rearrange for (cosx)^3
#help-13
subtle hinge
oblique lynx
ok, so do i get
$$
3\cos^2(2x)=\frac{3}{2}(1+\cos4x)
$$
wraith daggerBOT
konxmok
stone flame
correct
stone flame
let u = 6x
subtle hinge
just substitute 2x for x in this eqn and rearrange
oblique lynx
it should lead to this form
oblique lynx
just substitute 2x for x in this eqn and rearrange
what
cedar kilnBOT
@oblique lynx Has your question been resolved?
dark jackal
Y=x^2+x here domain is R
cedar kilnBOT
Y=x^2+x here domain is R
lyric narwhal
I got range and domain confused nvm
dark jackal
Whattt?
dark jackal
How to check function is onto or not?
dark jackal
Yes
hollow minnow
But the codomain is R
hollow minnow
?
dark jackal
I meant many points in co domain will not have pre image
hollow minnow
Onto/surjective means every elements in the codomain can be hit
dark jackal
so I have to check in reverse?
hollow minnow
You just haev to show there exists an element in the codomain that cannot be hit by any element in the domain R.
For example, (-1\in\R)
wraith daggerBOT
Pure
hollow minnow
[x^2+x=-1]
wraith daggerBOT
Pure
hollow minnow
solve for x and show it's no in R
dim tiger
checking if the function is onto/surjective or not you have to check the codomain
if the codomain and the range are the same then the function is onto
otherwise it is not
dim tiger
np i didnt do anything you and the others did the whole work
dark jackal
.close
stiff summit
i need some help here
cedar kilnBOT
i need some help here
stiff summit
only thing that i could think of to try was the binomial expansion of both and try see if the powers add up to 3n but i can't get to an answer
mortal hemlock
!original
cedar kilnBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
stiff summit
oh well
need to find N
my approach was to write it as x1 + x2 + x3 = 3n, and then the number of possible solutions to this would be the value of N
selecting x1 from the A's, x2 from the B's, and x3 from the C's
<@&286206848099549185>
alpine rune
i need some help here
what'd you try?
stiff summit
what'd you try?
effectively nothing honestly, i dont understand where to start
alpine rune
ok
stiff summit
this is the original question
stiff summit
alright
alpine rune
do you know the basics of binomial theorem
stiff summit
yes
alpine rune
sweet
stiff summit
so the left one is straightforward to expand
for the right one i know about the extended version, 1 + nx + n(n-1)/2 x^2 + ..
stiff summit
in the left one?
alpine rune
yeah
stiff summit
yeah the left one doesnt have it
alpine rune
nor would the right one
stiff summit
but maybe the sum from each
like they can combine to give 3n
which is what i am stuck at
alpine rune
yeah but maybe you got to the wrong spot while simplifying the question in your manner
alpine rune
n is the coefficient of x^3n in (1+x+x^2+x^3...x^2n)
stiff summit
number of possible solution to this is same as asking coefficient of t^3n in (x^0 + x^1 + ... x^2n)^3
stiff summit
yes
stiff summit
one side would be 1-3x^2n+1
how?
alpine rune
expand the left bracket in the equation you formed
alpine rune
other would be (1+3C1x + 4C2x^2 + 5C3x^3) and so on
ok I gotta go but I think you could take it from here
stiff summit
yeah i'll try
stiff summit
one side would be 1-3x^2n+1
oh since the 4n+2 and 6n+3 definitely won't sum to give 3n
alpine rune
yeah
rich kestrel
In a store there are globes from 3 suppliers: 20% from the first supplier, 60% from the second supplier and 20% from the third supplier. Each supplier also delivers globes that break during transport: the first supplier delivers 3% of broken globes, the second 2%, and the third 1%.
a) Calculate the probability that a globe chosen at random from the store will be broken:
Answer
b) Calculate the probability that a defective globe comes from the first supplier:
Answer
c) Calculate the probability that a defective globe comes from the second supplier:
split pike
In a store there are globes from 3 suppliers: 20% from the first supplier, 60% f...
denis you could assume the total amount of globes supplied be 100
then you could just calculate according to the q
rich kestrel
i solved how i learnt at uni it could help if someone can verify my answers
i got 0.02 for a)
split pike
okay
split pike
i got 0.02 for a)
correct
rich kestrel
i have to use with decimals instead of percent
split pike
Ig q says something different
the first supplier delivers 3% of broken globes, the second 2%, and the third 1%.
@rich kestrel i dont think 3% is the % of the globes supplied by the supplier
rich kestrel
that s the problem
the answers don't have to make sense or idk why you don't think it's 3%
split pike
So I don't think our answers are correct
Because I took an assumption that broken globes % is % of globes supplied
rich kestrel
the amount supplied is 20 60 20
cedar kilnBOT
@rich kestrel Has your question been resolved?
rich kestrel
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
turbid wren
a line that's not passing through (p , q) where both coordinates are both negative is...
a. y = x + 2
b. 3y = 4x -2
c. x + y = 2
d. 3y - 4x = 2
e. x - y = 2
turbid wren
do we determine by its gradient?
tropic oxide
easiest to just graph them all
pulsar dagger
or by intuition which one where if x and y are both negative the equation will never satisfy
turbid wren
ah, i just realised it, is it just the same as projecting linear programming?
turbid wren
then how do i graph it?
