i have the eccentricity and a,b from one subsection (https://en.wikipedia.org/wiki/Ellipse#Parameters) so i'm not sure what i'm doing wrong
#help-10
foggy vortex
dense imp
i have the eccentricity and a,b from one subsection (<https://en.wikipedia.org/w...
what exactly is the z you are defining supposed to be?
eccentricity?
dense imp
ah
foggy vortex
oh im a moron
dense imp
seems you missed squaring the eccentricity?
dense imp
was just getting around to it but glad you figured it out :p
foggy vortex
thank you 😄
dense imp
cheers
obtuse pebbleBOT
Available help channel!
grand obsidian
is iv true?
obtuse pebbleBOT
is iv true?
grand obsidian
is it by default a proper subset will has empty set
royal basin
is it by default a proper subset will has empty set
(iv) is true but up words mixed some here got
safe haven
is it by default a proper subset will has empty set
the subset of every set will have an empty set, no matter proper or not
royal basin
the subset of every set will have an empty set,
wording
the empty set is a subset of anything.
safe haven
english hard sorry
grand obsidian
the subset of every set will have an empty set, no matter proper or not
thanks that explain a lot
obtuse pebbleBOT
Available help channel!
ripe mortar
hello
brazen gorge
,rccw
warm shaleBOT
brazen gorge
1/2^6 (20c6) x²y^-2 ? insted of x²y²
why -2?
ripe mortar
yeah i see i see
brazen gorge
that does look wrong
ripe mortar
yup
obtuse pebbleBOT
@ripe mortar Has your question been resolved?
grizzled tinsel
help pls
grizzled tinsel
<@&286206848099549185>
wise turret
what abomination is that
grizzled tinsel
confusing?
wise turret
know remainder theorem?
grizzled tinsel
yah
wise turret
where did you find this horror?
grizzled tinsel
yearly revision 😐
wise turret
what textbook
grizzled tinsel
my friend sent the question to mea sking for help
wise turret
so we can't find the answers online right
wise turret
uh ping me if you discover how to do it
grizzled tinsel
ok
😭
@wise turret found it out 😎
basically i just followed that one guy on quora
went like this
well i found it
so
.close
chilly rock
Consider: f(x)=ln(x), for x in (0,1]
Let 0 < a < 1.
Show that the curve length of the graph f(x) for x in [a, 1] is bigger than ln(a).
I tried using L = Integral a -> 1: sqrt(1 + f'(x)^2), but got stuck.
Can someone please help?
obtuse pebbleBOT
Consider: `f(x)=ln(x), for x in (0,1]`
Let `0 < a < 1`.
Show that the curve leng...
obtuse pebbleBOT
@chilly rock Has your question been resolved?
chilly rock
<@&286206848099549185> Any help?
patent pagoda
Consider: `f(x)=ln(x), for x in (0,1]`
Let `0 < a < 1`.
Show that the curve leng...
probably need some sort of trig substitution. where did you get stuck?
chilly rock
I don't even know if finding the integral is the correct way of showing it...
I am getting integral: (1/cos*sin^2)
by trig subst
timid silo
obtuse pebbleBOT
timid silo
mind helping me with this work?
I am stuck on this for half a hour
I just need answer as this is my friends work
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
twilit thicket
alright
gleaming ridge
obtuse pebbleBOT
gleaming ridge
help
dapper thicket
,rotate ccw
warm shaleBOT
dapper thicket
So how many Q does Robin have?
gleaming ridge
yeah
dapper thicket
I’m asking
gleaming ridge
it’s confuzzling me
wanton hull
lol
he found 3Q one day and 4Q next
you have 3 candies and i give you 4 more
how many do you have now
dapper thicket
She found 3Q one day, then 4Q another right. So that’s 7Q. Whatever value Q is. She found 7 x that amount.
Then she gave 5 away
So that’s…?
wanton hull
,rotate
warm shaleBOT
dapper thicket
I believe when they say she gave 5 away it doesn’t mean she gave 5Q away. It just means 5
wanton hull
yes
gleaming ridge
💯
wanton hull
so now its equal to 6Q + 7
dapper thicket
Robin has 7Q -5. How about Roger?
wanton hull
so forming an equation we get $6Q+7 = 7Q -5$
warm shaleBOT
Bettim
dapper thicket
You’re not supposed to flat out give the solution tho
wanton hull
i dont think thats a solution
gleaming ridge
might not be getting a A+ on this one, not sure 🤔
dapper thicket
Can’t you solve for Q with the equation above?
