Thats question 45
#help-39
willow lake
What's thee answer of it
willow lake
And yes
Can u help with rest of the question
@trim willow
<@&286206848099549185>
<@&286206848099549185>
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pearl pondBOT
willow lake
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pearl pondBOT
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old marsh
pearl pondBOT
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upper obsidian
What is Sequence of:
5, 19, 41, ...
?
pearl pondBOT
What is Sequence of:
5, 19, 41, ...
?
upper obsidian
thats hard bruh
brave mason
5 7 11 13 17 19 23 29 31 37 41
It could be so many
You should tell us what you are studying
brave mason
5 7 11 13 17 19 23 29 31 37 41
Notice 4 primes in between each
brave mason
huh
wind wigeon
n^2 + n - 1
upper obsidian
n^2 + n - 1
thats wrong
rustic gate
the sequence could literally be anything
upper obsidian
wrong
rustic gate
you need to provide more context
upper obsidian
hmmm
rustic gate
,w Table[4n^2 + 2n - 1 + 41998C(n-1, 3), {n, 1, 4}]
upper obsidian
wtf
upper obsidian
i found that
jolly parrotBOT
upper obsidian
an = n^3 + 5n + (-1)^n
wind wigeon
that works too lol
i would argue they're looking for 4n^2 + 2n - 1 though
or something simpler
upper obsidian
that was hard
wind wigeon
its usually the simplest pattern
rustic gate
,w Table[n^3 + 5n + (-1)^n + 41984C(n-1, 3), {n, 1, 4}]
upper obsidian
,w Table[n^3 + 5n + (-1)^n + 41984C(n-1, 3), {n, 1, 4}]
how did u find that
jolly parrotBOT
rustic gate
upper obsidian
how
wind wigeon
he just added something to the sequence that equals 0 for n = 1, 2, 3
and then not 0 for n larger
a good illustration of why questions like these are dumb questions and dont really test any mathematical skill
so i feel for you having to take this test
upper obsidian
hummm
rustic gate
you can use the lagrange polynomials to construct any arbitrary sequence
with 0 thought
wind wigeon
finding the pattern in random sequences?
id hardly argue so
"patterns" are often misleading
proveable patterns
upper obsidian
but still i dont undrestand how did u find that
wind wigeon
these are not proveable patterns
wind wigeon
thats correct answer too
what if i asked you to find the pattern in 1, 2, 4, 8, 16 and asked you for the next term
what would you say
wind wigeon
that is the simplest pattern
but what if i told you i got 1, 2, 4, 8 and 16 by dividing a circle with 1, 2, 3, 4, 5 lines and counting in how many regions the circle gets split up
then if i use 6 lines
theres only 31 regions
so your pattern broke
upper obsidian
I'm confused
rustic gate
,w Table[C(n, 0) + C(n, 1) + C(n, 2) + C(n, 3) + C(n, 4), {n, 0, 6}]
jolly parrotBOT
wind wigeon
$a_{n}=\frac{1}{24}\left(n^4-6 n^3+23 n^2-18 n+24\right)$
jolly parrotBOT
Gijs
jolly parrotBOT
Requested by Gijs#0201
rustic gate
binomial coeff representation is better lol
wind wigeon
binomial coeff representation is better lol
true
point im trying to make is finding patterns is a dumb exercise if theres no way to prove the pattern to be correct
because you can make any sequence fit that sequence
upper obsidian
,w Table[n^3 + 5n + (-1)^n + 41984C(n-1, 3), {n, 1, 4}]
@rustic gate Did you get the answer using the code?
rustic gate
,w Table[-309 + 21913n/30 - 113749n^2/180 + 3209n^3/12 - 2081n^4/36 + 123n^5/20 - 23n^6/90, {n, 1, 7}]
ack
typoed
wind wigeon
rip
upper obsidian
bruh
jolly parrotBOT
rustic gate
wind wigeon
epic
pearl pondBOT
@upper obsidian Has your question been resolved?
upper obsidian
yes
pearl pondBOT
upper obsidian
thx guys
pearl pondBOT
Available help channel!