tropic oxide
you graph the straight lines the same way you would normally graph a straight line.
linear programming has nothing to do with it.
cedar kilnBOT
cedar kilnBOT
Available help channel!
chrome lotus
Anyone cna help?
cedar kilnBOT
Anyone cna help?
granite knoll
<@&268886789983436800> spam
cedar kilnBOT
@chrome lotus Has your question been resolved?
dire geode
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
Available help channel!
crimson sedge
what does this backslash represent ?(don't tell me the answer)
violet flume
what does this backslash represent ?(don't tell me the answer)
It's the set difference.
read "less"
green thorn
yeah, its set minus
violet flume
yes.
cedar kilnBOT
cedar kilnBOT
Available help channel!
calm hedge
cedar kilnBOT
calm hedge
for B)
its just asking for A,B,C. find ones that have a common one
like i just found {8,11}
right?
or no
coral jewel
yes, 8 and 11 is correct
calm hedge
ok
lets say
if I find AB
for example 1, 2 and 3
what if C has 1, 2 and doesnt have 3
i just get rid of the 3
right?
coral jewel
yes
proud jungle
Yes
calm hedge
what about f?
A intersection B are in brackets so im assuming i do that first
which is just 8,11
and then that to the union of C
so do i just do {8,11} addition into C whatever that is
tropic oxide
and then that to the union of C
the union of that with C*
tropic oxide
nothing, the asterisk is just me correcting your wording
tropic oxide
but yes $A \cap B = {8,11}$ and so $(A\cap B)\cup C = {8,11}\cup C$
wraith daggerBOT
Ann
calm hedge
ok đ
turbid wren
can anyone help me with this one?
cedar kilnBOT
can anyone help me with this one?
turbid wren
the root one
crimson sedge
hint: use the fact that $\s{ab} = \s a \cd \s b$
wraith daggerBOT
turbid wren
still don't get itđđđ
crimson sedge
and for an easier idea, convert $\s[m]{a^n} = a^{\ff nm}$
wraith daggerBOT
crimson sedge
still don't get itđđđ
okay I'll guide you for the first steo
crimson sedge
[ \nest{7}{\inline#1{\sqrt{6#1}}}{\hdots} = \s6 \cd \nest{7}{\inline#1{\sqrt{6#1}}}{\hdots} ]
crimson sedge
so how<:happy_cry_cat:636407813144576010>
can you repeat the process above and then rewrite the whole thing into a more readable notation?
supple flume
should be 2 square roots on the outside
turbid wren
can you repeat the process above and then rewrite the whole thing into a more re...
like that?
,rotate
wraith daggerBOT
supple flume
there has to be two square roots on the outside as its not just covering the 6 on the original
it covering both
turbid wren
now I'm completely lostđ
wraith daggerBOT
cursive sedge
crimson sedge
should be fixed
cursive sedge
cedar kilnBOT
@turbid wren Has your question been resolved?
uneven pagoda
Assume your first root sequence converges to x. Then sqr(6*x) = x
Solve for x
For the second sequence:
sqr(8:y) = y
minor crystal
hi dumb question but how to do this?
cedar kilnBOT
hi dumb question but how to do this?
minor crystal
opal basin
Have you heard of vieta's formulas? (If not don't worry)
minor crystal
Have you heard of vieta's formulas? (If not don't worry)
yes
how can i use it here when we need the other root
oh lol okay i see
minor crystal
Have you heard of vieta's formulas? (If not don't worry)
do u need me to solve for alpha?
from vietas
a + b = 1/3
ab = -1/3
wheat ocean
you don't really need it i think
minor crystal
i couldnât see how vietas would help when i tried it cuz the question isnât a linear combination (or any combination) of two roots
and those roots arenât repeated cuz discriminant > 0
opal basin
You are right probably, let me think actually
wheat ocean
i would solve it like this: $3a^3-4a^2=a(3a^2-4a)=a(3a^2-a-1-3a+1)=a(1-3a)=-3a^2+a=-1-(3a^2-a-1)=-1$
wraith daggerBOT
Alisia
wheat ocean
we just need that a is a root of equation f(a)=0
crimson sedge
<:meeku:1020766290434072677> <:meeku:1020766290434072677>
$f(\alpha)=3\alpha^2-\alpha -1=0$
Solve for alpha
minor crystal
i would solve it like this: $3a^3-4a^2=a(3a^2-4a)=a(3a^2-a-1-3a+1)=a(1-3a)=-3a^2...
i wouldâve never done that 
wraith daggerBOT
ĹĂŞro
crimson sedge
You can use quadratic formula
minor crystal
yes i know thatâs too convoluted anyway
itâs about solving it in a minute
youâll have something like (1 +- sqrt(13))/6
then youâre putting all that in 3a^3 - 4a^2
crimson sedge
Yea there must be some easier way
minor crystal
i would solve it like this: $3a^3-4a^2=a(3a^2-4a)=a(3a^2-a-1-3a+1)=a(1-3a)=-3a^2...
this one i guess ^
i donât get it though 
i get the algebra but hmm
wheat ocean
i donât get it though <:melody:880877652574097489>
what exactly?
solid juniper
why do you need to solve these problems in one minute
minor crystal
why do you need to solve these problems in one minute
idk they just have u solve these in a minute or 2
my schoolâs weird lol
not in a good way maybe
solid juniper
minor crystal
what exactly?
like the intuition
crimson sedge
**Alisia**
Yes thatâs good
I also thought of factoring the a^2 out
Because you want to use the things that are given
wheat ocean
i think the main point here is to just use that 3a^2-a-1=0 without evaluating the roots
crimson sedge
i think the main point here is to just use that 3a^2-a-1=0 without evaluating th...
