how
#help-27
ebon coyote
wooooo
ebon coyote
Then x = 1 is your turning point
Because this is an "n"-shape quadratic, this turning point is a maximum
ebon coyote
nps
orchid umbra
Oh did you multiply through by the right-most bracketed term?
Ya
ebon coyote
You know you can simplify root 32, right? @orchid umbra
orchid umbra
You know you can simplify root 32, right? <@776570662831259679>
yeah
the ans is
OH
NVM
wait
so my ans is correct?
ebon coyote
yh
ebon coyote
Yh
orchid umbra
oh yay
ebon coyote
It'd be a square if it were inscribed in a circle, yes
orchid umbra
ohhh
ebon coyote
But dis a semicircle
orchid umbra
It'd be a square _if it were inscribed in a circle_, yes
only in that case square maximizes area?
otherwise rectangle maximizes SA and V
ebon coyote
ye
ebon coyote
np
orchid umbra
đ
devout snowBOT
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thin geode
for d
thin geode
i dont really understand what they do here
i mean the root for -5 + 12 i was (2+3i) and (-2-3i), but why does the signs switch when it is -5-12i
acoustic leaf
in part c you show that the square of the conjugate = the conjugate of the square
so applying in reverse the same statement is true of square roots
thin geode
in part c you show that the square of the conjugate = the conjugate of the squar...
but shouldnt the roots be equal to each other then?
acoustic leaf
that means that since (-5 - 12i) = (-5 + 12i)*, then for any square root w of (-5 + 12i), then w* is a square root of (-5 + 12i)
they're conjugates of other roots, not of each other
thin geode
that means that since (-5 - 12i) = (-5 + 12i)*, then for any square root w of (...
"that means that since (-5 - 12i) = (-5 + 12i)*, then for any square root w of (-5 + 12i), then w* is a square root of (-5 + 12i)", doesnt this say the same thing? could you maybe draw it out or write it, cuz im still not getting the big picture
is this it ?
what u mean?
delicate siren
pretty much yeah
tldr: the square roots of the conjugate of any complex number is equal to the conjugates of the square roots of the complex number
dull inlet
im just so lost and the answerkey/online is notr helping at all, specifically i need help and how to find the equations for part b
devout snowBOT
im just so lost and the answerkey/online is notr helping at all, specifically i ...
languid ore
im just so lost and the answerkey/online is notr helping at all, specifically i ...
Do you remember what the coordinates of the points on a circle are
dull inlet
Do you remember what the coordinates of the points on a circle are
circle starts at oreigin (0,0) point B without moving (8,0), A(2,0)
languid ore
circle starts at oreigin (0,0) point B without moving (8,0), A(2,0)
What are the coordinates of the point theta radians around the circle?
dull inlet
What are the coordinates of the point theta radians around the circle?
unsure how to find that
languid ore
unsure how to find that
Do you remember your trig
dull inlet
i think so?
languid ore
i think so?
If I look at the unit circle and go theta radians around from 0, what will the x coordinate of the point I reach be?
dull inlet
costheata
dull inlet
sintheta
languid ore
Mhm. Now what if I look at a circle of radius 2 instead?
dull inlet
2costheta, 2sintheta?
languid ore
Yes
Now if I move at 3 revolutions per second, how many radians do I move at per second?
dull inlet
6pi
languid ore
Right, now if I've been moving for t seconds, how many radians have I moved?
dull inlet
6pit
languid ore
Now what should my x coordinate be?
dull inlet
2cos6pit
languid ore
And what's the y coordinate?
dull inlet
2sin6pit
languid ore
Yeah.
languid ore
Ah, I said something was right that I shouldn't have
It is true that if we move at 3 revolutions per second, we move at 6pi radians per second
dull inlet
ya
languid ore
Wait, we were right. They've just completely changed the problem?
If you look, they've written 1 rev/3 sec instead of 3 rev/1 sec
languid ore
Which makes you go 9 times faster, which is why we got a different answer
I'm not sure why they changed the problem, but that's where the difference comes from
woven fossil
hroughout the year, the times of sunrise and sunset change from day to day. The figure shows periodic graphs of the times of sunrise and sunset in De Bilt for a year with 365 days. The figure does not take daylight saving time into account.
The earliest time the sun sets is on December 12 at 16:30. The latest time the sun sets is in the summer at 21:00. Using this data, a model for the time of sunset can be established in the form:
Tsunset=a+bsinâĄ(c(tâd))Tsunset=a+bsin(c(tâd))
Here, TsunsetTsunset is the time of sunset in hours and tt is the time in whole days with t=0t=0 on January 1. For example, on December 12, t=345t=345. This gives Tsunset=16.5Tsunset=16.5, so the sun sets at 16:30.
After rounding cc and dd, the following applies:
Tsunset=18.75+2.25sinâĄ(0.0172(tâ71))Tsunset=18.75+2.25sin(0.0172(tâ71))
3 points: Show how the values of aa, bb, cc, and dd are derived from the data.
devout snowBOT
hroughout the year, the times of sunrise and sunset change from day to day. The ...
woven fossil
i honestly just have no clue where to start
tijdstip stands for timestamp
translated it from dutch to english so i hope nothing gets lost
devout snowBOT
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woven fossil
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true vapor
How to do the second q?
devout snowBOT
How to do the second q?
sly hamlet
How to do the second q?