twin sapphire
pearl pondBOT
tacit mulch
,rotate
jolly parrotBOT
twin sapphire
Any ideas ?
sharp quest
ratio test
twin sapphire
Sorry I don't know this property
sharp quest
oh wait, you have to actually find the limit.... bleh
pearl pondBOT
@twin sapphire Has your question been resolved?
twin sapphire
Can someone provide an idea ?
pearl pondBOT
@twin sapphire Has your question been resolved?
pearl pondBOT
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quasi fractal
pearl pondBOT
quasi fractal
I need to study the injectivity, through monotony
I guess, that's the only way, right?
f(x)=x^2+m is decreasing on (-inf,0] and increasing on [0,inf) and f(x)=-x^2-2x is increasing on (-inf,-1] and decreasing on [-1, inf), that's what i got
How to find m now?
m is a real parameter
.close
fair frost
Hey
fair frost
How do I factor this completely? I have to do a project where it needs me to explain most of the steps on how to factor it, thanks.
abstract locust
first you can factor out a 3 to make it simpler
then factor the remaining quadratic as a product of its two roots
fair frost
first you can factor out a 3 to make it simpler
Sorry, but can you walk me through the steps because I am really bad at this
abstract locust
don't wor ry
each term in this quadratic
is divisible by 3
so we can write it as 3(5m^2 + 7m + 2)
is that clear?
fair frost
so we can write it as 3(5m^2 + 7m + 2)
Kind of
3x5= 15
3x2 = 6
3x7 = 21
But what is the 2 at the end for
abstract locust
huh
you literally included it in your calculation
3x2 is 6
we have a 6 in the original quadratic
fair frost
Btw how do you know where to put the numbers or does it matter
abstract locust
yeah that's probably a good idea
organic chemistry teacher is v good
raw questions are best way to learn concept
fair frost
I’ll try this then YouTube
abstract locust
imo
fair frost
so we can write it as 3(5m^2 + 7m + 2)
What do I do after this
coarse dawn
Factor
abstract locust
the quadratic can be factored into (5m+2)(m+1)
coarse dawn
That's why I suggested the videos, so you understand how to factor when a isn't 1
fair frost
That's why I suggested the videos, so you understand how to factor when a isn't ...
Oh Alr
Imma watch it instead
Took some notes and
I’m doing this wrong
What am I supposed to multiply to and find something that adds to
<@&286206848099549185>
pearl pondBOT
@fair frost Has your question been resolved?
pearl pondBOT
@fair frost Has your question been resolved?
olive lantern
how do i write h=-44/21(t-0)(t-10) in standard form
pearl pondBOT
how do i write h=-44/21(t-0)(t-10) in standard form
bronze linden
don't you just expand it
last kestrel
olive lantern
thats standard form?
olive lantern
thats not right tho
plush bramble
how do i write h=-44/21(t-0)(t-10) in standard form
Can you show the whole problem.
olive lantern
Can you show the whole problem.
vertex form of it -44/21(x-5)^2+52.38
plush bramble
vertex form of it -44/21(x-5)^2+52.38
Is that the same equation?
olive lantern
ya but in vertex form
plush bramble
,w standard form y= -44/21(x-5)^2+52.38
jolly parrotBOT
plush bramble
,calc -44*25/21 + 52.38
plush bramble
vertex form of it -44/21(x-5)^2+52.38
They're not the same equation
Do you have exact values?
Looks like you're rounding
jolly parrotBOT
Result:
-9.5238095237704e-4
Plotting does not mean same equation
plush bramble
Can you show the whole problem.
Original question
olive lantern
okay so im givin
this
how do i write h=a(t-0)(t-10)
a=-44/21
and i need to find vertex and standard form
and i found vertex
plush bramble
vertex form of it -44/21(x-5)^2+52.38
You rounded here. Don't rely on graphing software for algebraic manipulations
plush bramble
i just subbed in
Explain
olive lantern
so
i know a
which is -44/21
so i put it for a
and ik the vertex
so i subbed for h and k
thats all
plush bramble
Whats h and k here?
plush bramble
How did you find k?
plush bramble
how do i write h=a(t-0)(t-10)
From here
plush bramble
how do i write h=a(t-0)(t-10)
The roots of this are t=0 and 10.