Thatâs right
wheat ocean
because it would be harder other way
minor crystal
but then you knew vietaâs wouldnât work either
did u check it or is this what u thought of after u realized u arenât evaluating roots
crimson sedge
I think vieta doesnât even work in this case since a is not 1
I mean the coefficient a of ax^2
minor crystal
it works for all a
vietaâs doesnât work cuz itâs like doing it with the quadratic formula
(in this case)
okay anyway, thanks alisia!
wheat ocean
vieta's formulas involve both roots while we need only one certain
no problem, happy to help đ
also, the other (a bit more easy) way is to divide polynomial 3a^3-4a^2 by 3a^2-a-1 and the remainder will be an answer
because 3a^3-4a^2=(a-1)(3a^2-a-1) - 1
minor crystal
also, the other (a bit more easy) way is to divide polynomial 3a^3-4a^2 by 3a^2-...
i donât get this either
i know how to poly divide
but hmm i donât get the part where you know the poly division of those 2 will give a remainder that is the answer
wheat ocean
if that would be bad task then we would get a remainder that depends on x so it wouldn't work đ don't consider that as an universal method, just another way
and about intuition... only practice will do đ
minor crystal
if that would be bad task then we would get a remainder that depends on x so it ...
đyouâre right
thanks~
minor crystal
and about intuition... only practice will do đ
what is this though?
not sure where i even see questions like this
wheat ocean
what is this though?
i think that's connected with quadratic functions and polynomials, i often see idea like this there
cedar kilnBOT
Available help channel!
cunning phoenix
I tried to solve the inequalities but I don't understand what range will k drop in
wraith daggerBOT
crimson sedge
I tried to solve the inequalities but I don't understand what range will k drop ...
show your work
tropic oxide
there is actually a very elegant way to solve this
but yes @cunning phoenix show what you did
zenith nacelle
can i give a hint?
crimson sedge
be patient
tropic oxide
let op share his work first
zenith nacelle
ok
cunning phoenix
I did this
crimson sedge
,rcw
wraith daggerBOT
cunning phoenix
there is actually a very elegant way to solve this
I would like to know this
cunning phoenix
Ye
tropic oxide
that gets you that the VERTEX is at or to the left of x=4.
not that both roots are.
zenith nacelle
1,2,3 do satisfy
cunning phoenix
Noted
tropic oxide
in order to have two roots which are both real and be ⤠4, you need:
- D > 0
- f(4) ⼠0
cunning phoenix
1,2,3 do satisfy
đ Im dying from 30 mins that my 3 2 1 = 7 and I marked the wrong ans
zenith nacelle
sad
cunning phoenix
in order to have two roots which are both real and be ⤠4, you need:
- D > 0
- f...
I tried f(4) > equal 0
Equation gets bad bad
cunning phoenix
its just a quadratic still no?
Quadratic with k which have imaginary roots tho
tropic oxide
Quadratic with k which have imaginary roots tho
that doesnt sound "bad" to me at all
if it's a quad inequality with imaginary roots this just means it holds either always or never
cunning phoenix
The question asks for +ve real values of k so?
cunning phoenix
if it's a quad inequality with imaginary roots this just means it holds either a...
But I wont get anything out of it, it's correct technically but
tropic oxide
let me take a look at it myself
cunning phoenix
Idk how it helps in my question
tropic oxide
16 - 8k + k^2 + k - 3 ⼠0
k^2 - 7k + 13 ⼠0
discriminant = 49 - 4 * 13 = -3
yeah so this holds for all k, simple as that
and that just leaves the discriminant of the original eq
which we also want to be >0
tropic oxide
it is necessary yes
cunning phoenix
it is necessary yes
Like why, the question asks for +ve real values so
cunning phoenix
Ah I see I get your point
Thank you anyways
It's kinda analogous to when if both the roots lie between x1 and x2 we do f(x1).f(x2) > 0
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
muted plaza
hi, idk what i have to do here, nor how is it i need to find 3x3 matrices
muted plaza
i know how to rotate points tho
opal basin
Do you understand why the matrices are 3x3 while the vectors are 2-dimensional?
muted plaza
nope
opal basin
what kind of class is this btw, I've only ever seen this in the context of graphics programming
muted plaza
linear algebra
which is used for graphics and whatnot, yes
but i'm not coding anything here xd
opal basin
Normally when you use matrices, the origin doesn't change. Here you want to apply a transformation though, so to do this the vectors have a third entry explicitly being 1
That way you can translate
opal basin
So you should see (-1, -1) as (-1, -1, 1)
and then find some matrix to translate points by (-4, 4)
So after the matrix multiplication (-1, -1, 1) should become (-5, 3, 1)
muted plaza
wait what
opal basin
btw, are you right-multiplying vectors? (so M * v, and not v * M)
muted plaza
So after the matrix multiplication (-1, -1, 1) should become (-5, 3, 1)
this matrix?