B?
sly hamlet
Yes I drew the strings wrong tho
have you started? or do you completely not know how to do B
true vapor
have you started? or do you completely not know how to do B
No idea man
devout snowBOT
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sharp bison
The vagabonds were 200 miles apart at 2 p.m and were headed toward each other. If they met at 6 p.m and one was traveling 10 miles per hour faster than the other, what was the speed of each vagabond
devout snowBOT
The vagabonds were 200 miles apart at 2 p.m and were headed toward each other. I...
sly hamlet
The vagabonds were 200 miles apart at 2 p.m and were headed toward each other. I...
wht dont you know how to do
sharp bison
I understand that
or i think
the equation is x+10
bc of the speed
and also it is 4 hours difference
but
my teacher did it this way
and it is confusing me
I am assuming t1 =t2=4 is the hour
and r1-r2+10 is x
x+10?
ebon coyote
T1 and T2 represent how long each vagabond travels
R1 and R2 represent the speeds of each vagabond
sly hamlet
x + (x + 10) = 2x + 10 is their combined speed
sharp bison
2x because x+x right
sly hamlet
from here we get x which is speed of vagabond 2 (the slwoer one)
sharp bison
and then move the 40 to the right
ebon coyote
Which is the third-to-last line on the answer you posted
the 8x + 40 = 200 bit, that is
sharp bison
third to last line is 8r2+40=200
sly hamlet
200=(2x+10)4 -> 200/4=2x+10 -> 50=2x+10 -> 50-10=2x -> 40/2=x
sharp bison
so u moved the 4 to the left
ah u canceled out the 4
and then moved it
right
hm
sly hamlet
it is
sharp bison
how come its not 20/4=2x+10+1?
sly hamlet
(2x+10)4/4
sharp bison
ohh
sharp bison
oh so yeah one is just useless
but if would be (2x+10) 1
ah i see
alright so im gonna explain it and lmk if im correct
200 miles
6 pm and 2 pm which is 4 hours
and x is one
and x + 10 is one
it makes it x+x making it 2x
so 200=(2x+10)
oh wait
and then 4 hours
so 200=(2x+10) times by 4
and to make it easier
you divided 4 by both sides
making it 50=2x+10
and you changed the equation to 50-10=2x
is their a specific way to do it everytime
like switch equation
40/2=x meaning x= 20
okie
The sum of two numbers is 40 and their diffrence is 20. what are the two numbers?
i dont know the equation for this
or how to do it
sharp bison
The sum of two numbers is 40 and their diffrence is 20. what are the two numbers...
^
.close i got it
devout snowBOT
sharp bison
.reopen
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â
sharp bison
Samson had 8.70 in dimes and quarters. If he had a total of 78 dimes and quarters, how many of each type of coin did he have?
ocean gale
Create a system of equations and solve
ocean gale
Itâs just advanced notation thatâs all
N is just a representation of number
And D is for dimes and Q is for quarters
So N sub D is number of dimes
sharp bison
because dime is 10 cents
right
and n sub q is 25 because quarter is 20 cents
vut what is the n sub d plus n sub q = 78 fo
doe
for*
ocean gale
Uhh no
So like N sub Dime/Quarter is just a variable
Just replace the n subs with like x or y
ocean gale
vut what is the n sub d plus n sub q = 78 fo
So this part is just saying that the number of quarter and dimes add up to 78
sharp bison
ohh
is their another way to do it
mroe simple
or no?
it turns into -10 n sub d on the bottom because your bringing it down?
why does it turn into -10 n sub
q
ocean gale
Just do x+y=78
And .10x +.25 y=7.8
X is the number of dimes and y the number of quarters
Then solve
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broken swift
yo guys is the catalanâs constant been proved irrational and trascendental because i may have been able to prove so
devout snowBOT
yo guys is the catalanâs constant been proved irrational and trascendental becau...
broken swift
if not who should i contact to publish my proof?
pseudo basin
your local university's math department
or your professor
assuming you are in uni and/or college
toxic grove
In the nicest possible way, you most likely haven't. You should try to have a "where did I go wrong" attitude for things like this, unless you really know what you're talking about
broken swift
In the nicest possible way, you most likely haven't. You should try to have a "w...
well i got that the catalan constant is the sum of powers of pi
which is the sum of trascendental numbers
is irrational and trascendental
toxic grove
To be clear I know nothing about this constant, I'm just saying that as a general rule
But transcendental numbers can add up to become not transcendental
$\pi$ and $1-\pi$ for example
woven radishBOT
depression
olive snow
is irrational and trascendental
this still can't be used
since its not a general thing
broken swift
olive snow
what about transcendental?
placid rover
literally AI at its peak clowning
broken swift
what about transcendental?
broken swift
literally AI at its peak clowning
ai looked up into sites
olive snow
interesting ai
broken swift
of but irrational i think it has been proven tho
pseudo basin
ai looked up into sites
!nogpt
broken swift
ill look up better when im home
devout snowBOT
ai looked up into sites
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
broken swift
yall made a command just for that lol
olive snow
it looks like a student that hasn't learn the lesson and still answer the question by taking terms that were in the question
upper schooner
Itâs a common enough problem that one needs to exist, sadly 
broken swift
idk i was asking if maybe one of yall knew that it was a general rule proven idk
as i said i look more deeply when im home but thanks anyway
olive snow
sum transcendantal = transcendantal
and sum irrational = irrationnal are both false
broken swift
sum transcendantal = transcendantal
and sum irrational = irrationnal are both f...
you sure bout this? even for pi it have been disproven so?
just asking
olive snow
its not a general proprety, so you can't say it as you said it.
maybe its true for this case, but its not how to prove it or disprove it
upper schooner
sum transcendantal = transcendantal
and sum irrational = irrationnal are both f...
