#help-17
vocal sleetBOT
paper depot
you mean the set of polynomials with integer coeffs vs. the set of integer sequences?
@steady musk
a polynomial can only have a finite number of terms. in terms of its coefficients, it means only finitely many of them can be non-zero at a time.
for an integer sequence there is no such restriction.
steady musk
vocal sleetBOT
vocal sleetBOT
Available help channel!
warm horizon
vocal sleetBOT
warm horizon
Could you do part (a) without remapping? It feels iffy doing it for this kinda question
vocal sleetBOT
@warm horizon Has your question been resolved?
wild notch
hollow sundial
lots of law of sines/cosines pretty much
hollow sundial
did you solve the angles of ABC
wild notch
Well i did the sin rule
hollow sundial
you know all the sides
wild notch
Yes , and then?
wild notch
You mean in numbers?
hollow sundial
yes
hollow sundial
well here you're trying to find angle ABC if you think about it
finding that means that angle EBD is 180 - ABC
(degrees)
wild notch
Ok
hollow sundial
if you have angle EBD, you already have lines BE and BD
so you can solve for DE in the triangle
wild notch
Ok
Then
I solve in trianglr MAD?
And i know angle MAD is angle BAC
@hollow sundial i don t think it s ok
I think I need to do smth with vectors
Because this is point b) of my problem, point a) was writing vectors FD and FE in function of vectors CA and CB
hollow sundial
ah
wild notch
And anyways the angles aren t natural numbers
So i don t really think he wants me to do this
hollow sundial
this linear alg right
hazy sluice
doing A-Level maths, can someone explain what im supposed to do in part A
hazy sluice
i dont know where to start, as i dont think i have enough information on the weekly temp and sales figures
vocal sleetBOT
@hazy sluice Has your question been resolved?
vocal sleetBOT
@hazy sluice Has your question been resolved?
pallid forge
what is a product moment correlation coefficient
tough nest
Hello, I'd like to show that the following set with the following norm is a Hilbert space but im struggling. I only managed to show that if i have a cauchy sequence phi_n then its gradient converges in L2 and phi_n/|x| converges in L2
vocal sleetBOT
Hello, I'd like to show that the following set with the following norm is a Hilb...
tough nest
also theres a mistake, its not L^2(R^3) but rather L^2(R^3\Adh(Omega)) where omega is an open set that contains 0 (i believe the argument will be the same)
vocal sleetBOT
@tough nest Has your question been resolved?
vocal sleetBOT
@tough nest Has your question been resolved?
onyx spade
how do i do this
vocal sleetBOT
how do i do this
bronze osprey
how do i do this
following the hint, you know you have $g(x) = \frac{1}{1 - (-x^2)}$
twin meteorBOT
south
bronze osprey
Ignore the - for ghe x
yeah if you ignore that, that's now correct
onyx spade
So then do derivative?
bronze osprey
mhm
bronze osprey
yeah now you need to shift the summation to start from n = 1
so you could just let n = N - 1
so that n = 0 becomes N - 1 = 0 or N = 1
there's a problem though, because 1 differentiates to 0
onyx spade
bronze osprey
so if you do N - 1 then add 2 to the exponent (x^0 to the x^2 that gets differentiated)
you should actually do n = N + 1
and then it starts from 1
onyx spade
is this correct
bronze osprey
no, read what I said
onyx spade
ok
bronze osprey
wait this is trippy
onyx spade
whats N
onyx spade
i se
bronze osprey
we need to reindex the sum
onyx spade
so
the new index is
N=0
but each N is n-1?
bronze osprey
also you're forgetting, if you differentiate g(x) you get -2x/(1 + x^2)^2
bronze osprey
also you're forgetting, if you differentiate g(x) you get -2x/(1 + x^2)^2
so you need to multiply this by -4 to get f(x)
bronze osprey
so
the new index is
N=0
but each N is n-1?
yes but 1 differentiates to 0, so you mess up the indexing even more
bronze osprey
if you sub 0 into here you get x^(-1) which is impossible
onyx spade
\i see
bronze osprey
okay so you should get $-2x + 4x^3 - 6x^5$ and so on
twin meteorBOT
south
bronze osprey
you need an (-1)^n for sure
then 2, 4, 6 has the pattern 2n where n = 1, 2, 3
putting it all together you have $g'(x) = \sum_{n = 1}^{\infty} (-1)^n (2n) x^{2n - 1}$
twin meteorBOT
south
vocal sleetBOT
@onyx spade Has your question been resolved?
vocal sleetBOT
@onyx spade Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
hi i need help
vocal sleetBOT
hi i need help
quiet echo
hi i need help
Is this homework?
quiet echo
did u just ask if it was hw for no reason?
