first make everything positive indices
#help-13
buoyant latch
wraith daggerBOT
wifix
sleek grove
I am not familiar with this mathematic editor😂
bold vine
first make everything positive indices
@celest comet I’d start with this
celest comet
<@670929799921008650> I’d start with this
alright
muted bear
celest comet
alright i made all the numbers in the fractions positive indices
now what should i do about the powers?
buoyant latch
what does it look like now
bold vine
Show your work
sleek grove
you can extract common index
manic glade
You can test it by trying 2^3 / 2^2
celest comet
Show your work
alright so i did this:
2^4/7^2 x 7^4/2^4
should i just simplify and be done with the problem?
buoyant latch
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
pray help me solve this
crimson sedge
<@&286206848099549185>
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
The sides of a right-angled triangle are integers. The length of one of the sides is 12. Then the sum of all
possible radius of the incircle of such triangles is.
crimson sedge
<@&286206848099549185> ??
crimson sedge
what about 9,12, 15
crimson sedge
and 12 35 37
sir, the thing is
i got the anser of 14
but the solution is 11
idk sir??
celest ledge
Idk, radius=ab/(a+b+c) right ? So
crimson sedge
yes sir
for right triangle
when i do it i get 14
2,3,4,5 are possible radiuses
adding them up gives 14?
celest ledge
Idk,I used area, ab=2 times area of triangle=r(a+b+c), I got 192/48,60/30,108/36,420/84
crimson sedge
answer key wrong sir??
celest ledge
Must be
crimson sedge
thank you sir
crimson sedge
oh, which grade?/
celest ledge
Graduate first year
crimson sedge
university??
celest ledge
Yeah
celest ledge
Np
crimson sedge
.end
celest ledge
“Close”
crimson sedge
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cursive oriole
cedar kilnBOT
shut reef
still dont know huh
cursive oriole
U know?
feral heath
it is r/s)^2 = (1+sintheta)/(1-sintheta)
so, make it (1+sintheta)^2 / cos^2theta
so, ur r/s is 1+sintheta / costheta
now u got the answer
feral heath
U mean part *i)
2
feral heath
U dont mind writing
sure
celest ledge
- trivial, omit
2)multiply r/s by cos^2(θ/2)+sin^2(θ/2) both above and below
cursive oriole
1) trivial, omit
2)multiply r/s by cos^2(θ/2)+sin^2(θ/2) both above and below
Ye i did that
But i got
A wierd figure
celest ledge
You got (1+2sc)/(c^2-s^2)
cursive oriole
U dont mind writing on a notepad too?
celest ledge
Which is (1+sin(θ))/cos(θ)=sec+tan
celest ledge
Sure
cursive oriole
Expecially foe trigo
celest ledge
You got (1+2sc)/(c^2-s^2)
c and s are cos(θ/2),sin(θ/2) respectively
feral heath
Wait ur first step
square them
feral heath
So squaring the half angle
cursive oriole
sin^2 a+cos^2a = 1
But this is 1/2
Not 1
The angle is half
Does it still work
feral heath
But this is 1/2
doesnt matter
cursive oriole
Rlly
feral heath
any angle it should work
cursive oriole
Oh
frosty ocean
any angle it should work
Naayagan meendum varaa'na bro? 
feral heath
Naayagan meendum varaa'na bro? <:kekw:752021756650455061>
tamil ah nee?
frosty ocean
yep!
feral heath
nice
cedar kilnBOT
@cursive oriole Has your question been resolved?
hazy stag
Okay, so, I'm working on this plugin for a game that adds a hunger/thirst system. The highest value for both is 100, lowest being 0. I went ahead and did some math for the thirst, based on how much water someone should drink before possibly dying from dehydration. (Takes 3 days w/o water.) Based on google, a person should drink 2 bottles of water per day, so by taking the number 100 (highest value) and dividing it by 6, gives us the value 16.6 (rounded down for simplicity). So each water bottle adds 16 points towards hydration.
Now, my problem is, I have no idea how to get a value for the hunger. Since google simply says 3 balanced meals, (350-600 calories), and 1-3 snacks (150-200 calories).