opal basin
Actually this one
muted plaza
oh
opal basin
It also works for (-1, -1, 1)
muted plaza
why
opal basin
So the 1 in the third entry stays
and the the other entries in the right-most column get added
So this is the identity matrix + a translation
muted plaza
i sort of understand
opal basin
What would happen if you were to calculate M * (x, y, 1)
muted plaza
(x+4,y+4,4)?
opal basin
yeah, (x-4, but that was probably a typo)
muted plaza
dehydrated brain goes brrr
opal basin
so this matrix translated the point (x, y) by (-4, 4)
opal basin
Yes, now the rotation matrix
what does rotating by 180 degrees look like in matrix form?
opal basin
You can find the 2d matrix first
opal basin
Yes, for the 3x3 matrix you want to go from (x, y, 1) to (-x, -y, 1)
so what should the entries be to leave the 1 alone
opal basin
Yes, 0 instead of 8
muted plaza
yes xd
opal basin
And now the final translation matrix
muted plaza
wait but what do i use with that intermediate matrix
opal basin
How do you mean?
The rotation works by first translating a point by (-4, 4) then rotating and then translating by (4, -4)
muted plaza
the fact that it's all matrices and not vectors for rotations make it harder to see for me xd
opal basin
ah, take your time
opal basin
It should be (x-4, y+4, 1) (oh a 1 at the end as well)
muted plaza
yes yes i remember the 1 at the end
i was just thinking that the -4 was at the second row
oh right
translation
- the first time
- the second
opal basin
No, the point you rotate about is (4, -4), so you first translate by -(4, -4) = (-4, 4)
muted plaza
the fact that it's all matrices and not vectors for rotations make it harder to ...
i told you having no vectors was weird xd
opal basin
Yeah, I got used to it with computer graphics
muted plaza
that reminds me, how xd
opal basin
(this is my final year of pre-university), but I've always liked programming and about 5 years ago I wanted to try 3d and came across 3blue1brown's videos, that's where I got the basics from
and the rest is from the internet as well
muted plaza
good to see 3B1b videos help someone xd
i only watch them then forget about them cough
ok so
what about the third matrix
is it the inverse of the first one?
wait that makes little sense xd
opal basin
it is, but explicitly calculating it might be a bit painful
muted plaza
oh
muted plaza
it is, but explicitly calculating it might be a bit painful
dw, i can use software xd
its use is permitted
opal basin
You can find the result without using any programs or calculations
muted plaza
how
opal basin
this matrix has to translate by (4, -4), right?
muted plaza
yes?
muted plaza
the identity matrix except for the last column
opal basin
Yes, the first two entries of the last column were the translation vector
this holds in general
this is from wikipedia:
muted plaza
ah, the math pages from wikipedia, my old enemy
muted plaza
it's always been hard to understand/parse math concepts in wikipedia to me, dunno why
opal basin
yeah, I don't think it's always the best resource to learn from
muted plaza
so
muted plaza
You can find the result without using any programs or calculations
what did you mean with this
muted plaza
oh so the same matrix is its inverse?
muted plaza
Actually this one
oh
i'm blind
wait
for the initial translation, dont i have to substract the point?
opal basin
Yes, point is (4, -4)
muted plaza
i need to sleep so badly xd
opal basin
what time is it for you?
muted plaza
14:18
i'm going to eat after this then sleep
and maybe when i wake up i see it's already night and go sleep more
opal basin
ahh, okay
Do you think you can calculate the combined matrix?
nvm, you can use software
(mind the order though)
muted plaza
i mean yes, but it's multiplying the matrices right?
opal basin
Yes
muted plaza
a la "PMP^-1"
opal basin
Yeah, depends on what you consider as P
opal basin
what do you get after multiplying the matrices?
muted plaza
i wait xd
opal basin
Isn't this the reverse order
right most matrix should translate by (-4, 4)
matrices are evaluated from right to left
muted plaza
opal basin
Yes, but the right most matrix should translate by (-4, 4), not (4, -4)
muted plaza
why should it go in reverse?
opal basin
If you have A * B * C, then if you multiply by a vector you do A * (B * (C * v))
the vector first encounters C
opal basin
you can just put brackets where-ever you want when working with matrices
muted plaza
wait a sec
opal basin
You can't swap the order of multiplication though
muted plaza
You can't swap the order of multiplication though
i know
isnt it literally this tho??
opal basin
I'm not sure, not very familiar with the notation
muted plaza
I'm not sure, not very familiar with the notation
tbh, i dont like how they've drawn it there either
the linear transformation represented by the red arrow is equal to those three multiplied
doesnt matter seems you're right
opal basin
Oh, this is where you PMP^-1 came from
muted plaza
yes xd
iirc linear transformations and the like also appear in 1b3B's videos about proyections
i cant write
ok so i'll switch it up
opal basin
Yeah, you can always multiply it by some vectors to see if it gives the correct result
opal basin
Youre welcome
muted plaza
isnt it literally this tho??
my current book, as you can see, it's not the best at visualising/explaining
opal basin
oh god
muted plaza
exactly
opal basin
You need a lot of matrices for this one
only the first and last one actually require a 4x4 matrix
others can be done with 3x3
muted plaza
huh?