gleaming ridge
yeah lemme see
dapper thicket
You move the Qs to one side and the not Qs to the other
dapper thicket
How did you get that?
gleaming ridge
was that wrong
dapper thicket
Yeah
gleaming ridge
SHOOT
dapper thicket
Can you show the steps?
gleaming ridge
oh golly
dapper thicket
It’s not far off. It might have just been a miscalculation
gleaming ridge
**Bettim**
i subtracted 6Q by seven which gave me one, and then i added 5 onto 7 which gave me 13
oh that’s 12
i’m brain dead
mb
gleaming ridge
thanks for the help
dapper thicket
Np
obtuse pebbleBOT
@gleaming ridge Has your question been resolved?
jagged prawn
Did I mess this up? If so, what did I do wrong
obtuse pebbleBOT
Did I mess this up? If so, what did I do wrong
tranquil arch
twilit flame
im im of class 7 from india can i ask
obtuse pebbleBOT
@jagged prawn Has your question been resolved?
lost widget
Let ABC a non-isoscelis triangle with orthocenter H and the feet of altitudes A1, B1, C1. Let A2, B2, C2 be the projections of H on B1C1, C1A1, A1B1. a) Show that the circumscribed circles of HA1A2, HB1B2, HC1C2 have 2 points in common. b) Show that the circumscribed circles of HAA2, HBB2, HCC2 have 2 points in common.
obtuse pebbleBOT
Let ABC a non-isoscelis triangle with orthocenter H and the feet of altitudes A1...
lost widget
The solution is using inversion
At a) inversion about the incircle of A1B1C1
Can someone explain the solution clear?
<@&286206848099549185>
tardy epoch
<@&286206848099549185>
!15m
obtuse pebbleBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@lost widget Has your question been resolved?
lost widget
<@&286206848099549185>
obtuse pebbleBOT
@lost widget Has your question been resolved?
obtuse pebbleBOT
@lost widget Has your question been resolved?
lost widget
<@&286206848099549185>
obtuse pebbleBOT
@lost widget Has your question been resolved?
obtuse pebbleBOT
@lost widget Has your question been resolved?
random bloom
Does it seem reasonable to go from basic math to about pre-calc level before may next year? If so what kinda study pace would be needed. This is my current math skills, green i know, yellow is iffy and red i dont know.
obtuse pebbleBOT
Does it seem reasonable to go from basic math to about pre-calc level before may...
daring sorrel
If you have time it is definitely possible
As in you can spend a couple hours a day
versed pier
Does it seem reasonable to go from basic math to about pre-calc level before may...
You can definitely do it, but make sure you are following a good book
random bloom
You can definitely do it, but make sure you are following a good book
Do you have any recommendations?
I'm not sure what books are really considered good
versed pier
Do you have any recommendations?
random bloom
Would you happen to know some lower level books? This book is def beyond me atm
daring sorrel
Would you happen to know some lower level books? This book is def beyond me atm
I havent used it but ive heard good things about khan academy. You should try that
toxic sierra
obtuse pebbleBOT
tight dome
is anyone here good at abstract algebra
lyric crane
is anyone here good at abstract algebra
!help
obtuse pebbleBOT
is anyone here good at abstract algebra
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
lyric crane
open a new help channel
lyric crane
up to at least the fifth line seems fine
tight dome
how do i do that
lyric crane
how do i do that
#help-5 is unoccupied
toxic sierra
up to at least the fifth line seems fine
Does square rooting everything not work
lyric crane
wait a mnute
freshman's dream
ofc
ok so
a^2+b^2=/=(a+b)^2
so sqrt(a^2+b^2) =/=a+b
the error is between lines 5 and 6
lyric crane
Is that da lie xiong da
its japanese
toxic sierra
Oh
lyric crane
but good try lol
lyric crane
same characters so i dont blame you
lyric crane
np
toxic sierra
.close
plush jasper
obtuse pebbleBOT
plush jasper
Hi! I need help to solve this definite integral, I don't understand how to do it.
fierce lagoon
Let u = x-1
You essentially wanna turn the cube root into a factor of something
@plush jasper
timid silo
then you solve for x to substitute it into the integral
so x = u+1
lmk what you got
obtuse pebbleBOT
@plush jasper Has your question been resolved?
timid silo
That’s not correct
obtuse pebbleBOT
That’s not correct
rich plume
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fresh copper
how?
alpine bison
you only know f's behaviour in x=-1
is does actually f(-1)=2
so you need to exploit that information
alpine bison
now you need to find a b such that you will compute f(-1) (because you already know it!)