Unfortunately, I cannot count simply by caloric intake, since food can sate more or less, independent of calories.
tropic oxide
you could look at minecraft's hunger system for inspiration perhaps
vernal palm
^^^
hazy stag
Well the base value for an apple in minecraft is 4, based on a 20 point system. So I'd have to multiply that by 5 to get a 100 point system, meaning 16. But I also have to take into account that the system for food is based over the span of 7 days, not 1.
tropic oxide
you could perhaps divide all nutritional values by 7 and then have it decay 7 times slower too
hazy stag
well if apples had a value of 20, that means that someone could survive w/o losing hunger by eating 5 apples throughout the course of 7 days
...do you think i could just half that for a more realistic number?
10 apples over the course of 7 days to stay fully satisfied?
hazy stag
or do you think 14 apples over the course of 7 days would be more realistic?
tropic oxide
how long does it take to starve
tropic oxide
7 days, right
i'm not sure minecraft's hunger system would have you go from full to zero in a single day
hazy stag
The hunger system takes 88200 seconds to go from 100 - 0
every 882 seconds, 1 point is taken off from the hunger system
hazy stag
the system itself is also based off of a different time value
tropic oxide
unless your in-game days are shorter than real life days
hazy stag
it assumes that each day is 3.5 hours long
wraith daggerBOT
Result:
7
Result:
12600
er. where was i going with this
hazy stag
lol i dunno but you were back tracking my math a bit there
tropic oxide
a day's worth of nutrition is about 14 points under your hunger system
you could base your nutritional values around that
hazy stag
,calc 14*7
wraith daggerBOT
Result:
98
it probably depends on like, what food items you have available in your game
hazy stag
that is close to 100
so assuming someone needed to eat 3 times a day, that would be 14/3
giving me 4.6
rounded up to 5 for simplicity sake
making each day of nutrition requiring 15 points to stay fully hydrated, assuming 5 points p/meal
alright ty!
have a wonderful day ann
cedar kilnBOT
cold briar
$\int \limits$
wraith daggerBOT
MarveI
cold briar
was that this?
versed fulcrum
Integral
Indefinite to be exact
$\int_{a}^{b}f\left(x\right)dx=F\left(b\right)-F\left(a\right)$
wraith daggerBOT
AirToastie
versed fulcrum
This one is definite integral
upbeat dune
cold briar
**MarveI**
you want to insert this into desmos? @versed fulcrum
versed fulcrum
wdym
cold briar
wait you deleted the message
versed fulcrum
Oh
cold briar
i meant like.. what was the symbol you posted
versed fulcrum
that one was a bit different
cold briar
havent learn that
versed fulcrum
cold briar
what is that called
versed fulcrum
You're subtracting sin(π) - sin(0)
cedar kilnBOT
Available help channel!
crimson sedge
is my answer and solution correct?
cedar kilnBOT
is my answer and solution correct?
random shale
To check put the values back into the original equations
velvet mortar
Just as the monkey said ^
crimson sedge
To check put the values back into the original equations
huh?
livid hound
show work, what are you unsure about
cedar kilnBOT
@crimson sedge Has your question been resolved?
velvet mortar
@crimson sedge what are you waiting for?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
tame lantern
cedar kilnBOT
tame lantern
how to solve
balmy apex
show work
tame lantern
i just put all sides as 10
eb db and the 3 stated sides
and said a+b>c
therefore bc > 15
so now im stuck but 17 20 and 10sqrt 2
@balmy apex
tame lantern
yea
sick orbit
that means BE=10
tame lantern
yes
tame lantern
ok
sick orbit
yes
sick orbit
now draw another right angle triangle
sick orbit
yes
sick orbit
yes
cedar kilnBOT
sick orbit
np
cedar kilnBOT
Available help channel!
crimson sedge
Is there an "analytical" way to find the epsilon value to check whether 3 vectors are coplanar?
crimson sedge
I cannot simply use 0 as the value for equality, because rounding errors might happen
So instead of doing the triple product between 3 vectors = 0,
I'd need to do triple product between 3 vectors <= epsilon
Currently I'm using epsilon = 1E-6, and I'm certain I've seen this value somewhere online (can't find the source anymore sadly). But I don't know if this value will in most cases be correct
dawn junco
I mean the threshold is just about "how small do I define close enough to 0"
eps = 1e-6 is a typical convention
but yeah unless you're working with tiny tiny tiny vectors, or you want to distinguish between vectors with a very small difference, you won't have any problem with that
crimson sedge
Another issue is that while 1e-6 might be good, the types of the elements might vary: they might be normal integers (so =0 would work), or floating-point values, or doubles, or other arithmetic types which have different ranges...
