perch
Size is cardinality of {maps from N_0 to N_0}
clear tendon
the problem is they what me to prove bigger than alef zero with Cantor's diagonal argument
oak perch
Not sure whether it’s greater than alef zero
oak perch
Size is cardinality of {maps from N_0 to N_0}
Okay so we prove this is greater than alef zero
clear tendon
they want me to prove it not countable set
oak perch
Got it:
clear tendon
Okay so we prove this is greater than alef zero
i try to do it but i prove it alef zero instead so i have a problem
oak perch
Suppose {g: g is a map from N_0 to itself } is countable, so it equals {g_1,g_2,…}
Then you have a list
g_1(1),g_1(2),…
g_2(1),g_2(2)…
…
Let g(n)=g_n(n)+1
Then g doesn’t equal any those g_n, contradiction
Therefore it’s greater than alef zero
clear tendon
i have hard time making the new function that don't have an origin
oak perch
N_0 includes 0? Then just fix the list
clear tendon
they want me to prove it not countable set
the condition in the middle is the problem
oak perch
And I proved it
oak perch
Suppose {g: g is a map from N_0 to itself } is countable, so it equals {g_1,g_2,...
This is the counterexample
If g=g_n for some n, then g_n(n)=g(n)=g_n(n)+1 contradiction
Your set has a bijection to {maps from N_0 to itself}
Mapping f to g where g(n)=f(3n)
clear tendon
sorry
oak perch
**Cogwheels of the mind**
I even constructed the inverse image of g
clear tendon
but I don't thing I'm following sorry my English is not good enough to discus
oak perch
Me neither, but I don’t think there is any obstacle made by language
Any part that you don’t understand?
clear tendon
let's start from what i did
oak perch
Your set has a bijection to {maps from N_0 to itself}
Mapping f to g where g(n)=...
Injective: f(3n)=f’(3n) then f(3n+1)=f(3n)+1=f’(3n)+1=f’(3n+1)
Similar for 3n+2, so f=f’
Surjective: any g from N_0 to itself define f(3n)=g(n), f(3n+1)=g(n)+1, f(3n+2)=g(n)+2
clear tendon
I made this set to describe any function that follow the conditions
oak perch
That is not true
Told you your original set is bijective to set of all maps from N_0 to N_0
clear tendon
but I think now it not enough and i forgot some
oak perch
Injective: f(3n)=f’(3n) then f(3n+1)=f(3n)+1=f’(3n)+1=f’(3n+1)
Similar for 3n+2,...
I told you why it is bijective
oak perch
**Cogwheels of the mind**
I even constructed the inverse map which doesn’t matter now
clear tendon
i don't really know what bijective to set mean
oak perch
Means there is a bijection from your original set, to the set of maps from N_0 to N_0
clear tendon
wiki after i know
oak perch
I let this bijection be such a map: mapping f to g, where g(n)=f(3n)
oak perch
Suppose {g: g is a map from N_0 to itself } is countable, so it equals {g_1,g_2,...
And set of maps from N_0 to N_0 is not countable, is proved here
clear tendon
I'm sorry i need to go thx for the help
oak perch
Whatever
clear tendon
.close
flat saddle
Need help checking if this is true
lone heartBOT
Need help checking if this is true
half epoch
Then it’s false, no? You found a value < 3.14 whose square is > 9.85, thus the proposition can’t be true
flat saddle
Book says it is true
vale wigeon
[your statement is] vacuously [true]
unless the pi is not meant to be taken as meaning the circle constant
flat saddle
I don't know what that means
half epoch
>>> [your statement is] vacuously [true]
unless the pi is not meant to be taken ...
Is it true? \pi = 3.1385 is a counter example
fresh parcel
How is pi less than 3.14
half epoch
Or 3.139
vale crag
Is it true? `\pi = 3.1385` is a counter example
unless the pi is not meant to be taken as the circle constant
half epoch
How is pi less than 3.14
That’s what’s meant by “vacuous” assume pi isn’t the circle constant but just a variable
flat saddle
In this case it is just a proposition
half epoch
*unless the pi is not meant to be taken as the circle constant*
Isn’t it false whether pi is the circle constant or not? The circle constant is definitely not < 3.14 and there exists values < 3.14 with squares < 9.85
vale wigeon
*unless the pi is not meant to be taken as the circle constant*
the world if people actually read what i said
vale crag
Isn’t it false whether pi is the circle constant or not? The circle constant is ...