I asked for obvious reasons.
manic bay
did u just ask if it was hw for no reason?
we can see that 1 point 😭
vast shale
wait til bro finds out hw is a grade
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
so help then
as u can see i already got the answer
but im confused how to do it
so help please
rain vault
well it is sort of a step by step calculation
u have the base balance, then you save a percentage of ur yearly salary, next year both ur salary and ur saving account increaase by some percentage
so u can do it the 27(?) times but there must be something that can describe the iteration
austere fog
I want to make sure I'm doing this right... Since u + any other solution to the pde is also a solution, I'm assuming the c_1x + c_2 is supposed to represent the solution of lambda = 0, is this right?
vocal sleetBOT
I want to make sure I'm doing this right... Since u + any other solution to the ...
austere fog
If that IS the case, how am I supposed to show it mathematically, could I just explain how the c_1x + c_2 is a solution to the pde and any solutions to the same pde summed together create a new solution?
gentle sleet
I want to make sure I'm doing this right... Since u + any other solution to the ...
have you tried to calculate $u_t$ and $u_{xx}$?
twin meteorBOT
Sepdron
austere fog
Like come up with my own solution of u? I think my professor wants me to show it "abstractly" for any solution u
There isn't any information provided for the variables which form alpha for example
gentle sleet
no, I mean do $\pdv{t} (u + c_1 x + c_2)$
twin meteorBOT
Sepdron
gentle sleet
you plug it in to the DE
your DE is $u_t = \alpha^2u_{xx} + F(x, t)$ right?\
so if $u + c_1x+c_2$ is a solution, you should be able to plug it into that DE and show that it satisfies it
twin meteorBOT
Sepdron
gentle sleet
np, sorry if it's a bit confusing
they used u as both a solution and the function in the DE and I got a bit confused
austere fog
@gentle sleet do I have the right idea? not sure where alpha comes from, and F(x, t) though...
gentle sleet
lemme just make the variable in the DE y instead of u, so it doesn't clash with the solution u
so we know that u is a solution to $y_t = \alpha^2y_{xx} + F(x, t)$
twin meteorBOT
Sepdron
gentle sleet
so that means that $u_t = \alpha u_{xx} + F(x, t)$ is true, because u satisfy the DE
twin meteorBOT
Sepdron
austere fog
ohhhh
the alpha and F are just applied
smh thank you so much!
wait
yeah that makes sense
gentle sleet
nice, what I'm trying to get is that the new solution has the same $\pdv{t}$ and the same $\pdv[2]{x}$
twin meteorBOT
Sepdron
gentle sleet
the c_1 x + c_2 doesn't affect the DE
vocal sleetBOT
gentle sleet
np!
vocal sleetBOT
Available help channel!
rustic dragon
vocal sleetBOT
rustic dragon
This equals 0.44444 no?
manic bay
This equals 0.44444 no?
yes
granite perch
$4* 1/10 * 1/10 =0.04$
twin meteorBOT
ASda
granite perch
Hence what you wrote approaches 0 right?
rustic dragon
4 + 41/10 + 41/10 * 1/10 * …. -4
hollow sundial
but the summation here computes the -4 for every n
so for n = 1: 0.4 - 4 = -3.6
would lead to negative infinity
hollow sundial
i think it just wants a general geometric series format
rustic dragon
Oh
hollow sundial
(without subtracting)
hollow sundial
remember the convergence formula is only for 0 < r < 1
also i think it wants you to use the geometric series sum formula
where n is x
(for 2)
rustic dragon
Wdym
modern quail
whats ur working
rustic dragon
For what
hollow sundial
well for your first question you have to remember the rules of convergence
rustic dragon
|r| < 1
modern quail
thats correct
modern quail
|r|<1 right
rustic dragon
So |8x| < 1
modern quail
then |8x|<1
rustic dragon
So |x| < 1/8
modern quail
yup
rustic dragon
I thought it said diverges mb
rustic dragon
And for 2
modern quail
for the second one i think you just applied the formula wrong
tell us your working though
modern quail
okay now this question doesnt accept that formula
can you find why
or do u want a hint
rustic dragon
I need to plug in the series for 1 and subtract
modern quail
okay yeah
rustic dragon
B/c a/1-r is only true for n = 0
rustic dragon
So (1/1-8x) - 8x?