opal basin
for the last translation the same principle applies as before, but with a 4x4 matrix
muted plaza
wait why does the first one require a 4x4 one
opal basin
because it's scaling about a point that's not the origin
so the origin doesn't get mapped to the origin
opal basin
the first matrix will be a translation, then scale, then translation
For all of this you will need 7 matrices
opal basin
Maybe you should get some rest before you try this
muted plaza
if i sleep i dont know if i'll wake up xd
question
you said 7 matrices, is it because of the 3 rotations?
i imagine it is so
opal basin
Yeah, the first transformation is 3 matrices and the other 4 each have 1 matrix
muted plaza
i think i'll close this for now, i need to move
muted plaza
Yeah, the first transformation is 3 matrices and the other 4 each have 1 matrix
ty again
.close
cedar kilnBOT
rocky umbra
I do some proofs and always end up with some "strange" numbers like this. Now I need to know which one is bigger, how would you calculate?
cedar kilnBOT
tropic oxide
!msgdel
cedar kilnBOT
The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.
rocky umbra
I do some proofs and always end up with some "strange" numbers like this. Now I need to know which one is bigger, how would you calculate?
This was message
tropic oxide
yeah but you deleted it
so you screwed up the system
the channel will sham shut on you
just open a new one
this happens all the time
rocky umbra
đ
cedar kilnBOT
Available help channel!
smoky falcon
how did the angles proven to be equal ?
cedar kilnBOT
how did the angles proven to be equal ?
hollow minnow
Some triangle shenanigans
mighty shuttle
the line Fn is perpendicular to the plane
mortal hemlock
similar triangles
mighty shuttle
similar triangles
yes, but honestly that's not necessary
smoky falcon
is there a Law name ?
mighty shuttle
is there a Law name ?
let the other angle of the small angle containig theta be x
x+ theta=90
crimson sedge
if you want to do it the dumb way you could
mighty shuttle
also x+y=90(Where y is the angle the force component makes with the plane)
so y=theta
crimson sedge
the third angle in that triangle formed by the g and the original theta is like
minor crystal
Notice that the red lines are perpendicular to their yellow counterparts
crimson sedge
theta+ 90 + x = 180
minor crystal
so the angle between the yellow = angle between their perpendicular counterparts
smoky falcon
i started a war
minor crystal
you can see it by rotating your frame
hollow minnow
three helpers giving 3 different approaches 
crimson sedge
ok ye im dipping
mortal hemlock
this is beautiful
crimson sedge
have fun boys and gals
mighty shuttle
Im at 1st year uni i need to be fancy
I'd suggest you give short solutions instead, keep them as simple as possible
smoky falcon
Notice that the red lines are perpendicular to their yellow counterparts
so this ?
split pike
Im at 1st year uni i need to be fancy
which univ?
crimson sedge
also u probs dont even need to explain anything
this is physics, physicists dont really care about your geometry as long as u do it right
smoky falcon
which univ?
Lebanese uni in lebanon
smoky falcon
this is physics, physicists dont really care about your geometry as long as u do...
yes u r right but a love basics
and going thro them give me a good base to build on
and just remembering the old stuff
what ur thoughts on that ?4
hollow minnow
crimson sedge
^
hollow minnow
Beautiful
crimson sedge
this or kannas method
smoky falcon
thanks pure. I flattered
hollow minnow
smoky falcon
wait whats flattered mean Im not native english
crimson sedge
Lebanese uni in lebanon
اŮŮŮع؊ Ů٠اŮ٠بتŮŘŻŘą ŘŞŘŻŮŘą اŮŮ ŘŤŮŘŤ اŮاؾŮŮ ŮŮŮŘł اŮŘ´ŮŮ Ůتبؚ اŮ؏اذبŮŘŠ ŮاŮزاŮŮŘŠ تبŮŮ ŘŤŮتا
ببساء؊
hollow minnow
,w flattered
wraith daggerBOT
hollow minnow
huh
smoky falcon
huh is that a good thing ?
crimson sedge
wait whats flattered mean Im not native english
English help channel time 
smoky falcon
اŮŮŮع؊ Ů٠اŮ٠بتŮŘŻŘą ŘŞŘŻŮŘą اŮŮ
ŘŤŮŘŤ اŮاؾŮŮ ŮŮŮŘł اŮŘ´ŮŮ Ůتبؚ اŮ؏اذبŮŘŠ ŮاŮزاŮŮŘŠ تبŮŮ ŘŤŮ...
aha thanks
split pike
اŮŮŮع؊ Ů٠اŮ٠بتŮŘŻŘą ŘŞŘŻŮŘą اŮŮ
ŘŤŮŘŤ اŮاؾŮŮ ŮŮŮŘł اŮŘ´ŮŮ Ůتبؚ اŮ؏اذبŮŘŠ ŮاŮزاŮŮŘŠ تبŮŮ ŘŤŮ...
english?
smoky falcon
Im gonna close if u dont mind
crimson sedge
same as what the others said except translated to Arabic which I assume is their native language
crimson sedge
Im gonna close if u dont mind
yes sure
smoky falcon
I will probably come back
hollow minnow
'I'm flattered' just means you feel proud because someone said smth good about you
.close
smoky falcon
.close
cedar kilnBOT
hollow minnow
hahaha
minor crystal
smoky falcon
.close
crimson sedge
no type it more it might close harder
cedar kilnBOT
Available help channel!
mental zephyr
cedar kilnBOT
mental zephyr
I need to find B , C , D
mortal hemlock
!status
cedar kilnBOT
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
1
mortal hemlock
can you find a triangle similar to OAB?
mental zephyr
oh its a rectangle I forgot to mention
mortal hemlock
can you find a triangle similar to OAB?