If pi is considered as the circle constant then pi isn't less than 3.14
But that means you have an implication with a false premise
Therefore the whole implication is true
flat saddle
I see, so they used pi as a reason, pi < 3.14 is false and pi squared < 9.85 is also false, false implies false?
vale crag
The otherway of interpreting the statement is thinking it is some sort of quantified statement
lean depot
I see, so they used pi as a reason, pi < 3.14 is false and pi squared < 9.85 is ...
False also implies true. False implies anything, in fact.
vale crag
Ie for all pi in R, if pi < 3.14 then pi^2 < 9.85
half epoch
But that means you have an implication with a false premise
LOL, that is actually true
vale crag
(The pi as a variable thing)
And yeah the quantified stuff is false if I trust matas' calculations
flat saddle
I'm lost 
vale crag
But that means you have an implication with a false premise
If you haven't seen quantifiers forget about my for all blabbering @flat saddle
vale crag
I'm lost <:flonshed:629835071465062410>
What point makes you lost?
flat saddle
Do I just treat pi < 3.14 as false and pi squared < 9.85 as false?
and then False implying false is true
vale crag
They are false (assuming pi is the circle thing)
vale crag
and then False implying false is true
Yeah
serene mist
To find the inverse function of square root of x + 1, would u swap square root of x with y or just x?
flat saddle
you have to do the inverse
to get f(x) you have to square root x and add 1
to get the inverse you have to do the steps backwards
oh
just swap the variables
serene mist
So just x and y? And not the square root
flat saddle
yes, just x and y, and you can see why because if you can see what the function does to x
f(x) takes x, square roots it and adds 1 to it
so the inverse would take y, square it and take 1 away
serene mountain
lone heartBOT
serene mountain
the answer is at the end
i just dont know how it got from the first step to the sexond
second
wary stream
Common denominator
Find a common denominator for the numerator, add/subtract them
Find a common denominator for the denominator part, add/subtract that
serene mountain
i just get x from the numerator and put it in with y/x
wary stream
What?
That makes no sense
Let's start one step at a time
What is the expression in the numerator?
wary stream
What is the expression in the numerator?
.
serene mountain
x divided by y
wary stream
The full expression that's in the numerator
serene mountain
plus 1
wary stream
You broke it into pieces, I'm asking you for the full expression, it one text statement
serene mountain
x divided by y plus 1??
serene mountain
1 
wary stream
You do not need to use decimals
serene mountain
6
serene mountain
im going into calculus how do i not know this shit this is embarrassing 
wary stream
So as I stated, for step 1 to get to step 2, you need a common denominator for the expression in the numerator
And you need a common denominator for the expression in the denominator
edgy flare
If you have two fractions 1/a and 1/b and you add them. You take the denominator of the first one and multiply the second one by that denominator over itself. (1/a) + (1/b) * (a/a)
Notice a/a = 1
So you’re not changing the value of the fraction, just changing the way it looks: like 1/2 is the same value as 5/10
Now do the same for the second fraction to the first: (b/b) *(1/a) + (1/b) * (a/a)
This will make any two fractions have the same denominator so that you can add the numerator over your new denominator.
So in my example you should end up with: (b/ab) + (a/ab) = (b+a)/ab
fresh parcel
im going into calculus how do i not know this shit this is embarrassing <:angery...
lmao
fresh parcel
its okay lmao
real gazelle
yeah it's okay I do stuff like that all the time
don't sweat about it
just practice :)
serene mountain
Now do the same for the second fraction to the first: (b/b) *(1/a) + (1/b) * (a/...
this might sound so stupid but when you multiply (b/b) (1/a) how come it isn't 1b/ba
edgy flare
b = 1*b
serene mountain
wait the 1 just makes it a b
lone heartBOT
@serene mountain Has your question been resolved?
azure trout
lone heartBOT
azure trout
Did I do this right?
karmic rapids
show work
azure trout
show work
there is no work lol i just plugged in the numbers
into these
so??
did i do it right
alpine sable
the +-
alpine sable
consider that first
azure trout
how is tan+
alpine sable
languid bolt
tan = sin/cos, negative/negative = positive
alpine sable
wdym
alpine sable
u dont have to do that
if cosA=-24/25 you can get sin cos tan csc sec cot
everything
alpine sable
oh
azure trout
coterminal
alpine sable
the angle?