fresh copper
now you need to find a b such that you will compute f(-1) (because you already k...
what do you mean compute
also b isnt even a part of f
its a part of g
g is the transformation of f
alpine bison
what do you mean compute
calculate=compute
or evaluate
so a(-1) -b = -8 is the first constrait on a,b
fresh copper
what next
alpine bison
the second one is $\frac{1}{a}(-9)+b=2$
warm shaleBOT
everg
alpine bison
so they are just two linear eqaution in two variables
fresh copper
why do you put
the coordinates of f = g on the first constraint
but the coordinate of g -> f on the second one
shouldit it be a(-8) - b = -1 then?
alpine bison
maybe this is a deep question ... in advanced math i would call it "pull back"...so i cannot answer to it ...btw you want that $f(\frac{1}{a}(-9)+b)$ will beequal to $f(2)$ because you know the latter
warm shaleBOT
everg
alpine bison
no...you have you said is correct a(-1) -b = -8
because f(2)=-1 (not -8)
and you want that g(...)=af(...)-b=-8 (not -1)
alpine bison
because you are do two different things ... on the one hand you want at the end to evaluate f(2), on the other hand you want that g(...)=-8
so is makes sense that you are doing the opposite
fresh copper
ok so let me get this more clear
cuz im a bit confused sorry
so we have
i will write it and send it
alpine bison
now i must go ... if you want you can write in chat
warm shaleBOT
fresh copper
<@&286206848099549185>
can someone just explain why it would be from -9 to 2 not from 2 to -9?
ignore my mistake on f(-1) = 2, i meant to write f(2) = -1
obtuse pebbleBOT
@fresh copper Has your question been resolved?
unique gulch
how would you solve (d)(ii)?
obtuse pebbleBOT
how would you solve (d)(ii)?
timid silo
how would you solve (d)(ii)?
Well, think of it this way: The probability of only one of those two happening is the combined probability of an individual event happening and the other not. I.e., in this example, the probability that she stops at the traffic lights but doesn't stop at the railway crossing, combined with the inverse of that (stops at crossing; not at traffic lights). In other words: $P(\mathrm{only\ one\ of\ A\ and\ B}) = P(\mathrm{A\ but\ not\ B}) + P(\mathrm{B\ but\ not\ A})$, if that makes sense
warm shaleBOT
kitty boy!
obtuse pebbleBOT
@unique gulch Has your question been resolved?
unique gulch
.close
obtuse pebbleBOT
unique gulch
.reopen
obtuse pebbleBOT
✅
unique gulch
Well, think of it this way: The probability of only one of those two happening i...
so the answer that I got was 33/80 and in decimal 0.4125, is that right?
timid silo
so the answer that I got was 33/80 and in decimal 0.4125, is that right?
Yep, that's what I got too!
autumn spade
do i need to do this the long way or is there some sort of trick to it cus this feels way too lengthy
obtuse pebbleBOT
do i need to do this the long way or is there some sort of trick to it cus this ...
pseudo swift
well you can just plug in the supposed eigenvectors, and check if they're indeed eigenvectors or no
instead of computing the eigen decomp from scratch
@autumn spade
obtuse pebbleBOT
@autumn spade Has your question been resolved?
autumn spade
well you can just plug in the supposed eigenvectors, and check if they're indeed...
idk how to do that
autumn spade
you do also know that the eigenvalues of your matrix are real, though.
how does that play a role?
pseudo swift
idk how to do that
you know, just multiply the vectors by your matrix
autumn spade
... so you don't know the defn of an eigenvector?
im a bit weak on that topic 😅
royal basin
we did this 2 weeks ago.
this is a basic definition. it should be in your notes, front and center.
autumn spade
we did this 2 weeks ago.
thats a different thing tho isnt it?
royal basin
it was for a different problem, but the concept of an eigenvector doesn't stop applying just because of that.
i just posted a screenshot in which you, with some prompting, were able to recall the definition of an eigenvector.
royal basin
you want to check which answer option lists eigenvectors of A.
do you understand this, yes or no
autumn spade
yes
royal basin
right.
do you know how to check whether or not a vector is an eigenvector of A?
yes or no
autumn spade
no
royal basin
you know the definition of an eigenvector
to show that something is an eigenvector (or establish that it isn't), you check it against the definition of an eigenvector.
x is an eigenvector of A <=> exists λ scalar s.t. Ax = λx
does that not make it obvious how you would want to proceed?
i feel as if it is on the surface
royal basin
lambda
but yes
is it not obvious that you would want to multiply A by all these vectors in each answer option?