So maybe I'm concerned too much, but there could be possibly different rounding errors between different types
dawn junco
If you're working with some floating points, everything will be converted to floating point at some point anyway
you'll have to write your functions in whole generality (double for example) anyway
crimson sedge
Alright, so 1e-6 is "good enough" for all types if I'm not concerned about too small vectors?
dawn junco
yeah
and if you see it's too huge for your application for some reason
you can just make it smaller
crimson sedge
Alright, thank you 🙂
crimson sedge
.close
vale ridge
This is kinda a dumb question but can someone help explain what im supposed to do with this question the wording has kinda confused me : Compare and contrast a function and its inverse. Represent your answer in a table of values and in a mapping diagram.
vale ridge
This is kinda a dumb question but can someone help explain what im supposed to d...
does contrast mean to create a function im unsure what im supposed to do here
amber ridge
cedar kilnBOT
@vale ridge Has your question been resolved?
crimson sedge
I'm unsure how to do f(-2) = lim f(x) when x approaches -2^- . the one on the bottom left.
crimson sedge
in addition, im thinking maybe (-2, 4) should go up to infinity?
this is what im thinking. still not sure about this line though
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
have to go away from my PC. but if anyone has an idea let me know pls, channel will probably close. thanks
wanton sail
I'm unsure how to do f(-2) = lim f(x) when x approaches -2^- . the one on the bo...
you already know what the right hand side is as a number (from the rest of the problem) so use that
wanton sail
this is what im thinking. still not sure about this line though
no there's no reason for that, it has to go to neg inf in both sides of x=5
also you can't have an x value corresponding to more than one y value
the rest is good though
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
no there's no reason for that, it has to go to neg inf in both sides of x=5
where would the line go then?
There is a HA so it can't go to - infinity
crimson sedge
that one yes but also (-2, 4) going up to infinity
wanton sail
that one has to go to -infinity
it can cross the HA
the HA is not really a boundary
only the VA is
wanton sail
can you send a pic of what you mean
wanton sail
yea like that except erase the current curve you have going under the red line
you can only have one curve at a time for any given x value
crimson sedge
ah
then that would mean the entire line would have to go?
under the red line
basically get rid of this entire one
wanton sail
yup get rid of that one
crimson sedge
ah I see
wanton sail
and the red line is good
crimson sedge
that makes sense since they go to -infinity at the end
then does the one on the left just go nowhere?
(-2, -3)
wanton sail
look at the bottom middle condition they give you
crimson sedge
its telling me everything on the left side should be going to infinity
i see
does "the left side" mean anything < 0?
wanton sail
no the left side means like in the long run, really really really big negative numbers
you only care about where it goes "at the end" so to speak except there is no end since numbers go on and on forever
cedar kilnBOT
cedar kilnBOT
Available help channel!
shell agate
cedar kilnBOT
livid fog
Hello! I need some help on this question. 🙂
cedar kilnBOT
Hello! I need some help on this question. 🙂
@livid fog Has your question been resolved?