modern quail
instead, we should use the "generalised" formula which is $\frac{a_1}{1-r}$
twin meteorBOT
leo
rustic dragon
I got it right Ty for help
rustic dragon
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
twilit crow
can someone tell me what the difference
vocal sleetBOT
can someone tell me what the difference
twilit crow
between this and
like what is different from the left side to the right
the right is the book method but our teacher said we can do left and its easier
but why dont u need to add the constant to both sides?
low cradle
the -4 u have on the left side is the constant u are adding
both of this are equivalent
twilit crow
the -4 u have on the left side is the constant u are adding
hmm
wait
so
wait i dont understand why is it the same
ive been doing the left method but i asked ai to do a question for me and it showed me how my way could be wrong?
low cradle
on the left, it is actually the same as doing
(x + 4/2)^2 +1 -(4/2)^2
twilit crow
ye
low cradle
notice how u kept the -4 term
twilit crow
yes
low cradle
that is the value that u added on ur right
twilit crow
but on the right side theres 2 (4 terms)
low cradle
these are equivalent, just that ur terms are on different sides of the equation
twilit crow
that is the value that u added on ur right
how come on the left its not being added
oh wait is it cuz x^2+4x+(4/2)^2 is the same as (x+2)^2
wait
low cradle
because ur (x + 4/2)^2 = (x+2)^2 is an expansion of x^2 + 4x + 4
yes
try it with an odd coefficient and u will see the difference clearly
do x^2 + 3x + 9 = 0
twilit crow
okay
lemme do both methods rq
ok so with the left side method i got x= -3+- square root of negative 27/4?
wait what
is that right? u cant square root a negative
low cradle
with the odd values u will realize that u are essentially doing the same operations, just one expanded and one not
twilit crow
is it possible with the other one
low cradle
by writing (x +b/2)^2 you are already taking a "shortcut"
low cradle
is it possible with the other one
it definitely is, you just have to see that x^2 + 3x + (3/2)^2 is the same as (x+3/2)^2
then u will realize what is the shortcut u took on the version on the left
twilit crow
(x +b/2)^2 is basically the one where its (x+2)^2 on the left which is the shorcut of x^2+4x+(4/2)^2
low cradle
yep yep
twilit crow
so we basically skipped 2 steps
twilit crow
ye ive been using it but i didnt quit understand
all i knew was half cooeficient of x then the 2nd part was u times that number
low cradle
u can try to understand the logic behind completing the square itself
twilit crow
is there any vids
low cradle
also understand what does the constants means when u look at a graph
shifts etc.
that will help alot
vocal sleetBOT
vocal sleetBOT
Available help channel!
turbid snow
What do they mean by positive orientation here?
Does the curve need to be ccw to have a positive orientation?
https://tutorial.math.lamar.edu/classes/calcIII/stokestheorem.aspx
vocal sleetBOT
What do they mean by positive orientation here?
Does the curve need to be ccw t...
@turbid snow Has your question been resolved?
turbid snow
<@&286206848099549185>
fast crag
What do they mean by positive orientation here?
Does the curve need to be ccw t...
What do you mean by CCW?
Also, please post the whole page/topic you are reading about. Looks like orientation theory, but I would need more context
calm light
What do you mean by CCW?
counterclockwise
fast crag
Ok, in general, simply saying counterclockwise does not mean anything, even for simple closed curves; think of a knot, what does ccw mean in that case? For the unit circle in $\mathbb{R}^2$, the positive orientation coincides with walking along it in the counterclockwise direction
twin meteorBOT
Enrico
fast crag
By positive orientation, they mean the only orientation on the boundary which is compatible with the orientation on the given surface
Are you familiar with the concept of tangent spaces/tangent bundle?
If you do, it is more or less clear what they mean by "positive"
vocal sleetBOT
@turbid snow Has your question been resolved?
turbid snow
By positive orientation, they mean the only orientation on the boundary which is...
Do we use the right hand rule? For example let’s say we have a loop located on the xy plane. The path of the loop goes in the clockwise direction, as viewed from above. Does that mean n is in the negative z direction?
vocal sleetBOT
@turbid snow Has your question been resolved?
turbid snow
.close
tight sleet
I've come across two definitions of periods for periodic matrices.
- k such that A^k = A
- k such that A^(k+1) = A
The second definition (the k+1 one) is also in the series of lectures I was watching, and according to the lecturer, while square null matrices are periodic, their period (k) is undefined. I get that that might be because a square null matrix raised to the power 0 is undefined, but then does that mean the period for any other idempotent matrix is 0? so the period of I, for example, is 0, but the period of a square null matrix is not 0?
vocal sleetBOT
I've come across two definitions of periods for periodic matrices.