autumn spade
supposed i get matrix B after i multiply A and x
what does B need to be
for x to be an eigen vector?
a scaled version of A?
or maybe A itself cus if its a hermitian matrix the eigen vectors are otrhonormal
and have length as 1
?
nvm
the eigen vectors are orthogonal
not orthonormal
so what should B beeeeeeee
royal basin
.....
obtuse pebbleBOT
royal basin
.reopen
autumn spade
.reopen
obtuse pebbleBOT
✅
royal basin
ok right so like
you want the equation Ax = λx to be true for some scalar λ.
i.e. you want Ax to be a scalar multiple of x
do you understand this
autumn spade
yeah
royal basin
do you understand why "Ax is a scalar multiple of x" is the same thing as the equation Ax = λx
autumn spade
yup
royal basin
or maybe A itself cus if its a hermitian matrix the eigen vectors are otrhonorma...
you overthought this massively
autumn spade
it would seem so
royal basin
would you like help with the computations themselves?
or are you ok doing them on your own
autumn spade
wait lemme try calculating Ax
bruh matrix multiplication with complex numbers is such a pain
i did it and got the wrong answer
i tried it on the calculator
multiplying these two i get
C is -1*B
so ig B is an eigen vector of A
obtuse pebbleBOT
@autumn spade Has your question been resolved?
royal basin
the first vector in the first answer option is an eigenvector of A with eigenvalue -1, yes.
you now need to check the other two vectors in that answer option.
autumn spade
bruh even this is very long winded
autumn spade
i need to get used to complex number multiplication
i get it now tho
i can take care of the rest myself ig
thx!
.close
warm dome
What’s inf? And what’s i?
I mean, this is just n|x-a_i| for all x.
It would be different if they wrote k instead of i
But they didn’t
warm dome
I mean, this is just n|x-a_i| for all x.
You’ll have to find the infimum for this
pseudo swift
I mean, this is just n|x-a_i| for all x.
Sounds like a typo tbh
wtf would i even be ?
warm dome
Yeah it’s most likely a typo
pseudo swift
Je te conseille de regarder cette somme de valeurs absolues comme une fonction par morceaux
Qu'est-ce qu'elle vaut pour x<a1 ?
Pour a1<= x < a2 ?
Etc...
obtuse pebbleBOT
@timid silo Has your question been resolved?
royal basin
@timid silo si tu appuies seulement sur l'ixe rouge et ne nous dis rien d'autre, on ne sait pas du tout ce qui te confond ...
obtuse pebbleBOT
@timid silo Has your question been resolved?
agile burrow
I’m being asked to solve 16x^3-48x^2+60x-31 by factorisation but I’m kinda struggling. I managed to get it down to 16(x-1)^3+12(x-1)-3 =0 which I then subbed y as x-1 to get 16y^3+12y-3=0, which I then further factorised to y(16y+12)-3=0, but I’m not sure what to do from there, if someone could please help that would be great thank you
obtuse pebbleBOT
I’m being asked to solve 16x^3-48x^2+60x-31 by factorisation but I’m kinda strug...
royal basin
did you mean 16x^3-48x^2+60x-31 = 0?
agile burrow
-31 = 0, but yes sorry
royal basin
which I then further factorised to y(16y+12)-3=0,
this factorization won't help
ok just to double check
,w expand 16(x-1)^3+12(x-1)-3
warm shaleBOT
royal basin
ok right, that's good so far
so you've got 16y^3 + 12y - 3 = 0
i'd throw the rational root thm at this.
agile burrow
Would you mind explaining what that is?
obtuse pebbleBOT
@agile burrow Has your question been resolved?
agile burrow
I had a little sneak peek at wolframalpha for the solution, but the real solution (only interested in the real solution) is not a rational number, so I don’t think rational root theorem would work?
obtuse pebbleBOT
@agile burrow Has your question been resolved?
obtuse pebbleBOT
@agile burrow Has your question been resolved?
agile burrow
.close
sullen roost
obtuse pebbleBOT
sullen roost
I’m trying to study for an upcoming test
I used Photomath after not being able to understand anything and I still don’t understand Photomath
tardy epoch
2(x-4) = ?
sullen roost
2x-8
I get the simplifying the denominator part
But the whole multiplication at the top makes no sense to me
tardy epoch
But the whole multiplication at the top makes no sense to me
Which term
tardy epoch
They multiplied the terms by the part that makes common denominator
$\frac{a}{b} + \frac{c}{d} = \frac{?}{bd}$
warm shaleBOT
riemann
sullen roost
ad+bc/bd?