violet flume
you need to show what you have tried, and spefically where you got stuck
@livid fog
livid fog
you need to show what you have tried, and spefically where you got stuck
oh
I didnt really understand what to do
but I tried writing out what each part of it had
livid fog
weve done a problem a lot like this before
I must have forgot
violet flume
so heres something that might make your life easier
livid fog
violet flume
something to an even exponent is always positive
do sign analysis on (x+1)(x-4)
but keep in mind where your zeros are
violet flume
👀
violet flume
youre good man
just do the sign analysis on the smaller function
lemme know what you get
try for 5-10 min see if you can figure it out
pretend its exam and you have no help but endless time
livid fog
pretend its exam and you have no help but endless time
Oh in that case
time to guess C
😏
violet flume
you didnt even try what i said did you 
livid fog
you didnt even try what i said did you <:bearlain:762653539092529182>
I hav ebeen
looking at the question
trying to observe
and make a hypothesis
on what it could be
and my guess conluded to those to
violet flume
you dont need to do that, fwiw
you need to do the work
and determine which is correct
its easier
livid fog
idk how
violet flume
look up sign analysis
violet flume
ah, alright
lets look
so really quickly
can you tell me where (x+7)^2 is positive
livid fog
ye
violet flume
okay
so we square it
(x+7) * (x+7)
somewhere that x+7 is negative
is the result positive or negative
livid fog
alright
violet flume
what do you mean?
violet flume
👀
violet flume
im asking you where (x+7)^2 is negative
livid fog
oh
violet flume
is it still negative where (x+7) is negative
violet flume
yea
its every positive (or 0)
i just wanted to remind you that
the other functions you ignored in the sign analysis
they are only contributing positive regions
(or zero)
here you said (x+1)(x-4) is only negative between -1 and 4
when we add back on the original factors of (x+7)^2 and (x-2)^4, do we gain areas that are negative? lose them? stay the same?
violet flume
where is (x-2)^4 negative
violet flume
it may help to remember that $(x-2)^4 = \qty( (x-2)^2 ) ^2$
wraith daggerBOT
jan Niku
livid fog
ok
wraith daggerBOT
jan Niku
livid fog
well its postive
violet flume
what would have to happen here to make this negative
violet flume
👀
violet flume
im not sure what your argument is
violet flume
if you think that (x-2)^4 adds negative area
give me an x value where (x-2)^4 is negative
and tell me why its negative there
if it doesnt add any, then why not?
violet flume
think about this
you have two factors on the right
to get an odd number, you need an odd times an even
or an even times an odd
violet flume
im going to tell you
then im gonna go back to packing
a factor raised to an even exponent is never negative
lol
violet flume
okay
the entire function
it has the same sign analysis as (x+1)(x-4)
all you add is zeros
you should be able to finish the problem now
livid fog
you should be able to finish the problem now
ok
livid fog
you should be able to finish the problem now
yea it's C
🤣
Woulda got it right either way
my lucky letter C
💪
ty
.close
mellow nimbus
cedar kilnBOT
mellow nimbus
that’s the question
i think my solution is wrong
oh wait i subtracted
i’m dumb
celest ledge
Any m>n, |a_m-a_n|<1/2^n
celest ledge
|a_m-a_n|<=Σ1/(2^k) k from n+1 to m, <1/(2^n)
For example
|a_4-a_2022|<1/16
So 9/16<a_4<13/16
So a_4 has to be 5/8
celest ledge
Yeah
mellow nimbus
how do i go from 3/4 to 5/8
celest ledge
|a_m-a_n|<=Σ1/(2^k) k from n+1 to m, <1/(2^n)
m=2022, n=2,3,4 respectively
celest ledge
how do i go from 3/4 to 5/8
-1/8
mellow nimbus
how did you get the -1/8
mellow nimbus
yes
celest ledge
a_3=a_2+1/4=3/4
mellow nimbus
yes
celest ledge
a_4=a_3-1/8=5/8
mellow nimbus
why did we add the rest and subtract this one
celest ledge
Because other possible values don’t belong to (9/16,13/16)
tidal knoll
cedar kilnBOT
tidal knoll
confused on how to start this
tropic oxide
do you know how to find the acceleration as a function of time?
compact junco
velocity is the first derivative of the function, acceleration is the derivative of velocity
tidal knoll
do you know how to find the acceleration as a function of time?
uhh can i have an example?
tidal knoll
velocity is the first derivative of the function, acceleration is the derivative...
ahhh gotcha
tropic oxide
i take that as a no from you
was going to say acceleration is the 2nd derivative of position
but fructosepear said the exact same thing
compact junco
just with an extra step
tropic oxide
i could still give you an example of taking the second derivative of some unrelated function if you so desire
tidal knoll
i could still give you an example of taking the second derivative of some unrela...
nope i got the correct answer i was just confused on how to do it
thanks tho!