1. k such tha...
tight sleet
wait if k = 0, A^(k+1) = A → A^1 = A
and ofcourse A^1 = A
so then are we to say that A^2 = A (i.e., k = 1 for an idempotent matrix A), if we are to show its periodicity?
but then why would we regard the period of null matrix as undefined? can't we say that its 1, just the same as for any other idempotent matrix?
vocal sleetBOT
@tight sleet Has your question been resolved?
vocal sleetBOT
@tight sleet Has your question been resolved?
vocal sleetBOT
@tight sleet Has your question been resolved?
spiral turtle
@tight sleet I've only heard of the second definition and it's subject to the condition that k > 0
tight sleet
<@760072922550239243> I've only heard of the second definition and it's subject ...
my lecturer used the second definition too.
if A^(k+1) = A where k is a natural number, then can we not have k = 1 for all idempotent matrices, null matrices included?
spiral turtle
Yes
tight sleet
then whatever my lecturer is saying about the period of null matrices being undefined is wrong then
cool
thanks!!
spiral turtle
No, actually?
I am not sure tbh, but what I'm seeing searching around says by convention null matrices have undefined period
tight sleet
huh
spiral turtle
This is probably the same sort of idea where f(x) = 1 is a zero degree polynomial, whereas f(x) = 0 is considered a -1 or -inf or undefined degree polynomial
It just makes things work nicer
tight sleet
i see
maybe i'll be able to understand/appreciate these conventions with time, as i learn more math
in any case, i guess for now i should just take it as truth
spiral turtle
There's probably a theorem that can combine periods
But the formula breaks on null matrices
tight sleet
it's a bit jarring to have these things pop up in math at times
spiral turtle
Like if A has period m and B has period m then AB has period lcm(n,m) maybe?
Except if a null matrix multiplied by anything will result in a period of 1
spiral turtle
Not sure
tight sleet
right
spiral turtle
That would be my best guess about motivation
tight sleet
i'll still try to think about the lcm thing you just came up with
tight sleet
That would be my best guess about motivation
welp
in any case, i'll put it on the back burner for now since what you said about it just being defined that way for convenience does sound likely
thanks for accompanying me!
spiral turtle
It's likely not quite that easy, because linear algebra has a lot of edge cases. But you're very welcome
vocal sleetBOT
spiral turtle
Ciao
vocal sleetBOT
Available help channel!
inner sonnet
Is continuity of a function at a point "a" sufficient condition for the function to be differentiable at that point? Explain.
"The continuity of a function as a point is NOT a sufficient condition for the function to be differentiable because a point may exist and be continuous but a tangent will not exist and so that point is not differentiable. e.g -> The function f(x) = |x| is continuous but at the point x = 0, it is not differentiable because at this specific point, there is a sharp turn/corner and a tangent would occur from two sides in which the tangent will not exists and that this point is not differentiable"
Is this explanation accurate?
vocal sleetBOT
Is continuity of a function at a point "a" sufficient condition for the function...
inner sonnet
.close
vocal sleetBOT
vast shale
Is continuity of a function at a point "a" sufficient condition for the function...
yes
vocal sleetBOT
Available help channel!
hot schooner
Hello everyone does anyone know another method I can use to solve this trinomial 6x squared −5x−21 besides finding the factors of the constant term and picking the right pair?
vocal sleetBOT
Hello everyone does anyone know another method I can use to solve this trinomial...
quiet echo
Hello everyone does anyone know another method I can use to solve this trinomial...
You could use the quadratic formula.
Or completing the square, but they're essentially the same method.
vocal sleetBOT
vocal sleetBOT
Available help channel!
wild iris
vocal sleetBOT
wild iris
hi could someone run me through this
atomic jasper
,tex .exp rules
twin meteorBOT
Bonk
wild iris
yeah Ive tried following the indice rules and my answer stays: 4 x^9/20
and not 2^4/5 x^9/20
atomic jasper
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
wild iris
bro im sorry i cant show my working its way too messy
would it be ok to solve the first steps yourself to show me where i went wrong
atomic jasper
simplify $\sqrt[4]{256x^3}$
twin meteorBOT
Bonk
atomic jasper
what about the 256?