tardy epoch
Do the same for the x-4 as d with the 3/(2x) term
tardy epoch
But there’s no equals sign
You're supposed to come up with the equal sign yourself
tardy epoch
That's what the solution is saying, just omitting the equals sign since it's implied
sullen roost
I don’t get it
obtuse pebbleBOT
@sullen roost Has your question been resolved?
obtuse pebbleBOT
@sullen roost Has your question been resolved?
timid silo
anyone got a good combining logs ruless chart i can copy into my notes?
obtuse pebbleBOT
anyone got a good combining logs ruless chart i can copy into my notes?
pulsar quarry
,tex .log xp rule
warm shaleBOT
🐱!Yajat! 【Catfan1398】🐱
tall silo
Hello. I am wondering if anyone can help me with understanding some concept on I GUESS throughput(?)
I don't know the terminology that well but I can give an example.
Suppose that I can press a button every 1.5 seconds for a total time of 1 minute, and every time I press that button, I get points of 650. I then want to calculate how many points I get per second.
Thank you
obtuse pebbleBOT
Hello. I am wondering if anyone can help me with understanding some concept on I...
dusk ruin
since it's a constant rate, you can calculate points / minute and divide by 60 to get avg points/second
tall silo
so that would be (650x60)/60 ?
dusk ruin
no? you get 650 points every time the button is pressed
you press the button once per 1.5 seconds, not once per second
tall silo
oh right, so what's the best way to calculate how many times I can press per 60 seconds?
dusk ruin
so, how many times is the button pressed per 60 seconds?
you know 1.5 seconds/press, over 60 seconds
and you need the unit "presses"
tall silo
I guess that's where I'm failing to see the process. Sorry
In my head all that I can map out is
0.0 Press 0.5 - 1.0 - 1.5 Press 2.0 - 2.5 - 3 Press ...
looking at it that's something akin to 33.333...% of the time you're able to press
so if 1% of 60 seconds is 60/100 * 30 or 60*0.3 than would that then be the amount of times you can click per second?
dusk ruin
nope
let's put it this way
we'll ignore pressing at 0 because that messes stuff up
how many times does a 1.5 second interval fit into 6 seconds?
tall silo
4 times
dusk ruin
so you can press a button 4 times in 6 seconds
how many times can you press it in 60 seconds?
tall silo
Well I just did 60/1.5 which is 40 which does fit in here as well
tall silo
so I guess it would be 40+1 since i forgot to add the caveat that the first press starts the timer
dusk ruin
so you have 41 presses over one minute, and 650 points per press
how many points is that total, over one minute?
tall silo
650x41 = 26650
and then 26650/60 is points per second I assume granted my total is correct
which would be 444.1666...
dusk ruin
that is the average rate of points per second yes
dusk ruin
you know 1 press/1.5 second, 60 seconds, multiply you get 40press * second/second = 40 presses, +1 at 0, = 41 presses/minute * 650 points/press * 1minute/60 seconds = 444.166...
it just took long because you didn't know how
tall silo
well I meant more akin to a shorter formula, like (x/t)/p or whatever
dusk ruin
that doesn't work because you have the extra press at t=0
but in this case it quite literally is time/rate*points
you just have to convert from /minute to /second, and add the t=0 bit
tall silo
so 60/1.5*650
dusk ruin
there is no one and done solution that fits all types of problems
tall silo
and then (+1) for the caveat
dusk ruin
it'd be (60/1.5+1)*650 / 60
tall silo
on calculator it would be (60/(1.5+1) ?
dusk ruin
no, it would be (1+(60/1.5))
1+60/1.5=60/1.5+1
this is just pemdas
addition happens last
tall silo
think in europe its bodmas
tall silo
ok so then it would be (1+(60/1.5)*650)/60 = 433.35 ?
dusk ruin
*(1+60/1.5)*650/60=444.16...
you messed up the parentheses
it's not 1+ (60/1.5)*650
it's (1+60/1.5)*650
presses * points
not 1 + (most presses * points)
vagrant kite
At 9:30 AM. Andrew left Exeter for Portsmouth, cycling at 12 mi/h. At 10:00 AM, Stacy left Portsmlith for Exeter, cycling at 16 mi/h. The distance between Exeter to Portsmouth is 20 mi/h. Find the time when they meet.
obtuse pebbleBOT
At 9:30 AM. Andrew left Exeter for Portsmouth, cycling at 12 mi/h. At 10:00 AM,...
vagrant kite
I know that you need to have their distances equal together so I did
20 = 12x but that's not the answer so I'm confused on what the distance of Andrew would be if it's not 12x
dusk ruin
what is the distance between exeter to portsmouth?