Also ditto for âproductâ in place of âsumâ
ebon coyote
Guys, just checking - is the following true?
Suppose x were transcendental, and there were some polynomial P such that P(x) is algebraic
Then as P(x) is algebraic, there exists some polynomial Q such that Q(P(x)) = 0 (by definition of algebraic)
But Q o P is the composition of two polynomials, and is thus a polynomial. So then x is algebraic #So there is no polynomial for x transcendental for which P(x) is algebraic âŹ
Because if so, that's probably where the AI-answers have gotten their hallucinations from
broken swift
its not a general proprety, so you can't say it as you said it.
maybe its true f...
so thereâs no proof that sums of powers of pi always give an âatleastâ irrational number :/
olive snow
sure rt(2)*rt(2) = 2 which is in Q
olive snow
so thereâs no proof that sums of powers of pi always give an âatleastâ irrationa...
you can try to do it and see what happen
broken swift
sure rt(2)*rt(2) = 2 which is in Q
yea bud but i think any power of pi is irrational
olive snow
i mean thats still an interesting exercice
broken swift
i think
feral agate
Guys, just checking - is the following true?
> Suppose x were transcendental, a...
this reasoning only works for finite polynomials though
ebon coyote
oh fok there's an infinite case as well
feral agate
P(x) can still be algebraic if P is an infinite polynomial
ebon coyote
Q is finite though right (just mesage-react this)
broken swift
don't think, prove it or disprove and be sure :)
alright thnks yall ill look up more bout this when i get home
olive snow
alright thnks yall ill look up more bout this when i get home
should be easy by looking at the definition of transcendantal and supposing pi^n is rationnal for any n
feral agate
Q is finite though right (just mesage-react this)
a polynomial is usually defined to be finite
ebon coyote
ah cool
feral agate
a number is algebraic if it is the root of some (finite) polynomial with integer coefficients
the finite part is implied
broken swift
should be easy by looking at the definition of transcendantal and supposing pi^n...
you meant irrational except 0 right(?)
ebon coyote
"Suppose for a contradiction"
sand dove
pi is trancendental, thus pi^n = P(pi) where P(x) = x^n, is irrational
olive snow
you meant irrational except 0 right(?)
if pi^n is rationnal then it would be the root of ax^n - b = 0
sand dove
there's no need for contradiction proofs when it's direct
broken swift
if pi^n is rationnal then it would be the root of ax^n - b = 0
and it is not because itâs trascendental
sand dove
well almost
olive snow
there's no need for contradiction proofs when it's direct
the thing is that im clueless on this kekw
sand dove
alr nvm
ebon coyote
I'm still gonna call an "If (this), then (that), but (that) means (not this)" argument a contradiction proof tbh
olive snow
and it is not because itâs trascendental
well pi wouldn't be transcendantal if pi^n is rationnal
so yeah
its irrationnal for any n
broken swift
ok
olive snow
now for your story of the sum i clearly have no idea
broken swift
now for your story of the sum i clearly have no idea
ill look up more later thanks anyways
olive snow
yw
devout snowBOT
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broken swift
.close
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wraith pumice
devout snowBOT
polar chasm
2(x-y) * (1 - y')
= 2(x-y) * 1 + 2(x-y) * (-y')
= that
tawny pewter
they distributed 2(x-y) as a whole on 1 and on -yâ
tawny pewter
at the end of the algebraic manipulation you want all the yâ on one side to factorize the yâ in front then yeet whatâs not yâ on the other side so this is a good way to get there imo
pseudo basin
bruh whaaat that's so weird
it is just algebra
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Available help channel!
split pivot
devout snowBOT
split pivot
Did i do smth wrong
wind mason
Ah, no, since the x^2 terms cancel
split pivot
Hold ip
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wraith pumice
hi can someone explain what this wants please
devout snowBOT
hi can someone explain what this wants please
wraith pumice
I'm able to solve for dy/dx but idk what the y(4)=-20 and y'(4) means
wraith pumice
đ€Ż
misty crest
dy/dx |_{x = 4}
misty crest
I'm able to solve for dy/dx but idk what the y(4)=-20 and y'(4) means
it means the point is (4, -20)
let x = 4
y = -20
wraith pumice
okay so just plug in 4 to the result after solving derivative?
misty crest
and y = -20
wraith pumice
dy/dx |_{x = 4}
also what does this | mean I see it everywhere but I forgot
misty crest
evaluated at
wraith pumice
okay cool, I should be able to figure it out. thanks sm
misty crest
youâre welcome
wraith pumice
.close
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snow fjord
hmmmmmm
pseudo basin
one moment
snow fjord
yh that looks right to me but wait for ann to check
willow elk
Appreciate it guys
pseudo basin
ok the first one looks correct if it's to 2dp
that second one looks way off though
P(Z<1.36) is about 0.9131 not 0.4125
what method are you using for these btw?