wild iris
im not sure, what do i do with it? i removed the root sign and removed the bracket and multiplied the indices
i didnt think i need to do anything with the 256
atomic jasper
$\sqrt[4]{256x^3}=\sqrt[4]{256}\cdot\sqrt[4]{x^3}$
twin meteorBOT
Bonk
wild iris
what is that
atomic jasper
yes
and you can simplify 256^(3/4)
and do smth similar for the denominator aswell
wild iris
so id get 64^4/5x^4/5 for denominator
which leaves me with : 256^3/4x^3/4 / 64^4/5x^4/5
atomic jasper
yes
atomic jasper
you want to rewrite it as the product of their prime factors
like, 10=2*5
20=2^2*5
24=2^3*3
15=3*5
etc
<@&268886789983436800>
wild iris
Is this correct so far ?
wild iris
ok
atomic jasper
makes 2^2/2^(6/5) easier
twin meteorBOT
kaynscereal
atomic jasper
,tex .exp rules
twin meteorBOT
Bonk
atomic jasper
should i do product rule or quotient rule first
wdym
atomic jasper
doesnt matter
atomic jasper
its cuz product rule here doesnt work
there is nothing to product
2 and x are not the same terms, so you cant combine them
atomic jasper
got the answer now?
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
@wild iris Has your question been resolved?
Available help channel!
mellow wigeon
does gcd(ab, ac) = a gcd(b, c) ?
if yes can someone prove it to me please?
wary hull
does gcd(ab, ac) = a gcd(b, c) ?
if yes can someone prove it to me please?
What are the restrictions on a, b, and c?
wary hull
<@1340453306207572073>
Then yes it is true, since ab and ac would have at least a common factor a.
i.e., $\gcd(ab, ac)\ge a$.
twin meteorBOT
mathisfun
twin meteorBOT
mathisfun
wary hull
i.e., b and c are coprime.
wary hull
**mathisfun**
That would be part of the statement here.
wary hull
**mathisfun**
$\gcd(ab, ac)=a\gcd(b, c)$, since the above is true
twin meteorBOT
mathisfun
mellow wigeon
That would be part of the statement here.
what if gcd(b, c) isn't 1 ?
bitter pilot
Just apply Bezouts lemma
wary hull
what if gcd(b, c) isn't 1 ?
It still works.
Because the numbers still have at least common factor of a.
vocal sleetBOT
@mellow wigeon Has your question been resolved?
floral pebble
Could someone please help me with this question?
vocal sleetBOT
Could someone please help me with this question?
oak magnet
You want to write a regex that make stuff that don't end with 01 ?
winged kite
Could someone please help me with this question?
The way to do such problems is to make a regex/dfa that does accept strings ending in 01 and taking the complement of it (flipping the accepting and rejecting states)
vast shale
$\delta(\sqrt{x^{2}+1}-x-1)$ how do u find the roots of this?
vocal sleetBOT
$\delta(\sqrt{x^{2}+1}-x-1)$ how do u find the roots of this?
twin meteorBOT
Tibbs.
vast shale
of $(\sqrt{x^{2}+1}-x-1)$ that is
twin meteorBOT
Tibbs.
vast shale
obviously x = 0 is a root. but is there some sort of formula i can use
hard atlas
set up the equation and solve it
sqrt(x^2+1)-x-1=0
add x+1 on both sides
square
rearrange a bit
vocal sleetBOT
vocal sleetBOT
Available help channel!
floral pebble
Could someone please help me with the problem in the image attached?
floral pebble
I have (b+(a*|b**)b+) so far
snow dune
actually forget that
lilac pebble
what is **?
peak matrix
Does this work? My regex skills are poor ||(b(ab)*)*||
snow dune
my guess would be
b+(ab+) *
peak matrix
Does this work? My regex skills are poor ||(b(ab)\*)\*||
it doesnt :(
oak magnet
:(
lilac pebble
it doesnt :(
why not?
lilac pebble
b\*(ab)\*b* would no ?
it doesn't generate babbab
oak magnet
it doesn't generate babbab
Indeed
peak matrix
does it need to generate all valid substrings? Or does it suffice that it tells if the input string is valid or not
lilac pebble
is there a difference?
peak matrix
is there a difference?
* is greedy, isnt it?
floral pebble
what is **?