20 mi/h is not a distance.
then, you'll want to make an equation
remember they're starting at opposite ends
so if stacy has traveled 10 miles and andrew has traveled 8, then it means andrew is 8 miles from the left, and stacy is 10 miles from the right
not that they are two miles apart....
obtuse pebbleBOT
@vagrant kite Has your question been resolved?
proud gyro
I'm trying to compute the integral $\int_{0}^{2\pi} e^{e^{i\theta}} d\theta$. My first step was to substitute in $z=e^{i\theta}$, which gives me $\int_{|z| =1} \frac{e^{z}}{zi} dz$
obtuse pebbleBOT
I'm trying to compute the integral $`\int_{0}^{2\pi} e^{e^{i\theta}} d\theta`$. ...
warm shaleBOT
interpolate
proud gyro
This question takes place in a chapter where I learned about cauchy's formula, but I'm not sure how to apply this here
I know about cauchy's forumula in the form above
but I'm not sure how to really apply it here
alpine bison
here your f(z)=e^z
and a=0
1/i can go out of the integral
now you can apply that formula
proud gyro
ahh ok
and i can multiply by 2pi/2pi
so the 2pi in the denominator get eaten by cauchy's and I'm left with e^{0} * 2pi
@alpine bison thank you!
.close
timid silo
obtuse pebbleBOT
timid silo
how would u solve this? Also, wht type of indeterminate form is this?
fresh trail
how would u solve this? Also, wht type of indeterminate form is this?
It's a bit easier to see the trick if you re-write it as x/e^x, you can do that since the exponent is negative
timid silo
hmmm ok
timid silo
It's a bit easier to see the trick if you re-write it as x/e^x, you can do that ...
would it not be indeterminate form of type "inf/inf"
fresh trail
Right, that's the one
sudden goblet
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
I'm thinking since the highest degree is odd, one side will rise & one will fall
and since theres a negative coefficient itll be flipped
so as
x -> -inf, y->inf
x -> inf, y -> -inf
would that be the correct way to answer this question
trim pawn
That is the long term behavior of the function
I would use p instead of x because that is the variable the problem uses
fluid snow
Let $a, b, c, d, n \in \mathbb Z$ with $n \mid ad - bc, \quad n \mid a - b$ and $\gcd(n, b) = 1$. \ Prove that $n \mid c - d$.
obtuse pebbleBOT
Let $a, b, c, d, n \in \mathbb Z$ with $n \mid ad - bc, \quad n \mid a - b$ and ...
kind hawk
not sure what identity you mean but how about you just try it out and see?
fluid snow
Btw this is similar to what we've done before @sonic raptor
fluid snow
not sure what identity you mean but how about you just try it out and see?
It's gcd(n, b) = 1 iff qn + cb = 1 for some q, c in Z
It doesn't seem very helpful here though
kind hawk
thats usually called bezouts identity
so in terms of modulo we have ad=bc mod n and a=b mod n and we want to conclude c=d mod n
how can we do that?
fluid snow
so in terms of modulo we have ad=bc mod n and a=b mod n and we want to conclude ...
ad = bc mod n?
kind hawk
yes
fluid snow
How
fluid snow
Oh
fluid snow
so in terms of modulo we have ad=bc mod n and a=b mod n and we want to conclude ...
I'm sure you can do manipulations like with normal equations for mod ones
Right?
kind hawk
well at least most of them, yes
fluid snow
We haven't had that in my course yet though, so I'm sure if we're supposed to do that
But we could just subtract the second equation from the first
And we'd be done
wait nvm
kind hawk
how would subtracting the second from the first do anything
kind hawk
ok so you would want ad=ac mod n and then cancel the a
fluid snow
Yeah
kind hawk
you cant do that in general
fluid snow
Oh
kind hawk
you can only do it if gcd(a,n)=1
but well ok if you havent done this whole thing in terms of modulo then you arent really supposed to frame it like this anyway
without modulo, what does n|a-b mean
fluid snow
n * k = a - b for some k in Z
fluid snow
Yeah
kind hawk
what happens if you plug that into n | ad-bc
fluid snow
n | (b + kn)d - bc you mean?