.close
echo canyon
Hi there I'm currently reviewing for an entrance test and I'm getting stumped by this problem:
echo canyon
Won't the Greatest Integer Function be 1? We were already given that the answer would be 0 but idk how it got there
flint plinth
does your notation [[ x ]] mean floor, ceiling, or round?
echo canyon
Floor
flint plinth
thx
echo canyon
Whatever x from (1/2,1),that thing equals 0
Could you explain it more in detail if that's okay?
celest ledge
?you just simply calculate it
flint plinth
if x is smaller than 1 but close to 1, then [[x]] is zero and [[x-1]] is -1, and the only thing varying as x approaches 1 is the second term in the denominator
echo canyon
Ohhh I see I see
x will never be 1 but only close to it
And since the notation requires it to be a floor
It'll be 0
I get it now, thank you guys!
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
static fern
cedar kilnBOT
static fern
Once again, I need to use p-adic valuation.
I'm wondering if I can use WLOG or not, because in that case I could rewrite the equation in terms of minimums and maximums and simplify.
<@&286206848099549185>
I need help please.
wraith pebble
Once again, I need to use p-adic valuation.
idk what p-adic valuation is but if you are allowed then use that $$lcm(a, b) = \frac{|a\cdot b|}{gcd(a, b)}$$
wraith daggerBOT
Nathan_
static fern
I don't think I am. My instructor made it very clear that I need to apply p-adic valuation...
wraith pebble
like i said idk what that is so nvm then if that formula cant be used
crimson sedge
**Nathan\_**
yeah, use the gcd-lcm formula and the answer falls out immediately ^
if you dont know that formula, it can be proved fairly easily by using unique factorisation
wraith pebble
they said they arent allowed to use that formula for this question
crimson sedge
well they arent allowed to assume its true, so they just need to prove it
ig it can be proved by using the p-adic valuation and looking at prime powers, but I think that overcomplicates it
cedar kilnBOT
@static fern Has your question been resolved?
static fern
well they arent allowed to assume its true, so they just need to prove it
Exactly, but my instructor said that I need to solve it using p-adic valuation.
crimson sedge
how strong is the "need"
would it be enough to prove the lcm-gcd formula using p-adic valuation
static fern
Umm, I'm not sure. Is there a way I can solve w/out that formula?
crimson sedge
sure
just look at every p dividing a or b and make sure it has even padic valuation
cedar kilnBOT
Available help channel!
eager nacelle
cedar kilnBOT
cold briar
ok so
lets start with B.
easiest one
| | means absolute value
so | rp | is positive
eager nacelle
im stock between B and D
cold briar
- ( positive) = negative
eager nacelle
they both make sense
cedar kilnBOT
cedar kilnBOT
Available help channel!
opaque wraith
Can any one help me with this
why axiom of pairing is true?
cedar kilnBOT
Can any one help me with this
why axiom of pairing is true?
crimson delta
it's an axiom
opaque wraith
True but ther is a explanation?at least?
opaque wraith
OK
Is there a moral proof of this?
crimson delta
you mean why it should be true?
opaque wraith
Yes
crimson delta
dunno. I only know the very basics of stuff like that. but it seems like a very reasonable axiom
I don't see why it shouldn't be true
maybe get yourself the advanced role and ask in #foundations
opaque wraith
The thing that annoys me is that x could not be equal to u(for example)
and the whole Statement still be true
opaque wraith
maybe get yourself the advanced role and ask in <#537009662654939167>
I will try
Thank
crimson delta
I don't get what you mean
B is the set {u,v}. and then x in B if and only if x=u or x=v
but of course x could be anything else. then it just wouldn't be in B
opaque wraith
I thought we trying to define B using x
I didn't know B was pre defined
crimson delta
well the axiom tells you that B exists
or rather that such a set B exists satisfying x in B if and only if x=u or x=v
fair geyser
i think it's supposed to let you make sets from objects
like it's about pairs but as a consequence you can make singletons
hm, but what if I want a triple...