I cant do kleene star of a with kleene star of b on discord
It italicizes the text
lilac pebble
oh, you can write \*
lilac pebble
I have (b+(a*|b**)b+) so far
unfortunately this generates baab
snow dune
my guess would be
b+(ab+) *
.
floral pebble
unfortunately this generates baab
Oh dang
peak matrix
I have (b+(a*|b**)b+) so far
this also allows at most one "bab" substring in the text
floral pebble
Im struggling hard with this and I have an exam with this stuff this upcoming Tuesday
snow dune
actaully mine doesnt validate empty string so nvm
lilac pebble
oh
peak matrix
you could probably just use logical or for that or sth like that idk
its one case
(b(ab)*)*
this should still work tho
floral pebble
my guess would be
b+(ab+) *
This worked
How can I get good at this stuff by Tuesday?
peak matrix
How can I get good at this stuff by Tuesday?
practice is the best ig
vocal sleetBOT
@floral pebble Has your question been resolved?
quick island
find the set of values of x satisfying the inequality 3|x-1| < |2x+1|
granite perch
Take positive and negative of modulus
queen root
find the set of values of x satisfying the inequality 3|x-1| < |2x+1|
try squaring both sides
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
quick island
Take positive and negative of modulus
apparently 3 cases
quick island
try squaring both sides
including the 3 in lhs outside of modulus?
granite perch
apparently 3 cases
No?
granite perch
including the 3 in lhs outside of modulus?
Yes
queen root
including the 3 in lhs outside of modulus?
ofc
granite perch
3(x-1) < 2x+1
-3(x-1) < -(2x+1)
quick island
Yes
wait but for ur method
3(-(x-1)) < -(2x+1)
3(x-1) < (2x+1)
ok
thanks @granite perch @queen root
granite perch
Alg
quick island
don't close lemme try it
quick island
Lemme try doing it rq
ok
granite perch
I got same smh
granite perch
try squaring both sides
I think we beter try this
More straightforward
,wolf solve 5x^2 -22x +8 =0
twin meteorBOT
quick island
I think we beter try this
how come it doesn't work here?
granite perch
$\frac{2}{3} <x< 4$
twin meteorBOT
ASda
granite perch
how come it doesn't work here?
I'm not actually sure
quick island
I'm not actually sure
would like to know 🫠
granite perch
Tryna figure it out rn
granite perch
would like to know 🫠
I recently learnt using abs value recently myself
quick island
I recently learnt using abs value recently myself
it's fine
quick island
Ig we just ping helper
kk
queen root
x<=-1/2
-1/2<x<=1
1<x
u excluded 1 and -1/2?
atomic jasper
u excluded 1 and -1/2?
you have to include it into the cases
queen root
then include them
queen root
wow
quick island
x-1=0=>x=1
2x+1=0=>x=-1/2
men what are you doing
quick island
(so 5 cases total)
...
queen root
(why r u speaking like this)
atomic jasper
no reason
quick island
do you understand that part?
nah
twin meteorBOT
Bonk
atomic jasper
what you just said doesnt make sense
granite perch
we take minus and plus
That's what i was taught too
quick island
if |x| = 4
x = -4, and 4
atomic jasper
you mean $|x|=\begin{cases}x\text{ for }x\geq 0\-x\text{ for }x<0\end{cases}$
twin meteorBOT
Bonk
atomic jasper
i know what you mean, it just doesnt make sense what you wrote
granite perch
- and +
- and -
- and -
- and +
quick island
+ and +
+ and -
- and -
- and +
💀
quick island
anyway, lets go back to |x-1|
x-1 and -x+1
atomic jasper
for x<1 we get |x-1|=-x+1
atomic jasper
x-1 and -x+1
yes
so we have 2 cases now, x>1 and x<1
now lets look at the other one
|2x+1|
which two cases do we get here
quick island
2x+1 and -2x -1
atomic jasper
for which x though
quick island
for which x though
x > 1 and x < -1
atomic jasper
no.
quick island
im so confused
atomic jasper
for what x is 2x+1=0
quick island
for what x is 2x+1=0
-1/2
atomic jasper
perfect
now we have our two cases
x>-1/2
x<-1/2
$|2x+1|=\begin{cases}2x+1\text{ for }x\geq -\frac12\-2x-1\text{ for }x<-\frac12\end{cases}$
twin meteorBOT
Bonk
atomic jasper
this is what i was asking for
quick island
oh
atomic jasper
so we have 4 cases
x>1 and x>-1/2
x<1 and x>-1/2
x<1 and x<-1/2
x>1 and x<-1/2
now, which one of these is not possible?
quick island
uh
3 and 4
quick island
whoops
atomic jasper
case 4 is the impossible one
quick island
ye
atomic jasper
x cannot be greater than 1 and less than -1/2 at the same time
atomic jasper
so we have 4 cases
x>1 and x>-1/2
x<1 and x>-1/2
x<1 and x<-1/2
x>1 and x<-1/2
case 1: x>1 and x>-1/2 => x>1
case 2: x<1 and x>-1/2 => -1/2<x<1
case 3: x<1 and x<-1/2 => x<-1/2
this is the 3 cases i outlined earlier
agree now?