.
mental zephyr
can you find a triangle similar to OAB?
yes
mortal hemlock
where
mental zephyr
DOC
mental zephyr
why do I need triangles
cedar kilnBOT
mortal hemlock
it gives me a triangle with a right angle
and then you have a similar triangle with OAB and BCC'
cedar kilnBOT
Available help channel!
ripe ermine
"A polynomial of degree one is called a linear polynomial.
Some more linear polynomials in one variable are 2x â 1, 2 y + 1, 2 â u. Now, try and
find a linear polynomial in x with 3 terms? You would not be able to find it because a
linear polynomial in x can have at most two terms. So, any linear polynomial in x will
be of the form ax + b, where a and b are constants and a â 0" This line is from my maths book and I have some confusion here... Linear polynomial is a polynomial with degree 1, so how does having more than two terms affect the degree...Like I can have it in the form ax + bx + c? Second thing is that, in every example the polynomial is of the form ax + b...why not ax + bx or ax + by?
vestal hedge
"A polynomial of degree one is called a linear polynomial.
Some more linear poly...
so here is the thing
lets consider ax+bx+c
isnt it same as (a+b)x+c?
and lets say a+b = d
then its the same as dx+c
which is the base form of ax+b
ripe ermine
woww woowww! Never thought it that way!
vestal hedge
ax+bx is same as (a+b)x
ripe ermine
Interesting stuff!
vestal hedge
lets say a+b = d
then we get dx
dx+0 is still the same dx
dx+0 is that same base form of ax+b
ripe ermine
and can I have two different variables? in one polynomial?
vestal hedge
so basically, anything you make up we can bring to the base form
vestal hedge
and can I have two different variables? in one polynomial?
its gonna be with two variables, a different thing
the definition you are given in the book is about single variable polynomials
I dont think you should go into that stuff if you are just starting polynomials tbh
just think of single variable for now
blazing willow
Specify the value area of the function
y= (x-7)^0
cedar kilnBOT
Specify the value area of the function
y= (x-7)^0
blazing willow
plssss help
cedar kilnBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
blazing willow
mortal hemlock
do you mean the domain and range?
blazing willow
maybe
blazing willow
do you mean the domain and range?
blazing willow
do you mean the domain and range?
i I think the second option
mortal hemlock
but anything to the power 0 is 1
so how could the range be anything other than 1?
if they mean the domain it makes more sense
blazing willow
idk iâm scared
mortal hemlock
can x be 7?
blazing willow
yes
cedar kilnBOT
@blazing willow Has your question been resolved?
cedar kilnBOT
@blazing willow Has your question been resolved?
blazing willow
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
hot rampart
How can I solve $3^x+4x+5=0$?
cedar kilnBOT
How can I solve $3^x+4x+5=0$?
wraith daggerBOT
Faq
hot rampart
Not like graphing or numerical method
hollow minnow
You'd do some lambert W shennigans
opal basin
Isnt there a video by blackpenredpen?
hot rampart
Oh let me check that out
cedar kilnBOT
cedar kilnBOT
Available help channel!
sharp sequoia
whats the answer for this
cedar kilnBOT
whats the answer for this
sharp sequoia
mortal hemlock
!noans
cedar kilnBOT
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.
sharp sequoia
nvm i got it its 0
cedar kilnBOT
@sharp sequoia Has your question been resolved?
severe igloo
Yo I just solved a linear algebra proof and thought I could get some confirmation or a better proof if possible, since it feels like I kinda cheated my way to it
severe igloo
$\text{Consider general vector} (w) in (V).
[w = a_1 v_1 + a_2 v_2 + a_3 v_3 + a_4 v_4]
If we make the assumption that (span(v_1 - v_2, v_2 - v_3, v_3 - v_4, v_4) = V), then we can also write w as
[w = c_1 (v_1 - v_2) + c_2 (v_2 - v_3) + c_3 (v_3 - v_4) + c_4 v_4]
[w = c_1 v_1 + v_2 (c_2 - c_1) + v_3 (c_3 - c_2) + v_4 (c_4 - c_3)]
By equating the two, we can determine that:
[a_1 = c_1, c_2 - c_1 = a_2, c_3 - c_2 = a_3, c_4 - c_3 = a_4]
And with some further algebra:
[c_1 = a_1, c_2 = a_2 + a_1, c_3 = a_3 + a_2 + a_1, c_4 = a_4 + a_3 + a_2 + a_1]
Hence as we can express all (c_1, c_2, c_3, c_4) in terms of (a_1, a_2, a_3, a_4), which we know exist as (v_1, v_2, v_3, v_4) spans V, it thus follows that (span(v_1 - v_2, v_2 - v_3, v_3 - v_4, v_4) = V).$
wraith daggerBOT
Shehab
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
mighty drift
that's the idea yes, but the wording is a little off:
Assume w is in the span
Then the linear combination can be solved for as linear combinations of the ai
Since the ai exist, the ci exist
Well no, the ci exist because you assumed so
opaque harbor
what you want to do is define the ci as you found them at the end of your working
mighty drift
instead, take w as a linear combination of the vi, and write it as a linear combination of the second set of vectors
therefore argue the ci exist because the ai do, without first assuming the ci exist in order to solve for them
mighty drift
what you want to do is *define* the ci as you found them at the end of your work...
which, in practice, translates to doing this
severe igloo
From my (relatively poor) understanding, I assume defining the ci would equate to expressing them in terms of ai?
severe igloo
instead, take w as a linear combination of the vi, and write it as a linear comb...