alpine sable
the angle?
alpine sable
what quadrant is 290 on
azure trout
fourth?
alpine sable
Yes
azure trout
ok
alpine sable
now what trig is positive and negative in quad 4
azure trout
no clue lol
alpine sable
yes
azure trout
thank youu
jade zenith
What's 9 +10 ?
alpine sable
the answer you are looking for is 21
jade zenith
That's wrong
alpine sable
cap
lone heartBOT
@azure trout Has your question been resolved?
wind bloom
how do i find m<OAP
lone heartBOT
how do i find m<OAP
wind bloom
hi
lone heartBOT
@wind bloom Has your question been resolved?
stiff geyser
how do i find m<OAP
"The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference"
alpine sable
help pls
keen socket
u know 20^3 =8000
and theres 8000 numbers
so theres 20 cubes between 1-8000 inclusively
so 20/8000 =1/400
lone heartBOT
@alpine sable Has your question been resolved?
wind bloom
wait to find <R do i do tan^-1(72/25)=70.9 lol
lone heartBOT
wait to find <R do i do tan^-1(72/25)=70.9 lol
real gazelle
do you know that tangent = opposite / adjacent
lone heartBOT
lone heartBOT
Available help channel!
harsh nimbus
can someone help with couple of these problems
lone heartBOT
can someone help with couple of these problems
tight locust
does it give you a particular order with which to perform the integration?
harsh nimbus
wait sorry i just realized i flipped my x and y axis around lol
harsh nimbus
does it give you a particular order with which to perform the integration?
no it's based on approximation so i did it using area of rectangles
This was my second question if anyone can help
tight locust
draw the region
harsh nimbus
yeah i have made it
lone heartBOT
@harsh nimbus Has your question been resolved?
static ibex
lone heartBOT
lone heartBOT
@static ibex Has your question been resolved?
static ibex
<@&286206848099549185>
abstract fractal
Show your work
static ibex
am i correct?
abstract fractal
No
abstract fractal
How am I supposed to know if you don't show your work
static ibex
no i mean in the equation
warm apex
well first of all, multiplying x would compress the graph, not stretch it
iron mulch
Show your work broski
abstract fractal
The -3 looks right. That's about it. Now show work
iron mulch
Otherwise we can’t see where you went wrong
knotty spire
well the +4 is probably also correct
iron mulch
also it’s in degrees 
knotty spire
also it’s in degrees <:luffyTragic:476211388419801088>
We don't know 🤷
Maybe it's a really stretched out sin
abstract fractal
Maybe. I didn't think about it, I just saw x=0 doesnt give 4, but if the input is wrong, then that'd make sense
iron mulch
I’m saying it’s in degrees and that’s disgusting
knotty spire
sin in degrees is like riding a bike with training wheels
knotty spire
Maybe. I didn't think about it, I just saw x=0 doesnt give 4, but if the input i...
I just looked at the graph and visually found the average over several periods
warm apex
The -3 looks right. That's about it. Now show work
wouldn't the -3 and the +4 be right?
abstract fractal
Maybe. I didn't think about it, I just saw x=0 doesnt give 4, but if the input i...
.
knotty spire
@static ibex So, concluding our thoughts here, send your work.
(Also do tell us whether your sin is in degrees or radians)
abstract fractal
Yeah on second thought +4 is def right
static ibex
i think it might be degrees
everything seems right except the 180 im just looking how to fix that
warm apex
horizontal stretch and translation are off
static ibex
?
knotty spire
or, from my physics perspective, angular frequency and initial phase angle
warm apex
oh wait hold on mb
knotty spire
There is definitely some kind of phase shift.
look at x=0
it's neither the maximum/minimum nor 4
static ibex
i found a from doing max-min and becuase its sin its -
and c from max+min/2
but i got something wrong finding B
static ibex
well i thought you just count the length between at the peeks
but thats wrong so idk
knotty spire
well and you got 180 as the distance between peaks?