quick island
ye
atomic jasper
okay great
now, in these cases, the values are x=-1/2 and x=1 are not in an interval
cuz it can be both
it doesnt which interval we put it in, so im just going to put it in a random one
case 1: x>1 and x>-1/2 => x>=1
case 2: x<1 and x>-1/2 => -1/2=<x<1
case 3: x<1 and x<-1/2 => x<-1/2
now, lets go case by case
in case 1, what does the equation become?
quick island
in case 1, what does the equation become?
wdym?
quick island
oh
atomic jasper
and we assume x>=1 (in this case), so then what do the brackets simplify to?
quick island
3(x-1) < 2x + 1
quick island
x < 4
quick island
1 <= x < 4
quick island
wait can u hold on for 30 seconds
atomic jasper
sure
quick island
because we have the condition that x>=1
ok btw, why x>=1 instead of x>1
quick island
do you even read my messages?
yeah but I don't understand why both aren't </> and =
atomic jasper
wdym?
atomic jasper
cuz i put it in the other interval
quick island
cuz i put it in the other interval
why not both?
atomic jasper
it cannot be in both
quick island
it cannot be in both
y
atomic jasper
but it doesnt matter whcih interval we pick
quick island
ok
crimson jetty
The method you've chosen is to divide the real number line into 3 segments right?
split into 3 cases?
quick island
can it be x > 1, rather than x >=1 and x >-1/2 instead of x>=-1/2
atomic jasper
yes
atomic jasper
can it be x > 1, rather than x >=1 and x >-1/2 instead of x>=-1/2
why?
quick island
omg @crimson jetty u knw flame?
crimson jetty
If so, you will want to choose a partition of 3 disjoint segments to divide the real line into
atomic jasper
like why are we bringing the =
we have to put the x=1 and x=-1/2 into a interval
it doesnt matter which one
quick island
kind of confused
quick island
can I just sketch mb?
atomic jasper
can I just sketch mb?
go ahead
crimson jetty
this is one example of dividing into 3 cases
you don't want to repeat numbers in different cases
atomic jasper
how can we sketch if there can be two possible intervals
just choose one
doesnt matter
crimson jetty
You need to ensure -1 and 1 are in some of the cases though, and not just skip them
quick island
You need to ensure -1 and 1 are in some of the cases though, and not just skip t...
??
quick island
just choose one
ok
crimson jetty
This is your original problem.
3|x-1| < |2x+1|
You want to find the subset of the real numbers for which x satisfies the inequality
One approach (the one you're using) is to split the real numbers into 3 cases to do this
quick island
One approach (the one you're using) is to split the real numbers into 3 cases to...
does this always work
crimson jetty
there is no always
it works in this case though
since you know you can remove those absolute symbols
if you split around x=1 and x=-1/2
quick island
it works in this case though
what's a method for any abs questions
crimson jetty
i drew this with the wrong numbers, but its the same idea
queen root
what's a method for any abs questions
this one about case disjunction
crimson jetty
quick island
this one about case disjunction
elaborate
quick island
yes but I still don't have an explanation why only either -1/2 or 1 should have >= / <= the equal sign. Why not both
atomic jasper
the reason we split at -1/2 and 1 is because they align neatly with the positive and negative cases of the absolute values
quick island
the reason we split at -1/2 and 1 is because they align neatly with the positive...
I get that
bro
the = sign
crimson jetty
yes but I still don't have an explanation why only either -1/2 or 1 should have ...
You are splitting into 3 cases of consideration
why would you want to consider a number twice
in 2 cases
you only need to consider it once
for example, take x = 1
you only need to consider it in either case 2
or case 3
quick island
nah nvm it I'll just learn this w/o fully understanding that equals part cz I lowk don't get it
can y'all help me w sth else
crimson jetty
(-infty, -0.5] u (-0.5, 1] u (1, infty)
(-infty, -0.5) u [-0.5, 1) u [1, infty)
(-infty, -0.5] u (-0.5, 1) u [1, infty)
(-infty, -0.5) u [-0.5, 1] u (1, infty)
Look, there's 4 ways you can split up the real number line to help with this problem
It doesn't matter which
quick island
okay thank you @crimson jetty @atomic jasper @queen root
the variables x and y satisfy the equation y^n = ax^3 where n and A are constants. It is given that y = 2.58 when x = 1.20, and y = 9.49 when x = 2.51
another q
atomic jasper
open a new channel for this
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
im confused how it went from 81(10/9sec\theta to just \sqrt(sec^2\theta)
vast shale
they skipped so many steps at once
silk osprey
factor out 10
silk osprey
$\cancel{81}\left(\frac{100}{\cancel{81}}\right)$
twin meteorBOT
knief
vocal sleetBOT
silk osprey
sqrt(100) =10
vast shale
but they don't take the squart root of sec^2x
silk osprey
by factoring out 10 you factor 100 from the sqrt
$\sqrt{\cancel{81}\left(\frac{100}{\cancel{81}}\right)\cdot \sec^2 \theta - 100} = \sqrt{100(\sec^2 \theta - 1)}$
twin meteorBOT
knief
vocal sleetBOT
Available help channel!