that doesn't follow
crimson delta
we probably have other axioms for that
fair geyser
perhaps the union in the screenshot yeah
opaque wraith
like it's about pairs but as a consequence you can make singletons
And it could be single since since there is a or ?
fair geyser
yes
crimson delta
you could take u=v
opaque wraith
Is this true ?
opaque wraith
you could take u=v
Yes but there is no info on that
crimson delta
wdym no info. we know there exists a B such that x in B if and only if (x=u or x=v=u). so x in B if and only if x=u
opaque wraith
wdym no info. we know there exists a B such that x in B if and only if (x=u or x...
For pairing axiom of have this
And there isn't any info on the sets u and v are the same
That's why I said there isn't any info on that
crimson delta
it says that it is valid for any sets u and v
so we can take u and v to be the same
we don't have to
but we can
opaque wraith
it says that it is valid for any sets u and v
True but shouldn't it be noted so we would know we are more specific about this?
Then the general any u an v?
crimson delta
why should we say something more specific if the general case covers it
I think I don't understand what you mean
opaque wraith
Then it wouldn't be tautologically equivalent?
Because the specific would not be true every where the general is true?
crimson delta
?
the specific is a subcase of the general
if x^2>=0 for all real x and 5^2 >=0. but why would I write the second statement down when I already have the first
opaque wraith
🤔
I'm not sure I understand what is going on
I'm going to search a little bit about this
And thanks for the response
.close
coarse wagon
I don't understand this
cedar kilnBOT
I don't understand this
calm agate
That symbol between ABC and DEF which I can't find on the keyboard means that the two triangles are similar
~
Found it
cedar kilnBOT
@coarse wagon Has your question been resolved?
coarse wagon
That symbol between ABC and DEF which I can't find on the keyboard means that th...
ok
so um how do I solve it?
opaque wraith
If I remember correctly
ΔABC~ΔDEF
means every angle of them is the same which means you can use ratio of each adjacent edge to figure out the answer
*at the end it should've been 10/x not 4
Sorry
I hope it helped
calm agate
ok
You can make a proportion with the corresponding sides (the sides in the same position in the two triangles):
10:4=x:6
Then solve for x
In two similar shapes the angles are the same and the corresponding sides are proportional to each other
cedar kilnBOT
@coarse wagon Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
young flame
hmmmm
the obvious first step is to find the area of the white region
no, the white region
the unshaded region
they are quarter circles
do you know the formula for finding area of a circle?
nope
that's the circumference
cedar kilnBOT
cedar kilnBOT
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weak root
does this type of equation have a specific name? its like the simplified form of an exponential growth equation with a rate of growth that has a rate of growth, which has a rate of growth, and so on (in this case, 3 layers of exponential growth/decay)
just want something to google
weak root
expanded form
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hot smelt
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hot smelt
How do I solve this
tropic oxide
do you know how to rationalize the denominator?
hot smelt
do you know how to rationalize the denominator?
multiply by the denominator
tropic oxide
$\frac{4\sqrt{2}}{2}$?
wraith daggerBOT
Ann
tropic oxide
yes, that is correct. though one would think this could be simplified a bit further
to just 2sqrt(2)
hot smelt
**Ann**
Has to be in this form
wait
can i write it as 2 root 2 over 1
Damn got it right
tender flame
im not sure how to do this; i got the answer 496, but im not too confident in it- could anyone help confirm the answer? if im wrong, id love to hear the correct explanation!
balmy apex
im not sure how to do this; i got the answer 496, but im not too confident in it...
show work
quartz vale
im not sure how to do this; i got the answer 496, but im not too confident in it...
your answer's correct yea
cedar kilnBOT
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tender flame
your answer's correct yea
ah, thanks!
violet cobalt
I'm wondering what the ratio of valid UTF-8 strings to all strings is. This is a discrete probability theory question.