knotty spire
well that's because you misunderstand
what you measured is the period
but the coefficient b is the angular frequency
static ibex
ok how i find that
knotty spire
$\omega = \frac{2\pi}{T} = \frac{360^{\circ}}{T}$
ocean sealBOT
Remavas
knotty spire
where omega is the angular frequency and T is the period
static ibex
ok ty
knotty spire
For an intuitive sense, the period of a "bare" sine function is 2pi
So since your period is actually 180, you need to multiply your x by a factor of 2pi/180, to "slow it down"
,w plot -3sin(x*pi/90) + 4
static ibex
so b = 2?
ocean sealBOT
static ibex
oh
knotty spire
well, you choose the appropriate version, for whether your sin is in degrees or radians
but as you can see, it still doesn't match your graph
static ibex
yea what happened there
knotty spire
there is a phase shift
knotty spire
horizontal stretch and translation are off
As this smart man said, there is a horizontal translation
static ibex
so is c 2.5 then
ocean sealBOT
static ibex
bruh
knotty spire
Your actual equation actually needs to look like $$y = A\sin\left[{\omega(x + \delta)}\right] + C$$
ocean sealBOT
Remavas
static ibex
💀
knotty spire
which leaves me to wonder why you didn't include phase shiftfrom the very beginning 🤷
knotty spire
well finding the phase shift is easy
knotty spire
find out by how much you need to shift this to the left/right to get the same graph as you have
knotty spire
y=-3sin[??????]+2.5
we already determined the vertical shift is +4
knotty spire
You may want to study this: https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html
And then retry
static ibex
🗿
knotty spire
no it's an innocent sinusoidal
warm apex
the distance between your peaks is 180, so your period will be 2pi/180
warm apex
I don't like using proper language :(
I called the phase shift horizontal translation a second ago lmao
knotty spire
but this is kinda important 💀
warm apex
to be fair they're technically the same but anyways
static ibex
yall are confusing me
warm apex
wait
static ibex
whats the equation supposed to look like
warm apex
yeah my bad you're right
static ibex
yes
warm apex
so your equation will be y = -3sin(2pi(1/180x + phase shift))
static ibex
can soemone just give the equation and explain it
knotty spire
can soemone just give the equation and explain it
The main goal of this server is to help you solve it, and giving you the solution might help you short-term, but won't help you long-term
especially when you did all the hard work already
finding the horizontal shift i easy
warm apex
to take the phase shift into account, we want to shift 30 to the left
static ibex
ok yes but u just confusing me
i dont mean liek give it i mean explain it
like show the answer and how u got it
so i can understand
knotty spire
$$y = -3\sin\left[{\frac{\pi}{90}(x + \delta)}\right] + 4$$
ocean sealBOT
Remavas
knotty spire
This is what we have so far
static ibex
or do it with a smiliar equation or something
graph*
ok
what is that weird symbol
static ibex
i thought there was no phases shift
warm apex
hm?
warm apex
wouldn't it be delta/2?
knotty spire
wouldn't it be delta/2?
why?
knotty spire
again why
knotty spire
again again why
static ibex
ok so is the phase shift like -1.5
knotty spire
,w plot 2x^2 + 5x
warm apex
how did you go from how did you go from 2pi / 180 x to pi/90 x
ocean sealBOT
knotty spire
@warm apex shift this to the right by 5 units for me
static ibex
how do i find delta
warm apex
2(x-5)^2 + 5(x-5)
knotty spire
take the orange function, and find out by how much you need to shift it to match the blue one
knotty spire
2(x-5)^2 + 5(x-5)
so you replaced each x by (x-5)
warm apex
yes indeed
warm apex
oh my god i'm an idiot mb
knotty spire
take the orange function, and find out by how much you need to shift it to match...
I honestly can't explain it any other way
Literally take any peak
and find the distance between the peak of our untransformed fucntion and the real one
warm apex
Idk why I thought we were shifting by 30
warm apex
so I was confused as to why it would be 15 instead
warm apex
ok i cant measure from your graph tho
this is -3sin((pi/90)(x))
knotty spire
With no phase shift, at x = 0, the sin(...) part will go to zero
And we will be left with y = 0 + 4 = 4
knotty spire
However, we see that at x=0, y \neq 4
So then we find out by how much it is shifted
warm apex
we want y to be 1 at x = 30
this means we need to shift 15 to the left
static ibex
-3 sin[pi/90(x+15)] + 4 ?
knotty spire
assuming your sin is in radians
knotty spire
-3 sin[pi/90(x+15)] + 4 ?
also, note
in most regions, implicit multiplication by juxtaposition binds more strongly than /
with the exception of the US because yes
I wonder which convention wolfram follows
warm apex
if sin is in degrees, you can just replace pi/90 with 2
knotty spire
,w 6/2(1+2)
ocean sealBOT
knotty spire
Ah, the American one
warm apex
well i mean
warm apex
in most regions, implicit multiplication by juxtaposition binds more strongly th...
why is this?
knotty spire
why is this?