velvet jolt
yooo
simple mason
What do you know about parallel lines
velvet jolt
not much
i forgot everyting
about
qudarilatearal
proofs
sorry for dumb spelling
simple mason
Ok but I am asking about parallel lines
simple mason
You say not much
So you know sum right?
simple mason
Parallel lines can not intersect
velvet jolt
i mean if they are cut by a transversal
simple mason
Ok good point, you will need this in the proof.
So according to you if I could proof that BAC = ACD and DAC = ACB
Then that should be enough to tell me that AB || CD and BC || AD
Now what do you know about proofing congruent triangles
?
@velvet jolt are you still here?
simple mason
Now what do you know about proofing congruent triangles
So ...?
velvet jolt
bro this doesn’t work
velvet jolt
So ...?
I know everything
about that
But lol
lol
Look
It’s says im wrong
Whenever I put that
simple mason
I think because that's the right time yet to put that here
velvet jolt
Bro can you just tell me the answer 💔
I want to go to sleep
It’s due today
I’m tired
I don’t kno how
simple mason
About congruent triangles
If you know how to prove that
$$\triangle ABE\congurent \triangle CDE$$
twin meteorBOT
Sherif Player
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vocal sleetBOT
Bro can you just tell me the answer 💔
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.
vocal sleetBOT
Bro can you just tell me the answer 💔
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
velvet jolt
Alright sorry damn
Got everybody in this channel
ok man so what do I need to do
for the first step
simple mason
Just prove ABE is congruent to CDE
That will automatically tell you that angle BAE is equal to DCE
velvet jolt
no it doesn’t let me
simple mason
Which says that AB || CD
simple mason
Yeah because you haven't proven that the 2 lines are parallel
You need to prove first that they are equal be proving congruent triangles
simple mason
Then it well tell you that the 2 lines are parallel
glass surge
weary inlet
What have you tried so far
weary inlet
hold on i misread the question
wary hull
How did you get this?
wary hull
There are 6 possible digits for the first slot...?
glass surge
how
wary hull
1, 9, 8, 3, 7, 4...?
glass surge
but we have to remove an even number? or not
cuz an even number is used for the last digit
wary hull
all except 0
You could still include it (range isn't restricted to only 4-digits) but yes this is the concept
wary hull
cuz an even number is used for the last digit
Where does it say
vocal sleetBOT
Available help channel!
glass surge
You could still include it (range isn't restricted to only 4-digits) but yes thi...
wdym
wary hull
positive *even* numbers
I cannot read
weary inlet
its just the order in which you multiplied resulted in a bit of confusion thats all
glass surge
I think your answer was fine
but the answer was supposed to be 3020😭
weary inlet
what
wary hull
Then answer is fine...? I have feeling this is casework
glass surge
wary hull
This is precisely what I was thinking
glass surge
cases😞😞🔫
glass surge
This is precisely what I was thinking
dyk how it leads to that solution
vocal sleetBOT
@glass surge Has your question been resolved?
glass surge
<@&286206848099549185>
glass surge
Switch a digit 🗣️
wym
vocal sleetBOT
@glass surge Has your question been resolved?
hidden turret
lmao i got 7200
hidden turret
I keep arriving at 3200<:soynoo:885331816322592809>
wait i got 3200 the second time around
no clue what you are doing wrong
i am pretty sure you are right
glass surge
.close
opaque shell
vocal sleetBOT
wary hull
shouldn't it be 0
Yep
wary hull
why does desmos show this undefined
Desmos can be trippy sometimes with small approximations
vocal sleetBOT
@opaque shell Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
primal hedge
vocal sleetBOT
primal hedge
why is this wrong
heavy grail
Bc the second term is a corrupt government
primal hedge
huh