ah hold on
i misread the question my bad
ok 1.36 is correct (to 2dp) for P(0<Z<z) = 0.4125
warped marsh
Iâve got this extremely simple geometry problem but for some reason the line I get doesnât meet the requirements needed, it doesnât cross through one of the lines. Iâve tried to solve it using planes so I would preferably want someone to help me with it using planes too. Itâs a very basic question so Iâve probably made some stupid mistake somewhere
devout snowBOT
Iâve got this extremely simple geometry problem but for some reason the line I g...
warped marsh
This is the same question in English since the original one is in Spanish
wind mason
Iâve got this extremely simple geometry problem but for some reason the line I g...
You prefer English or Spanish?
warped marsh
Spanish preferably but I donât really mind
wind mason
This is the same question in English since the original one is in Spanish
Hmm, the intersection would be at z=0.
wind mason
Spanish preferably but I donât really mind
Okay.
What have you tried?
Do you have work?
El recto r es ||y=1-x||.
warped marsh
Iâve found the intersection of the plane which contains r and PrP, (being PrP a line connecting r and the point) and the other plane which contains S and PrS. The intersection of both planes should be the line Iâm looking for but while checking I found that it didnât cross through S.
warped marsh
Do you have work?
Yeah let me take a picture
wind mason
Iâve found the intersection of the plane which contains r and PrP, (being PrP a ...
Raro...
Pienso que utilizar las formas parĂĄmetros por el recto s es bueno.
Porqué $-\infty< \lambda <\infty$ (loosely) entonces podemos hacer s en una forma parametrico.
woven radishBOT
;(
devout snowBOT
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warped marsh
warped marsh
Pienso que utilizar las formas parĂĄmetros por el recto s es bueno.
Si, habĂa pensado hacer eso, pero como querĂa usar planos solo me hacĂa falta el vector director y un punto los he dejado asĂ separados
devout snowBOT
@warped marsh Has your question been resolved?
wind mason
Si, habĂa pensado hacer eso, pero como querĂa usar planos solo me hacĂa falta el...
Lo siento, estoy estudiando ahora.
En una hora puedo ayudar.
devout snowBOT
@warped marsh Has your question been resolved?
quaint rampart
I spent like an hour looking for X and y but I couldnât find it help pls
quaint rampart
Idk what the name of the thingy is in English but itâs translated to triangle similarity or smth
I tried all the combinations I could think of but it didnât hit the right answer
strange nimbus
For question part a or b?
quaint rampart
Both lol
strange nimbus
OK, let's look at a.
quaint rampart
Ok
strange nimbus
What kind of triangle is the upper triangle?
quaint rampart
Isosceles
strange nimbus
OK, what does that mean about the left-side angles?
strange nimbus
The left-side angles of the upper triangle.
quaint rampart
Ik itâs one big triangle
strange nimbus
You were right that the angles are equal.
quaint rampart
Oh I meant the sides but
strange nimbus
Oh.
quaint rampart
Which angles are u talking about
quaint rampart
OK, what does that mean about the left-side angles?
Oh u mean the bottom angles for the isosceles triangle?
strange nimbus
These:
strange nimbus
OK, so what is an expression for each angle?
strange nimbus
Like alpha is an expression for the upper angle.
alpha + 5 degrees would be an example.
quaint rampart
OK, so what is an expression for each angle?
Oh the same
strange nimbus
Yes, but give an expression with alpha in it for the angles.
quaint rampart
Like b+b+alpha=180?
quaint rampart
b+b=180-alpha
strange nimbus
OK, so what's b?
quaint rampart
Idk how much alpha is though
strange nimbus
Leave alpha as a variable.
quaint rampart
b*2 = 180-alpha idk
strange nimbus
OK, solve for b.
quaint rampart
Sorry idk what Iâm supposed to do there
quaint rampart
At bottom ones?
twin kayak
wdym
quaint rampart
Oh the top
twin kayak
yes
strange nimbus
quaint rampart
Mhm
strange nimbus
Yeah, the 9 long straight line has angles in the middle that add to 180 degrees.
twin kayak
ye
quaint rampart
Yeah, the 9 long straight line has angles in the middle that add to 180 degrees.
Mhm
strange nimbus
So, what's an expression for the unfilled in angle?
strange nimbus
OK, good.
quaint rampart
I mean the way my teacher explained it to me itâs just triangle similarity stuff
Like
y/4=5/5 or smth idk
Then u multiply it crossing
And u get Y
Well idk it was an example idk if that gets u y
strange nimbus
Well, these aren't similar triangles. Similar triangles have their three angles the same.
twin kayak
yes
strange nimbus
What two angles in each triangle?
quaint rampart
Uh yeah I think
strange nimbus
Sorry, I mean which two angles in the lower are equal to which two angles in the upper?
quaint rampart
Like isnât the alpha at the top also looking at X in the big triangle
quaint rampart
Sorry, I mean which two angles in the lower are equal to which two angles in the...