1-byte code-points: 128 out of 2^8 are valid UTF-8
2-byte code points: 1920 out of 2^16 are valid UTF-8
3-byte code points: 63488 out of 2^24 are valid UTF-8
4-byte code points: 1048576 out of 2^32 are valid UTF-8
UTF-8 strings are any of those combined. E.g. if we want to calculate the ratio for 2-byte strings, it'd be (128^2 + 1920)/2^16 ≈ 27.93 %
What would be the ratio for a string of length n -> inf? Or, even better, the limit (N -> inf) of sum(n = 0 to N, number_of_valid_strings(n)) / sum(n = 0 to N, 2^n), but I guess it'll the same.
elfin hemlock
violet cobalt
wow it uses generating functions
smart
i don't quite understand what's happening there though
why is that true?
so the answer is 0
if i understand correctly
elfin hemlock
Yes
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violet cobalt
why is that true?
this question remains
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dire geode
this question remains
Use a convergence series test
violet cobalt
Use a convergence series test
how is it related?
dire geode
why is that true?
Oh nevermind the answer's here
dire geode
Read this https://math.stackexchange.com/questions/750551/probability-that-rando...
.
Use formula (*3)
violet cobalt
yeah, I understand that part
violet cobalt
why is that true?
what I don't understand is how they've got this
everything else is more-or-less clear
dire geode
why is that true?
If you expand the right side and match coefficients, you get formulas for N_n in terms of the four alpha variables.
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violet cobalt
If you expand the right side and match coefficients, you get formulas for N_n in...
So something like this (if we assume that n is divisible by 12, otherwise ignore the corresponding terms)
N_n t^n = [1]A(256 t)^n + [2]A(256 t)^(n/2) + [3]A(256 t)^(n/3) + [4]A(256 t)^(n/4)
N_n = a1 * 256^(n - 1) + a2 * 256^(n/2 - 2) + a3 * 256^(n/3 - 3) + a4 * 256^(n/4 - 4)
So even if this is correct, I don't see any useful implications
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pseudo skiff
.close
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gaunt lake
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gaunt lake
could anyone help example 11?
this is where I've gotten so far
I'm not sure how to find the range tho
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gaunt lake
<@&286206848099549185>
gaunt lake
<@&286206848099549185>
gleaming cloud
I'm not sure how to find the range tho
Graph fg
gleaming cloud
Ok? You can still graph fg
gleaming cloud
If you understand what it means to graph a function, it should be easy
gleaming cloud
I've never learnt how to graph to the power of a power
This sentence doesn't make sense
gleaming cloud
Sure
gaunt lake
ah ty I got the answer
gaunt lake
but when do I use these equations
gleaming cloud
?
gaunt lake
when do I use these equations
gleaming cloud
When you encounter a question relevant to them
gaunt lake
and when are those equations not applicable
what do you mean a question relevant is it relevant to any composite function?
gleaming cloud
No idea what you mean by that so I'll just see myself out
frozen tendon
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spiral radish
Where is the mistake
cedar kilnBOT
Where is the mistake
spiral radish
Is there even one?
mighty drift
The property with sqrts doesn't hold in C until you prove it
Therefore you can't because it leads to a contradiction
spiral radish
What is C? Just contant?
mighty drift
C the set of complex numbers
R the real numbers. Q rationals. Z integers. N natural integers
spiral radish
Oh right. I have not had them yet so I think I will leave the question for when I learn about the rules
mighty drift
That's one rule that doesn't work anymore yeah
cedar kilnBOT
mighty drift
Oh right. I have not had them yet so I think I will leave the question for when ...