Although this would suffice too
opaque harbor
it would be plucking them out of thin air in terms of ai yes
what bezier is proposing is you start writing w = a1v1 + a2v2 +...
and then add / subtract the same term w = a1v1-a1v2 + a1v2 + a2v2...
and collect terms (v1-v2) etc.
mighty drift
From my (relatively poor) understanding, I assume defining the ci would equate t...
that's the only way of defining them that could work.
Since they must depend on the ai
severe igloo
Ah okay okay
opaque harbor
what bezier is proposing is you start writing w = a1v1 + a2v2 +...
and then add ...
which avoids the 'plucking them out of thin air' issue
severe igloo
So no assuming, just try to bring it out naturally?
opaque harbor
yeah
mighty drift
or skydrop it
It's technically a correct proof
proofs need not explain where they come from
Though for teaching purposes, it is better if they do
mighty drift
but you as the student, can skydrop it and produce a correct proof
because you argue this solution works, without explaining where you got that solution from
severe igloo
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
gloomy bough
cedar kilnBOT
inland sky
I can plug in two and get a number
which number can you plug in and run into a problem?
gloomy bough
idk thats why I am here for help
warm marsh
Are there more options are just these 5?
inland sky
Hint: when the denominator of a fraction is 0, that makes the function undefined
gloomy bough
what it means by function is undefined
warm marsh
I think there is a mistake in the question because x+3 will cancel out and it is a constant function
inland sky
I think there is a mistake in the question because x+3 will cancel out and it is...
it's still undefined at some value with a hole
gloomy bough
I think there is a mistake in the question because x+3 will cancel out and it is...
its ACT question they always make tricky question
warm marsh
it's still undefined at some value with a hole
there are no holes in a constant function
warm marsh
isnt the function f(x) = 2
gloomy bough
guys chill out please
inland sky
we're chill
anyway, set the denominator equal to 0 and solve for x. that is how you do this problem
gloomy bough
thats all?
inland sky
yes
gloomy bough
dang
warm marsh
if you are talking about the denominator being zero when x = -3, well so will the numerator and applying the limit you will still get a well defined value of 2
gloomy bough
thank you
warm marsh
I would still recommend asking your teacher if there is mistake in the question as the function is defined everywhere
gloomy bough
I would still recommend asking your teacher if there is mistake in the question ...
I am doing a practice test of ACT
and I don't have a math teacher đż
compact bone
isnt the function f(x) = 2
it's not when x=-3
undone epoch
isnt the function f(x) = 2
It is, but you have to consider the original function.
compact bone
you can't just cancel out 0 đ
latent scaffold
Are sinâťÂš(x) and arcsin(x) the same thing?
cedar kilnBOT
Are sinâťÂš(x) and arcsin(x) the same thing?
latent scaffold
And does the same go for other trigonometric identities as well?
Just making sure
.close
cedar kilnBOT
dire geode
And does the same go for other trigonometric identities as well?
Can't know unless you show them
dire geode
Those aren't usually referred to as "trigonometric identities"
latent scaffold
Oh sorry, I misworded it
analog arrow
if you mean the inverse the arc ones are the same
cedar kilnBOT
â
latent scaffold
.close
lethal vigil
Each of the twelve edges of a cube of edge a is tangent to a sphere. Find the volume of that portion of the cube which lies outside the sphere.
Thanks for the help!
analog arrow
can you draw a diagram
lethal vigil
can you draw a diagram
analog arrow
-
The volume of a cube (( V_{cube} )) is given by ( a^3 ), where ( a ) is the length of an edge of the cube.
-
The diameter of the sphere is equal to the side length of the cube since it touches the midpoints of the edges. Therefore, the radius ( r ) of the sphere is ( \frac{a}{2} ), and the volume of a sphere (( V_{sphere} )) is given by ( \frac{4}{3}\pi r^3 ).
-
The volume of the portion of the cube outside the sphere (( V_{outside} )) is then ( V_{cube} - V_{sphere} ).
wraith daggerBOT
timliniscool
lethal vigil
why a/2 is the radius?
lethal vigil
**timliniscool**
there is a bulge from the sphere that is greater than the cube?
analog arrow
Each of the twelve edges of a cube of edge a is tangent to a sphere. Find the vo...
Find the volume of that portion of the cube which lies outside the sphere.
dire thorn
Each of the twelve edges of a cube of edge a is tangent to a sphere. Find the vo...
Can you use calculus?
lethal vigil
Can you use calculus?
I can but I want to solve it only using basic geometry methods
lethal vigil
but you re king of calculus
I'm no king, I'm a failure.
civic coral
I'm no king, I'm a failure.
I will take over your place then
So I found this after examining the description deliberately
However, im not sure how to compute the blue underline, that is, im stuck
dire thorn
I can but I want to solve it only using basic geometry methods
I think there might be smth with thinking about a smaller sphere that fits perfectly in the square, and a bigger cube that the bigger sphere perfectly fits into, and looking at how they scale
civic coral
I think there might be smth with thinking about a smaller sphere that fits perfe...
how you come up with this idea
talent or experience from the past questions solved?
sounds like both
I have a question
this questions is unsolvable via high school calculus right?
civic coral
for the computation of the blue underlined is left untaught
lethal vigil
this questions is unsolvable via high school calculus right?