Uh
strange nimbus
To have angle-angle similarity, two angles in one triangle have to be equal to two angles in the other.
quaint rampart
This is my books explanation
quaint rampart
To have angle-angle similarity, two angles in one triangle have to be equal to t...
Yeah
strange nimbus
We don't have that yet.
quaint rampart
Oh
quaint rampart
What about the bottom one
strange nimbus
OK, so what's an expression for the bottom left angle?
twin kayak
the bottom one should also be filled
u use 180
the angles u got before
fill out the system
quaint rampart
strange nimbus
Both what?
twin kayak
its for the small and big triangle
quaint rampart
its for the small and big triangle
Ya
twin kayak
that s what you ll use
quaint rampart
Donât they share 2 angles now?
strange nimbus
Oh, I see what you mean.
Yes, the bottom triangle and the combined triangle have angle-angle similarity.
quaint rampart
Yeah
quaint rampart
strange nimbus
The side between 90 + 1/2 alpha and alpha in the lower triangle is y. The side between 90 + 1/2 alpha and alpha in the combined triangle is 5.
quaint rampart
So, which sides correspond?
U look at the angle then see the side itâs facing
quaint rampart
The side between 90 + 1/2 alpha and alpha in the lower triangle is y. The side b...
I donât get it
quaint rampart
But look the last angles are filled now too
I just donât know how to make proportions with them
strange nimbus
I donât get it
Sorry. I'm trying to draw it, but I can't get GIMP to allow me to draw a line.
Ahh, got it.
quaint rampart
All good take your time
strange nimbus
Those sides correspond to each other.
They're between the alpha and 90 + 1/2 alpha angles in both triangles.
twin kayak
still he didnt figure it out?
quaint rampart
đ
strange nimbus
Then, we have between the alpha angle and the unlabelled angle.
twin kayak
he gave u the answer
strange nimbus
Basically, once you get that they're similar triangles, the sides that correspond are between one angle and another angle.
The same in both similar triangles.
Like here, we have three matching angles in each triangle.
quaint rampart
So what do you do next
strange nimbus
We have the alpha angle in both.
We have the 90 + 1/2 alpha angle in both.
We have the unlabelled angle in both.
So, we look at the sides between pairs of angles.
One pair of angles are alpha and 90 + 1/2 alpha.
quaint rampart
Mhm
strange nimbus
The sides between those angles is colored green.
One pair of angles are alpha and the unlabelled angle.
The sides between those angles is colored blue.
The last pair of angles are 90 + 1/2 alpha and the unlabelled angle.
That's in red.
quaint rampart
This is lowkey confusing
strange nimbus
Wait.
quaint rampart
How are you gonna figure out what X and Y are though
strange nimbus
OK, so now we write those paired up sides as ratios.
Like lower triangle : combined triangle.
quaint rampart
Ok yeah
strange nimbus
So, with green, it's y : 5.
y for the small triangle.
5 for the large triangle.
With blue, it's x : 9.
What is it for red?
strange nimbus
Well, the 4 can't be a side of the large triangle.
quaint rampart
Oh yeah itâs large to small
strange nimbus
No, it's small to large.
quaint rampart
X : 9?
strange nimbus
Yes, with blue, x is the small triangle side, 9 is the large triangle side.
quaint rampart
Mk
strange nimbus
y isn't a red line.
quaint rampart
Ik but
This is so confusing man idk maybe we should call quits im not learning much, its not your fault i just donât know this stuff yet
strange nimbus
You can try someone else here. There are other ways of teaching this.
quaint rampart
Eh I guess Iâll ask my classmate tmr maybe heâll know smth
strange nimbus
OK.
strange nimbus
No problem. Sorry I couldn't help.
quaint rampart
No dude you did great I just donât know or have ever seen that stuff you were doing
strange nimbus
The basic idea is just that similar triangles are the same shape. One triangle might just be a zoomed in version of the other.
So, you can find out how much the larger one is zoomed in.
Like maybe the sides are twice as big as the other one.
strange nimbus
The idea behind that is the triangles might be flipped over or rotated or whatever.
Since they're the same shape, just maybe zoomed in for one of them, you have to take a side of the small triangle and figure out which side of the large triangle it matches up with.
quaint rampart
Yeah
strange nimbus
Like maybe you have a 3-4-5 triangle and a 6-8-10 triangle.
The 3 and 6 match up. The 4 and 8 match up. The 5 and 10 match up.
quaint rampart
Yeah exactly
strange nimbus
That's what I was doing with the colored lines.
Those are the sides that match up.
strange nimbus
Oh, the blue one says the small triangle side is x. The large triangle side is 9.
Those match up.
quaint rampart
What about the green though how is an alpha looking at one but the other isnât
strange nimbus
The green lines mean y is the small triangle match for 5 on the large triangle.
quaint rampart
How though if alpha isnât looking at it
Thr bottom alpha needs to also be green though doesnât it
strange nimbus
Green is between alpha and 90 + 1/2 alpha.
quaint rampart
But both alphas mean the sides are proportional too no?,
strange nimbus
In the small triangle, that's the y green side. In the large triangle, that's the 5 green side.
Not exactly.
Similar triangles have sides that match up, like we said before.
quaint rampart
And u can see them by the angles right?
strange nimbus
If you have a side matching up with a side, the angles on the ends of those sides are the same.
quaint rampart
Yeah
strange nimbus
So, the green sides have alpha at one end and 90 + 1/2 alpha at the other end.