fluid snow
n | bd + knd - bc = b(d - c) + knd
kind hawk
good
fluid snow
This means n | b(d - c) and n | knd
kind hawk
well because n | knd this means n | b(d-c)
kind hawk
so n | b(d-c)
fluid snow
Yeah
kind hawk
and we havent used one given thing yet
fluid snow
n | ad - bc, yeah
kind hawk
we used that
kind hawk
we used that aswell
fluid snow
3 | 7-1 but not 3|7 and 3|1
Oh, so that only holds for addition?
fluid snow
Didn't we use that earlier
kind hawk
3 | 7+2 but not 3|7 and 3|2
if x|y and x|z, then x|y+z and x|y-z
that direction works. but not the other one
fluid snow
well because n | knd this means n | b(d-c)
Here, we said n | b(d + c) + knd and so n | b(d + c) and n | knd
Or was the argument different?
kind hawk
no I corrected you
because n | b(d-c) +knd and n|knd then n|b(d-c)
n | x and n | y where x=b(d-c)+knd and y=knd, therefore n | x-y = b(d-c)
fluid snow
because n | b(d-c) +knd and n|knd then n|b(d-c)
Why does n | b(d - c) follow from n | knd?
fluid snow
n | x and n | y where x=b(d-c)+knd and y=knd, therefore n | x-y = b(d-c)
But this is just the ==> direction?
Don't we want the <== direction
kind hawk
n | x and n | y => n | x-y
its exactly the direction we want
and the direction that is true
fluid snow
Oh
kind hawk
<= wouldnt be true
fluid snow
n | x and n | y => n | x-y
Oh, we subtract something off of x and use that to our advantage, yep
Ok we left off at n | bd - bc
kind hawk
n | b*something and gcd(n,b)=1
.
I know for a fact that you know the next lemma we want to use
fluid snow
n | b*something and gcd(n,b)=1
Bezout's lemma?
kind hawk
no
fluid snow
Euclid's lemma, n | b and n | something
kind hawk
euclids lemma, yes
fluid snow
Great, thank you!
lime scaffold
How do I prove this?
obtuse pebbleBOT
How do I prove this?
wintry isle
okay
so
you're really close tbh
what do you notice about the denominator, there's 1 important thing there
lime scaffold
can I factorise something out?
wintry isle
well the answer has 1 plus minus something
now, to get one in your expression you'd have to divide the top and bottom by something 🙂
so like this is true right? but instead of 7/7 it's gonna be another expression...
so what can you divide by, on the top and bottom such that when you do, you get a 1 somewhere on the denominator?
there's really only 2 options if you think abt it :)))
i hope i am not confusing you
wintry isle
no problem
talk to me if you want like to get it down "on paper"
oh i would also ignore this, as now you have to divide the top and bottom by some expression SO THAT you will get a 1 on the denominator!!
(cosxcosy plus minus sinxsiny) is so close to the form (1 plus minus tanxtany), don't you think? 😄
wintry isle
try it and see!
i have a good feeling abt it though haha
😉
so with these kinda proofs you just have to realise that the form they want it in is right in front of you!
wintry isle
❤️
lime scaffold
.close
honest flicker
obtuse pebbleBOT
honest flicker
I don't know what linear pair is
But is the measure of angle x equal to 108 fr
Idk
zenith spade
It is 108 ye
Basically a linear pair is two angles that form a straight angle
aka they are adjacent and, more importantly, supplementary
honest flicker
aka they are adjacent and, more importantly, supplementary
I forgor wat adjecent means
honest flicker
It is 108 ye
So is it the same as Y too
As then Z is 72?
@zenith spade
@zenith spade
Bro died😭 😭 🙏
<@&286206848099549185>
Is x and y equal to 108 and then Z is equals to 72?
fierce mica
Is x and y equal to 108 and then Z is equals to 72?
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
cinder hedge
obtuse pebbleBOT
cinder hedge
how to find the derivative of this function...
tardy epoch
Do you know algebra?
cinder hedge
yes
cinder hedge
could you provide the solution
tardy epoch
could you provide the solution
No
cinder hedge
ok?
tardy epoch
Against server rules
tardy epoch
Solve for y using algebra
Did you do this
cinder hedge
Against server rules
thats not true ?
tardy epoch
Did you do this
.
spice chasm
if you want to write $x+y-z$ do you have to write $x+(t)\big|_z^y$ or $x+\left(t\big|_z^y\right)$
obtuse pebbleBOT
if you want to write $x+y-z$ do you have to write $x+(t)\big|_z^y$ or $x+\left(t...