plush bramble
vertex form of it -44/21(x-5)^2+52.38
When you plug in t= 0 or 10 here you don't get 0
plush bramble
i got it from the word problem
Show the word problem
plush bramble
Result:
```
-9.5238095237704e-4
```
But it's close
olive lantern
plush bramble
,calc -44/21*(5)(-5)
jolly parrotBOT
Result:
52.380952380952
This is the exact value
plush bramble
i just took the first 2 decimals
That's practically the definition of rounding
olive lantern
😭😭
plush bramble
No
Use the exact fraction
When I say don't round, I don't mean round to more decimals
olive lantern
okok
plush bramble
,calc 44*25
jolly parrotBOT
Result:
1100
1100/21 is the exact value
pearl pondBOT
@olive lantern Has your question been resolved?
fossil harbor
I'm trying to find the volume of the area R between y=4-x^2 and y=3 revolving around the x axis
pearl pondBOT
I'm trying to find the volume of the area R between y=4-x^2 and y=3 revolving ar...
fossil harbor
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prisma anchor
Hey how are you guys takin g calculus 1 i was just curious when do I take the chain rule. I know its to find the derivative but when can i know oh this is when i use it
wind wigeon
whenever you have a composite function it is useful
prisma anchor
whenever you have a composite function it is useful
Like ln(x^2+6)
The composite function is X^2+6?
What about the Product and Quotient? quotient is when it is getting divided meaning as a Division?
Product ? Would be how?
wind wigeon
product rule is useful for functions like x^4 * e^2x
quotient is nice for functions like x^4/e^2x
wind wigeon
The composite function is X^2+6?
yes and ln(x)
pearl pondBOT
@prisma anchor Has your question been resolved?
brisk mulch
pearl pondBOT
midnight haven
A plane is named by a set of three points
Right?
So what combinations of three points wouldn't intersect ADH
brisk mulch
BCF
midnight haven
Any on the sides would intersect it obviously
Yes BCF is one
Here is three others though,
brisk mulch
The availible answers are BCf, BCD,BFE,And Feh
I need to know this 4 the quiz rmr
i dont get out bcd or feh could be it
midnight haven
is there supposed to be four answers
brisk mulch
yes sir
midnight haven
Can you show me the answer sets or whatever
brisk mulch
herse the whole question
midnight haven
I would say it should the three combinations on the top side (BCGF)
If you extend BFE out as a plane
And ADH out as a plane
They intersect
brisk mulch
which of athe ansewrs is right
midnight haven
If I just tell you the right answer it won't help on tomorrow's quiz if you don't understand why
Planes extend out in 2 dimensions infinitely
Based on those three points
So extend ADH as a plane and extend each answer as a plane and see if they intersect
I think it would be more clear if they wrote "Plane ADH" but given they highlighted it I assume they refer to the plane
pearl pondBOT
@brisk mulch Has your question been resolved?
pearl pondBOT
@brisk mulch Has your question been resolved?
brisk mulch
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pearl pondBOT
drowsy turtle
Why did that get pinned
regal herald
because it was your first message
drowsy turtle
Oh woops I'm so sorry I didn't realize that was how it worked
pearl pondBOT
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Available help channel!
gritty citrus
linear algebra: can someone please explain how to solve this question. cant find the solution anywhere in my text
earnest stratus
You multiply the third row by 4. And then R3 -> R3 + 2R1.
gritty citrus
You multiply the third row by 4. And then R3 -> R3 + 2R1.
so does that mean that the determinant of b is 5 too?
earnest stratus
No, because you clearly multiplied 4.
If you multiply a row or column by a scalar, then the determinant also gets multiplied by that scalar.
gritty citrus
If you multiply a row or column by a scalar, then the determinant also gets mult...
so the determinant of B would be 20 because of 4*5? What about the R3 -> R3 + 2R1?
earnest stratus
A single row operation doesn't affect the value of the determinant.