So, they match up.
quaint rampart
Alpha and 90+ 1/2 alpha is the same?
strange nimbus
No, each side has two angles. One at one end, one at the other.
If two sides match up, the angles will be the same.
Alpha and 90 + 1/2 alpha aren't the same angle.
They're the angles at the end of the green sides.
strange nimbus
Yes, red has unlabelled angle and 90 + 1/2 alpha on the ends of the sides.
What about blue? What are the angles at the end of both blue sides?
quaint rampart
I have no clue
quaint rampart
Alpha and 90 + 1/2 alpha
quaint rampart
I need to see what angle is looking at blue?
strange nimbus
Well, look at the upper blue side.
Look at the right end of it.
What's the angle there?
quaint rampart
Alpha?
quaint rampart
In labeled
strange nimbus
OK.
quaint rampart
Unlabeled
strange nimbus
Look at the lower blue side.
quaint rampart
Alpha
strange nimbus
What's the angle on the right end of it?
Right.
What's the angle on the left end of it?
quaint rampart
90+1/2 alpha
I just donât get how itâs matching them up but I gtg sleep now sorry
quaint rampart
Ty you too
strange nimbus
No problem.
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primal jolt
devout snowBOT
primal jolt
Using the following criteria (Quotient criteria) solve the following sequences:
wind mason
That doesnât work like that.
primal jolt
i see
wind mason
(n+1)!/n!=(n+1).
primal jolt
so i can't say that when n -> +inf (n+1)! is similar to n! ?
wind mason
No.
primal jolt
why not?
ohh
because it grows much faster than n!, right?
okay well
maybe not much faster
wind mason
Yes.
primal jolt
but i can see why they'd be different
primal jolt
(n+1)!/n!=(n+1).
so where do you get this from?
wind mason
Fast enough to the point where youâd be multiplying by really large numbers.
wind mason
so where do you get this from?
The definition of the factorial.
Notice that n!(n+1)=(n+1)!.
I gotta go.
wind mason
Youâre welcome.
primal jolt
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timber pebble
working on solving the difference equation
devout snowBOT
working on solving the difference equation
timber pebble
**jan Niku**
we can divide here each term by $\frac{1}{\prod _{i=1}^{n-1} p(i) }$
woven radishBOT
jan Niku
devout snowBOT
sand dove
we can divide here each term by $\frac{1}{\prod _{i=1}^{n-1} p(i) }$
that was a good idea
I think you can just look at $b_n = \frac{a_n}{\prod _{i=1}^{n-1} p(i)}$
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Available help channel!
sand dove
or is it multiplied
devout snowBOT
or is it multiplied
sand dove
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devout snowBOT
woven radishBOT
rafilou is not not born in 2003
sand dove
I'm indecisive
timber pebble
.repoen
sand dove
.reopen
devout snowBOT
â
timber pebble
@sand dove
so i can share my doubt
we can start from the given and get to easily here
sand dove
you know what
timber pebble
$\frac{ a_{n+1} }{ \prod ^n _1 p (i) } = \frac{ a_n }{ \prod ^{n-1} _1 p(i) } + \frac{ q(n) }{ \prod _1 ^n p(i) }$
woven radishBOT
jan Niku
timber pebble
but now we have a domain issue
is it clear if i call what is A_n and Q_n here
we cant immediately call $A_n = A_1 + \sum ^{n-1} _1 Q(i)$
woven radishBOT
jan Niku
timber pebble
because A_1 isnt clearly defined
timber pebble
how so
timber pebble
sand dove
timber pebble
its not empty though
sand dove
it is though, you are multiplying 0 terms together
timber pebble
i mean $\sum _{i=1} ^{-4} i = 0$???
woven radishBOT
jan Niku
sand dove
no, that's not well defined
timber pebble
right
sand dove
$\sum _{i=1} ^{0} i = 0$
woven radishBOT
rafilou is not not born in 2003
timber pebble
thats not well defined either 
sand dove
it is though
sand dove
also I'm pretty sure there's an easier way to do it
not having to worry about some A_n or Q_n being undefined
(due to one p_n being 0)
timber pebble
it is?
sand dove
by just starting with $a_{n+1} = p_na_n$
timber pebble
how do you know
woven radishBOT
rafilou is not not born in 2003
timber pebble
**rafilou is not not born in 2003**
ive actually done this problem too
sand dove
idk im sure we can
then we don't have any results for when p_n = 0 sometimes
timber pebble
this chapter is just throwing easy warm ups
i think
havent gotten to problems yet
sand dove
anyways once you have the formula for "p_n != 0"
you can prove the general formula by induction
sand dove
?