warm shaleBOT
Jash
latent walrus
what is t
spice chasm
what is t
arbitrary variable where ur evaluating from t=z to t=y
like what u do in a definite integral
latent walrus
on that basis, either of the things you wrote would be legitimate i think
maybe leaning to the second one
obtuse pebbleBOT
cinder hedge
(ty)
obtuse pebbleBOT
Available help channel!
white ingot
How do you solve the #3😭
obtuse pebbleBOT
How do you solve the #3😭
white ingot
I don't understand how
high lily
can you express 12.25 as an improper fraction
white ingot
12 1/4..?
high lily
that's a mixed fraction,
can you convert that to an improper fraction
white ingot
49/4
high lily
yes, and can you continue from there?
high lily
$$\frac{5^{2b}}{5^a}$$
they want something in the form $5^{k}$ so there's one more step after that
warm shaleBOT
ℝαμΩℕωⅤ
white ingot
5^2b-a.. I don't think this is it though😭
white ingot
Okay thank you
quiet drum
obtuse pebbleBOT
quiet drum
shouldnt the final answer be y = (x+1)^2 -1
i thought h was the x coordinate of the T.P
latent walrus
yeah but its always opposite sign
(x-h)^2+k means turning point is (h,k)
(x+h)^2+k means turning point is (-h,k)
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
bleak skiff
Hello, what are the subgroups of $\mathbb{Z}{/}18\mathbb{Z}$?
obtuse pebbleBOT
Hello, what are the subgroups of $\mathbb{Z}{/}18\mathbb{Z}$?
warm shaleBOT
lilisworld
bleak skiff
and the elements
so i now the subgroups but i don't know how to find the elements
<@&286206848099549185>
.close
tidal relic
help
sacred barn
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
3
sacred barn
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
tidal relic
ok one sec
sacred barn
Ok, you got x=0 as the only max or min?
tidal relic
oh
royal basin
that's what is wrong with your answer
tidal relic
wait so if its [0,2pi] they will be included right
also how do i get the min value, i used desmos for that part
sacred barn
Your critical points will give you the candidates for max/min
tidal relic
so this shouldbe the answer right
tidal relic
Your critical points will give you the candidates for max/min
yeah but i only got 0 as a critical point
sacred barn
That's incorrect, as I was getting to
royal basin
yeah your solution of the trig equation is kinda scuffed
sacred barn
When you find x s.t. sin(3x)=0, there are multiple x
royal basin
from sin(3x)=0 you should have gotten 3x = k*pi
writing only sin^-1(0) throws out infinitely many solutions
sacred barn
any integer
tidal relic
how do i determine the integer i need to use
sacred barn
And this indicates that you should review trig, btw
tidal relic
yes i suck at trig
tidal relic
what is s.t.
sacred barn
Sorry, such that
sacred barn
You basically just loop through the integers (0, 1, 2, etc) until k*pi is more than 2pi
Don't include the endpoints
tidal relic
so it would get to x=kpi/3 then i plug in 1, 2, 3, etc until the last value under 2pi
sacred barn
yeah
tidal relic
but like
ok
so then i would test each of those with the first derivative test?
to know if its a min or max
sacred barn
That would be one way to do it, yeah
sacred barn
Yes, they will alternate
sacred barn
np
tidal relic
.close
timid silo
obtuse pebbleBOT
plain stag
,rccw
warm shaleBOT
balmy wind
multiply both the sides with opposite denominator
then you will get a quadratic at end
then solve it
timid silo
Yeah got it
balmy wind
ok
timid silo
Roots as 9 and 1
balmy wind
oh
timid silo
Yea
So shouldn't 1 be ans
Given ans is 9
I mean the quadratic in a
D>0
or equal to
balmy wind
let me try
timid silo
Can you help with 1st of the decimal type
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
royal basin
open \ open ≠ open generally.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
vital frigate
hello
vital frigate
I need help in period of pendulum
tacit scarab
!da2a
obtuse pebbleBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
vital frigate
What is the period of a pendulum if it is 4.0m long, 9.0 m and 14.0m long
tacit scarab
do you know the formula for period?
vital frigate
T= 2pi √length/gravity
royal basin
careful with parentheses
but ok, $T = 2\pi \sqrt{\frac{l}{g}}$... so what is troubling you?
warm shaleBOT
Ann
vital frigate
royal basin
that looks like an instruction sheet
let me ask again:\
you have the formula $T = 2\pi \sqrt{\frac{L}{g}}$. are you able to apply it, yes or no?
warm shaleBOT
Ann
vital frigate
What is the period of a pendulum if it is 4.0m long, 9.0 m and 14.0m long
this is my question, I need to know the step by step answer