Because it makes more sense
warm apex
this is why we use brackets 😊
knotty spire
Here, Julia uses the more international/scientific standard
warm apex
well I think it's because of bedmas/pemdas
knotty spire
this is why we use brackets 😊
indeed, brackets make it clear and not depend on convention
warm apex
if we follow that, first is parentheses so 6/2(3)
after that, 2(3) is just seen as 2*3
hold on
warm apex
yeah
interesting, although maybe it's best to just write things out how they're meant to be
also I should say that with a lot of math software, typing a / will immediately give you a fraction
knotty spire
yep, hence why I brought it up 😉
knotty spire
also I should say that with a lot of math software, typing a / will immediately ...
Most programming languages don't have multiplication by juxtaposition
And / and * have the same precedence
so there you have no problems
warm apex
,w 6÷2(1+2)
ocean sealBOT
warm apex
magical
knotty spire
yeah, wolfram decided to use PEMDAS
warm apex
how do you find values of x where y is at its maximum?
knotty spire
Heh, one reason I heard for the convention where juxtaposition binds more strongly is because of distribution. Obviously if you write something in front of parentheses, you want to distribute it
AND
6/2x
Pemdas would give you 3x
instead of 6/(2x)
,w 6/2x
ocean sealBOT
knotty spire
see, PEMDAS treats it as 6/2*x
warm apex
@static ibex the maximum of your equation is 2
knotty spire
see, PEMDAS treats it as 6/2*x
left to right this gives us 3x
warm apex
we know that x=30 gives y=2, how can we find out what other values for x are y=2?
static ibex
what does it mean by other values of x
knotty spire
we know that x=30 gives y=2, how can we find out what other values for x are y=2...
Also note how it is a sinusoidal function, so how often (at what distance) do maximums repeat?
,w plot sin(x)
ocean sealBOT
knotty spire
e.g. sin(x) has a maximum at pi/2
warm apex
what does it mean by other values of x
it's a cos function, it has multiple peaks
knotty spire
And those maximums repeat periodically
warm apex
how can you find the x values of the peaks for 2cos3(x-30)?
static ibex
so cant you find it by simply adding
warm apex
well, that and the equation
knotty spire
so cant you find it by simply adding
adding what?
static ibex
x
ocean sealBOT
static ibex
ok so what is an equation to find other values of x
knotty spire
I would suggest having an understanding of periodic functions
warm apex
i believe you can just add any multiple of 360 to x
knotty spire
especially after our last struggle
knotty spire
i believe you can just add any multiple of 360 to x
That would assume the period is 360
warm apex
well it isn't
but I just distributed the 3 in
the period for this one happens to be 120
knotty spire
well, if you want to solve it algebraically
warm apex
that's how I prefer to do it for this one
y = 2cos(3x-90+n*360)
n can be any number
integer
knotty spire
$\cos{360^{\circ}n} = 1, , n \in \mathbb{Z} \implies 3x - 90 = 360n$
ocean sealBOT
Remavas
warm apex
it's the number of the peak you're looking at
knotty spire
but again, this is the more tedious and boring version
warm apex
so at x=30, 2cos(3x-90+0) = 1
then at x=150, 2cos(3x-90+360) = 1
and so on
once you figure out your period is 120 you can just add 120 as many times as you want for x values
and if you want a formula, x=120n+30
knotty spire
How to find the answer in seconds: A periodic functions repeats after 1 or more period is either added or subtracted. The angular frequency here is 3 by equating this function to the general form for a sinusoidal. Therefore, the period is 360 deg / 3 = 120 deg. We know one maximum is at x = 30 deg. Therefore, every maximum is at x = 30 + 120n, where n is any integer.
warm apex
worded it better than I ever could
knotty spire
But if you are not sure, you can do it the algebraic way Neem did
static ibex
.close