No I'm not from highschool. I'm a college student
just reading some old math books
civic coral
it is just different curriculums.
vital phoenix
this questions is unsolvable via high school calculus right?
These/are*
civic coral
thank you
lethal vigil
it is just different curriculums.
Yeah my country's curriculum in engineering is messed up.
lethal vigil
I think there might be smth with thinking about a smaller sphere that fits perfe...
https://math.stackexchange.com/questions/4832365/sphere-and-cube-overlapping-problem
Here is my analysis, I do not know how to compute the volume of the "bulge" of the sphere.
cedar kilnBOT
@lethal vigil Has your question been resolved?
pulsar carbon
We are given the random variable X that follow an exponential distribution such as:
X ~ Exp ( 1 / 9.848 )
- Find the expected value
- Find the standard deviation
3)Find P(X<12) - Find P(8<X<14)
Answers to Question 1 and 2 is 9.848 correct?
How to calculate Question 3 and 4, what can be expected Answer?
tropic oxide
do you know the CDF of the exponential dsitribution?
pulsar carbon
What's CDF? and No That is the question
"We are given the random variable X that follow an exponential distribution such as:
X ~ Exp ( 1 / 9.848 )
- Find the expected value
- Find the standard deviation
3)Find P(X<12) - Find P(8<X<14)"
tropic oxide
What's CDF? and No That is the question
cumulative distribution function.
also you did not need to post the question a second time, it was clear on the first.
$P(X < x) = 1 - e^{-\lambda x}$
wraith daggerBOT
Ann
pliant stag
I think the answer to the Question 3 and 4 will be: P (X < 12 ) â 0.707 and P ( 8 < X < 14 ) â 0.404?!?!
tropic oxide
I think the answer to the Question 3 and 4 will be: P (X < 12 ) â 0.707 and P ( ...
!nosols
cedar kilnBOT
I think the answer to the Question 3 and 4 will be: P (X < 12 ) â 0.707 and P ( ...
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.
pulsar carbon
$P(X < 12) = 1 - e^{-1/9.848 * 12}$
wraith daggerBOT
A Veteran Weeb
tropic oxide
$e^{-\frac{1}{9.848} \cdot 12}$
wraith daggerBOT
Ann
tropic oxide
you should not use the letteer x as a multiplication symbol.
dusk goblet
đ
tropic oxide
and in latex, you should be using \cdot, or \times if you want Ă.
i am specifically correcting your latex here.
does this answer your question? @pulsar carbon
pulsar carbon
**A Veteran Weeb**
Yes almost so If it calculate this I will get the answer to question 3? and this solution is Correct?
tropic oxide
yes...
pulsar carbon
$P(8<X<14)=F(14)âF(8)=e^{â1/9.848 1â\cdot 8} -e^{-1/9.848 1\cdot 14}$
and is this Correct for Question 4?
wraith daggerBOT
A Veteran Weeb
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
pulsar carbon
@tropic oxide is this Correct solution for Question 4
tropic oxide
missing minus signs in a couple places
pulsar carbon
Couple? I did add the - in the latex but its not showing (noob in using latex)
tropic oxide
latex doesn't recognize the â symbol
you need to do the hyphen
-
$P(8 < X < 14) = F(14) - F(8) = e^{-\frac{8}{9.8481}} - e^{-\frac{14}{9.8481}}$
wraith daggerBOT
Ann
cedar kilnBOT
Available help channel!
humble oriole
why canât it be done like this
cedar kilnBOT
why canât it be done like this
crimson sedge
actually
there is a mistake upper
but regardless
x(x+3) = 0 should give you solutions
and there is not only 1 solution
there are 2
crimson sedge
If x=0 u get 0(0-3) which is still 0
humble oriole
there are 2
i know there are two
one solution is -3
other is zero
but how do i get zero with that
crimson sedge
i told you
humble oriole
can u b specific
humble oriole
idk iâm slow
crimson sedge
Basically you have 2 terms on the left side; (x) and (x-3)
humble oriole
i onky know one case and that is divide x with 0 and then x=-3
crimson sedge
x(x-3)=0, you can cancel out one of these terms by dividing the entire thing by that term
If you divide through by x, you get x-3=0
but you can also divide through by (x-3) and get x=0
quick fulcrum
yo I need to say which of this are true and which are false
can someone explain to me pls how to see that?
mortal hemlock
is the graph on the right f(x) or f'(x)
quick fulcrum
is the graph on the right f(x) or f'(x)
its f(x)
quick fulcrum
I know how to calculate f'(x) when you have f(x)
I also know that the roots of f'(x) are the highest or lowest points of f(x)
carmine whale
I know how to calculate f'(x) when you have f(x)
||f'(x)=0 basically means local maxima or local minima||
quick fulcrum
||f'(x)=0 basically means local maxima or local minima||
ok
im not good with this english words
carmine whale
So do u know what does local minima and local maxima means
quick fulcrum
yeah
carmine whale
im not good with this english words
Np
quick fulcrum
Higehst and lowest points of f(x) I think