timber pebble
we end up with $a_n = \qty( \prod _1 ^{n-1} p(i) ) \qty[ \dots ]$
woven radishBOT
jan Niku
timber pebble
im joking
sand dove
xd
timber pebble
okay so
do we end up with
$a_n = a_1 \prod _{i=1}^{n-1} p(i) + \frac{ \prod _{i=1}^{n-1} p(i) }{ \prod _{j=1}^n p(j) }\cdot \sum _{i=1}^{n-1} q(i)$
woven radishBOT
jan Niku
timber pebble
this simplifies things
sand dove
uhhh
timber pebble
it doesnt seem right though
sand dove
you did a missimplification
timber pebble
im so confused 
when we sum over all $\frac{q (n) }{ \prod _1 ^n p(i) }$ dont we get a product that has no dependence on summation var
woven radishBOT
jan Niku
sand dove
$a_n = a_1 \prod_{i=1}^{n-1} p(i) + \prod_{i=1}^{n-1} p(i)\cdot \sum {i=1}^{n-1} \frac{q(i)}{\prod{j=1}^{i-1}p(j)}$
timber pebble
yea
woven radishBOT
rafilou is not not born in 2003
sand dove
$a_n = a_1 \prod_{i=1}^{n-1} p(i) + \sum {i=1}^{n-1}\left(q(i)\prod{j=i}^{n-1}p(j)\right)$
woven radishBOT
rafilou is not not born in 2003
sand dove
and yippie
sand dove
mmh wait
timber pebble
dont we get
we get a moving lower index on the summed prod
with a solid upper limit
as each prod in the deno eats more and more terms
sand dove
there's a little bit wrong inside the product
timber pebble
sand dove
so the product in the sum should be empty
timber pebble
yea see
moving from the general form to the specific is kinda hard
i mean the A_n+1 = A_n + Q_n
sand dove
this trips me up a bit
woven radishBOT
jan Niku
timber pebble
i almost think you could start here
sand dove
and has recurrence x_n = p_n x_(n-1) + q_n
timber pebble
why not just start here and then start subbing
or you could even just start doing other stuff
sand dove
why not just start here and then start subbing
this would give you an idea of the formula
timber pebble
exponentiate or log
something something
yea
ill have to try it out tomorrow
thank you 
.close
hardy void
hi, im trying to help my girlfriend with this but i have absolutely no idea what any of this even means or how to sketch this, can anyone help me?
devout snowBOT
hi, im trying to help my girlfriend with this but i have absolutely no idea what...
autumn girder
woven radishBOT
HitenTandon
hardy void
is this correct?
devout snowBOT
@hardy void Has your question been resolved?
jade scroll
Yes
hardy void
it said it was incorrect
supple knot
it said it was incorrect
what did you input
devout snowBOT
@hardy void Has your question been resolved?
toxic pike
"suppose you hit a baseball 4 feet above the ground with an initial velocity of 55ft/s at an angle of 42deg with the horizontal. find its maximum height and time at which it occurs"
devout snowBOT
"suppose you hit a baseball 4 feet above the ground with an initial velocity of ...
toxic pike
so this is a parametric, and x=55cos(42)t
faint zinc
Parenthesis?
faint zinc
16 being half the acceleration due to gravity right?
toxic pike
a=-16, b=~ 36.8, c=4
faint zinc
I'll take your word on b, I haven't put it through a calculator myself
So, do you remember where to find the vertex of a parabola in terms of a and b?
toxic pike
yea, the x coordinate is -b/2a
faint zinc
In this case our "x coordinate" is actually t.
So -b/2a will give us the time of the maximum height
toxic pike
why tho?
faint zinc
Why what?
toxic pike
why is the x coordinate time
faint zinc
Because our variables in that equation are y and t
toxic pike
i mean like i understand that time is the variable
faint zinc
Rather than y and x
toxic pike
why is it that we can find the vertex of just the parabola formed by y rather than the parabola thats formed with the whole parametric equation
faint zinc
Well, ok so
If we remove time, by solving for x in terms of t, and substituting, then we can solve our equation in y and x for the vertex in terms of x
toxic pike
alr
faint zinc
The idea is this technique works no matter what the two variables represent
As long as their relationship is quadratic, we can get the vertex using this
toxic pike
alr so then if we apply -b/2a, its -1.15, but that doesnt make sense?
bc it looks like this
toxic pike
yea it should be t=1.15
faint zinc
1.15s is a perfectly fine amount of time for a baseball to find itself at the top of its trajectory
faint zinc
Yw
toxic pike
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devout snowBOT
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Available help channel!
brazen hare
hi! i'm having trouble with part a of this question. we were just introduced to the use of integrals in rectilinear motion problems, and i dont even know how to approach it. first steps would be super helpful! thanks <3
devout snowBOT
hi! i'm having trouble with part a of this question. we were just introduced to ...
stable flare
@brazen hare I would recommend using this equation:
v^2 = (v_0)^2 + 2a(x - x_0)
V and X are your final velocity and position while V_0 and X_0 are your initial Velocity and Position respectively.
Using algebra, we can manipulate the equation so we can go straight to finding Acceleration.