You can check such relevant properties on the internet if you find all those at one place.
pearl pondBOT
@gritty citrus Has your question been resolved?
tiny shore
stone locust
How to solve 1^x =3
pearl pondBOT
How to solve 1^x =3
stone locust
What is the imaginary solution ?
rustic gate
,w 1^x = 3
stone locust
What is ,w
rustic gate
bot ded
rustic gate
there's no solution
stone locust
Not even imaginary ?
rustic gate
1^x = 1
stone locust
Yeah but raised to an imaginary power
rustic gate
1^x = 1
stone locust
That’s disappointing
rustic gate
you can take a branch that isn't the principal branch
stone locust
What
stone locust
According to the red pen black pen guy there is a solution
rustic gate
(e^2ipi)^x is not 1 in general
there is only a solution if you don't take the principal branch
stone locust
there is only a solution if you don't take the principal branch
Yeah I was wondering about not using real number
.close
pearl pondBOT
rustic gate
no that has nothing to do with real numbers
it's to do the the principal branch of the logarithm
stone locust
Oh
stone locust
it's to do the the principal branch of the logarithm
What does that mean ?
rustic gate
it means how you determine the argument of a complex number
the principal branch takes values between -pi and pi
so arg(1) = 0
and nothing interesting happens
if you take another branch
rustic gate
well
unfortunately that's what's going on here
so
it depends on how you interpret complex exponents
and they're inherently multivalued
quasi pollen
pearl pondBOT
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Available help channel!
midnight haven
https://cdn.discordapp.com/attachments/905285721886187580/1033407893929734144/unknown.png
i need a little help on the last question
pulsar lark
,rcw
jolly parrotBOT
midnight haven
the zeros are (x-5)(x+6)(2x-1)(x+1)
i think the y int is -15
but when i tried it on desmos it gave me anothr graph
pearl pondBOT
@midnight haven Has your question been resolved?
odd sand
hi
odd sand
im not sure what these questions are asking
is the second part asking show matrix multiplication is a linear transformation?
foggy mason
Yes, show that v-->Av is a linear transformation
odd sand
what is the first part asking
oh wait is it asking show matrix multiplication of a 2x2 and and mxn matrix is a linear transformation
pearl pondBOT
@odd sand Has your question been resolved?
odd sand
then the general case of mxn
im not sure how to prove for the 2x2
i know this is what u must do
but not sure how to apply it to this problem
tropic saddle
you need to show that if $v,w\in \bR^2$ are vectors and $\alpha\in\bR$ is a scalar, then $T_A(v+w)=T_A(v)+T_A(w)$ and $T_A(\alpha v) = \alpha T_A(v)$
jolly parrotBOT
Denascite
tropic saddle
and you can do that just by plugging in the definition of T_A and using properties of matrix vector multiplication
odd sand
so that 2x2 matrix they give represents the scalar?
tropic saddle
ah fuck I should not have used the letter alpha
the 2x2 matrix is a 2x2 matrix
T_A(v) is defned by T_A(v)=A*v
where v is a vector and A is the matrix
odd sand
so $T_A(v+w)=matrix*(v+w)$
jolly parrotBOT
Infectia
tropic saddle
yes
odd sand
is the $a_{1,1} = \alpha(v+w)$
jolly parrotBOT
Infectia
odd sand
ok
tropic saddle
do you know how matrix vector multiplication works?
odd sand
do you know how matrix vector multiplication works?
should i expand $\alpha(v+w)$
jolly parrotBOT
Infectia
odd sand
well a_1,1
odd sand
is it not the matrix they gave me?
tropic saddle
if $A=\begin{pmatrix} \alpha & \beta \ \gamma & \delta \end{pmatrix}, x=\begin{pmatrix} x_1 \ x_2 \end{pmatrix}$, then $A\cdot x= x_1 \begin{pmatrix} \alpha \ \gamma \end{pmatrix} + x_2 \begin{pmatrix} \beta \ \delta \end{pmatrix} = \begin{pmatrix} \alpha x_1 + \beta x_2 \ \gamma x_1 + \delta x_2 \end{pmatrix} $
jolly parrotBOT
Denascite
tropic saddle
this is the definition of matrix vector product
x_1 times the first column of A plus x_2 times the second column of A
the the first column is (alpha, gamma) and the second column is (beta, delta)
tropic saddle
well did you manage to show addition?