That's also part of why we don't typically use the sqrt symbol when working in C
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fossil wadi
i have another question. If you are counting change and lets say the item was $10.25 and the customer gives you $5.25, you start the count the change back and you are going to give them back 5 dollars but they hand you an extra quarter that they found. how would you go about giving them the correct amount of change
crystal raptor
I assume you mean the item is $5.25 and the customer gives $10.25
tropic oxide
i have another question. If you are counting change and lets say the item was $1...
if you meant that the item is 5.25 and the customer gives you 10.25 and then produces an extra quarter (totalling 10.50 money paid), then their change will be 5.25
however, from a practical standpoint you would instead start over to ensure you were not having a sleight of hand pulled on you
fossil wadi
ok so basically you count up from what they gave you
tropic oxide
no, you count up from the cost of the item to what they gave you.
and if the original question was meant exactly as stated (i.e. they give you 5.25 for a 10.25 purchase), you tell them they're $5 short
fossil wadi
ok srry guys im dumb
hallow elm
ok srry guys im dumb
you're not dumb man we're here to help
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ocean badger
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ocean badger
Complex Variables:
This is what I came up with for part a
I need to know if that works and how to come up with part b. I have an idea for b. I’ll write it down.
This would make both a and b true
wanton sail
are alpha and beta analytic functions?
ocean badger
are alpha and beta analytic functions?
Sure
I just assume it’s a function with no zeroes at 0
wanton sail
I think if you write that alpha and beta are analytic at z=0 then it works
ocean badger
So both parts would be true?
I’m just not sure if there is some function that is not a polynomial that would make these false.
Also with the Laurent series wouldn’t I still just get a term like I have already written? Some a/z^2 and b/z^3?
Plus the series of no poles?
wanton sail
yeah I think both parts are true
if you represent them as laurent series it should be clear I think
ocean badger
What do you mean as Laurent series?
If I do that won’t I get what I have written + a sum of the other terms that are positive powers of z?
wanton sail
Also with the Laurent series wouldn’t I still just get a term like I have alread...
yes but a and b will be numbers
ocean badger
Okay. I’ll make that adjustment and add the Laurent series aspect. Thank you.
.close
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ancient spire
how can i go from this to a polynomial equation?
cedar kilnBOT
how can i go from this to a polynomial equation?
ancient spire
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crimson oyster
lost parrot
how can i go from this to a polynomial equation?
is this quadratic?
ancient spire
believe so yes
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stark shell
The second differences have to be the same
lost parrot
ax^2 + bx + c
that's 3 unknowns, so you could use 3 equations to solve it by substituting the values
stark shell
Oh woops mb
lost parrot
you want the polynomial equation, which is in the form f(x) = a + bx + cx^2 + dx^3 + ...
however, i think this question wants you to find the second order (up to x^2) polynomial equation
you can solve for this second order by solving the simultaneous equations
if it's not a second order polynomial, when you check if other points fit into it, it won't
if it is, then the others would fit
tribal sonnet
how do I plot this function rect(w/8pi)
rect = rectangular function
cedar kilnBOT
how do I plot this function `rect(w/8pi)`
rect = rectangular function
@tribal sonnet Has your question been resolved?
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plucky holly
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plucky summit
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plucky summit
i understand problem 1-2...
but problem 3 just flips my head upside down
i know its asking me to find
the antiderivative?
if im correct
but those little numbers dont make sense to me
bold kernel
so you know how to do the first two questions right?
bold kernel
okay thats great
plucky summit
subinterval
bold kernel
since question 3 is pretty much the same thing
plucky summit
(b-a)/n
bold kernel
do you know what an integral is?
plucky summit
is that an antiderivative
bold kernel
yes but also it is the area under a curve
bold kernel
$\int_a^b F(x)$ is the area under $F(x)$ from the endpoints a to b
plucky summit
but not the understanding of the area
obsidian coral
$\int_a^b F(x)$ is the area under $F(x)$ from the endpoints a to b
:( Bot still dead
bold kernel
fr
@plucky summit the integral of F(x) from a to b is the area under F with endpoints a and b
so problem 3 is essentially asking you for the area under the curve x^3-3 for 1<= x <= 3
plucky summit
mmm
bold kernel
which is the same as problems 1 and 2
plucky summit
its using the notation
bold kernel
you pick you many subintervals you want to use
plucky summit
that it should be expressed as
bold kernel
its just different notation
bold kernel
like problem 1 told you to use 6 subintervals
plucky summit
would that alter an answer
plucky summit
so with that notation
how is that like
like whats the correct answer
if u chjoose what subintervals to use
bold kernel
like whats the correct answer
any answer found using a reasonable amount of subintervals is correct