Hereâs how the equation can be changed:
v^2 = (v_0)^2 + 2a(x - x_0)
v^2 - (v_0)^2 = 2 x a x (x - x_0)
A = (v^2 - (v_0)^2)/2(x - x_0)
brazen hare
<@471787199290015746> I would recommend using this equation:
v^2 = (v_0)^2 + 2a...
sorry just to clarify here, a = A = acceleration?
or different as
stable flare
Yeah, sorry! Iâm on mobile so automatic capitalization for Line breaks
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Available help channel!
snow fjord
devout snowBOT
snow fjord
i've tried to make a substitution and transform it into some version of the gamma function
cos it feels vaguely gamma-esque
however I can't figure out how still
help :)
devout snowBOT
@snow fjord Has your question been resolved?
pulsar sand
Without putting a lot of thought into it, this seems like a candidate for a Monte Carlo based approach to replace the ln(x1...xn)/n with something nicer
snow fjord
how though
misty crest
did you just ask this on stack exchange
snow fjord
yup
gotta ask on both places
yeah fine with monte carlo and strong law of large numbers, you can get the limit is 1/2 but i'm unsure
devout snowBOT
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devout snowBOT
kind tiger
.reopen
devout snowBOT
â
kind tiger
where'd this come from
devout snowBOT
@snow fjord Has your question been resolved?
magic gust
Hello, I have an error in my python program
devout snowBOT
Hello, I have an error in my python program
magic gust
but I don't understand why the list "L" has no len according to python
open oasis
A is not properly defined.
open oasis
try printing A before checking your length. This will give you an idea of what's wrong with it
magic gust
I can print it
open oasis
Try this:
def Det(A):
print(A)
try:
(put your code here)
except Exception as e:
print(e)
This will print A and still spit out the error
tight canyon
Hello, I have an error in my python program
what does scalaire return value?
magic gust
Try this:
```
def Det(A):
print(A)
try:
(put your code here)
except Ex...
ok thanks
magic gust
what does scalaire return value?
scalaire returns the matrix ” Delta(k,1,A)
open oasis
Hmmmm....
remote sun
huh isn't A=L from the function call, it seems right to me...
open oasis
Yeah, I copied it and I'm not getting any errors....
remote sun
Hello, I have an error in my python program
btw the code will work just fine even without the condition for len(a)==2
other than the error ur currently getting that is
tight canyon
can you send scalaire code
magic gust
btw the code will work just fine even without the condition for len(a)==2
it doesn't work without this
anytime i keep " len(A)" in the code there is an error wtf
magic gust
can you send scalaire code
def scalaire(A,”):
if carrée(A):
for i in range(len(A)):
for j in range(len(A)):
A[i][j] = ”*A[i][j]
return A
def carrée(M):
Trouve = False
if len(M) == len(M[0]):
Trouve = True
return Trouve
remote sun
anytime i keep " len(A)" in the code there is an error wtf
no i meant like... well nvm lets fix this first
tight canyon
def scalaire(A,”):
if carrée(A):
for i in range(len(A)):
...
what if caree(A) is False?
remote sun
def scalaire(A,”):
if carrée(A):
for i in range(len(A)):
...
ok so scalaire basically scales the matrix by a constant
olive snow
Un produit par un scalaire ne marche pas que sur des matrices carrées
remote sun
what if caree(A) is False?
but its true in this case, isnt it?
magic gust
yeah it is true
magic gust
ok so scalaire basically scales the matrix by a constant
yes
tight canyon
yeah it is true
what does delta do?
magic gust
def Î(j0,i0,A):
#assert carrée(A)
a = len(A)
B = [[A[i][j] for i in range(a)]for j in range(a)]
for i in range(a):
if i == i0-1:
B.pop(i)
for j in range(a-1):
for k in range(a-1):
if j == j0-1:
B[k].pop(j)
return transposee(B)
def transposee(A):
M = [[0 for i in range(len(A))]for j in range(len(A))]
if len(A) == len(A[0]):
for i in range(len(A)):
for k in range(len(A[i])):
M[i][k] = A[k][i]
return M
else :
return "Error"
restive river
what object type is A
remote sun
what object type is A
Its clearly a nested list from the function call isnt it
restive river
not necessarily
a list would have a defined length function
he can either make a 2D list type of thing for matrix math or create a custom class but then a length method would need to be defined
olive snow
def carrée(M):
if not M or not M[0]:
return false
return len(M) == len(M[0])
What about smth like this for carrée ?
Here it avoid calling len on type none
tight canyon
def Î(j0,i0,A):
#assert carrée(A)
a = len(A)
B = [[A[i][j] for i in ...
B.pop(i) ? maybe this is changing the length
remote sun
Hello, I have an error in my python program
Can you send your det code as well let me try running it
magic gust
def transposee(A):
M = [[0 for i in range(len(A))]for j in range(len(A))]
if len(A) == len(A[0]):
for i in range(len(A)):
for k in range(len(A[i])):
M[i][k] = A[k][i]
return M
else :
return "Error"
def Î(j0,i0,A):
assert carrée(A)
a = len(A)
B = [[A[i][j] for i in range(a)]for j in range(a)]
for i in range(a):
if i == i0-1:
B.pop(i)
for j in range(a-1):
for k in range(a-1):
if j == j0-1:
B[k].pop(j)
return transposee(B)
def Det(A):
if len(A) == 1:
return A[0][0]
if len(A) == 2:
return A[0][0]*A[1][1]-A[0][1]A[1][0]
else :
s = 0
for k in range(len(A)):
” = A[k][0](-1)**k
u = scalaire(Î(k,1,A),”)
s = s + Det(u)
return s
that's it
magic gust
B.pop(i) ? maybe this is changing the length
I will try !
tight canyon
B.pop(i) is changing the length and caree(A) is returning False?
magic gust
No, carree(A) is true