then it should really be the same thing
just don't call the scalar alpha like I did
odd sand
yes. i just made a vector v and vector w instead of x
did each one
then added it
then i did where x = v+w and computed and showed that the two were equal
tropic saddle
ok
and now for scalar multiplication its the exact same process
just instead of x=v+w you do x=c*v
where c is some scalar
odd sand
so would it be $ Cx=\begin{pmatrix} Cx_1 \ Cx_2 \end{pmatrix}$
jolly parrotBOT
Infectia
odd sand
oh lol not sure how to make matrices on latex
fallen forum
I don't quite understand this did I do it right?
pearl pondBOT
I don't quite understand this did I do it right?
round vigil
yes i believe that is correct
fallen forum
Thank you
sick adder
👍
fallen forum
So do I just multiply to get the number and write the numbers i used?
round vigil
yes
upbeat flint
hi, i'm revising for a test and i'm stuck on a non-calc question, please help: "Two brothers, Gethin and David, share a sum of money in the ratio 2:7. David gets £30 more than Gethin. Calculate how much money the brothers share." I'm not sure what method I should use to figure this out
upbeat flint
oh, thanks a lot
meager mango
no worries
upbeat flint
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rose creek
This is correct right?
pearl pondBOT
This is correct right?
rotund talon
yes
rose creek
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stray matrix
Right?
jolly parrotBOT
shrewd basin
Well seems right assuming the last bracket you just forgot to write x^2 and x
proud kiln
pearl pondBOT
shrewd basin
Resolve the force and F=ma
bronze linden
pearl pondBOT
bronze linden
So i know cot = 1/tan which is 1/sin/cos which is cos/sin
abstract locust
So i know cot = 1/tan which is 1/sin/cos which is cos/sin
ok nice, so you have 2cos = cos/sin
what can you do to simplify this further
bronze linden
This is what i have
It's just that
I'm having trouble mirroring the unit circle
mossy canopy
sin+cos is not 1
mossy canopy
we have:
2cos(x)=cos(x)/sin(x)
so now we have 2 cases
either cos(x)=0
for which we have a trivial solution
so think about when cos(x)=0
the other is when cos(x) does not equal 0
bronze linden
Right
mossy canopy
then we can divide by cos(x)
to get
2=1/sin(x)
sin(x)=0.5
in total we will get three solutions
mossy canopy
cos(x)=0 has two solutions actually
oops nevermind we will get 4 solutions
in total
mossy canopy
yes
bronze linden
I also get 5pi/6
for the reflecting blue one
but i don't get how the other 2 solutions come
mossy canopy
the other two come from cos(x)=0
bronze linden
so when we divide by cos(x) we have to include cos(x) = 0 and find the solutions for those?
mossy canopy
yes
mossy canopy
👍
bronze linden
Given:
plane 1 = 2x-4y-z=-1
Express in scalar (normal form) an equation of a second plane that passes through P(2,1,-3), Q(3,2,-2) and is perpindicular to plane 1
So I know the normal of plane 1 is <2,-4,-1>
I can make a line equation which passes through P
line 1 = <2,1,-3> + t<2,-4,-1> where t belongs to real numbers
line 2 = <3,2,-2> + t<2,-4,-1>
These would both be perpindicular since i'm using the normal of plane 1
however i'm not sure how to get a second plane
mossy canopy
1 = 2x-4y-z=-1?
mossy canopy
yeah sry i need some time, im in a game rn
wont take long tho
bronze linden
👍
pearl pondBOT
@bronze linden Has your question been resolved?
mossy canopy
ok
so
we have plane 1
and the normal vector of plane 1
then
we know two points in plane 2
bronze linden
ye
mossy canopy
from which we can create a vector (which goes from P to Q)
now notice
the normal vector of plane 2 will be perpendicular to this vector
lets call this vector v
another thing is
bronze linden
Why would we create a vector from PQ
mossy canopy
the idea is that we will get two statements:
n2 (normal vector of plane 2) is perpendicular to two vectors
from this we will be able to identify n2
bronze linden
lets call this vector v
And this vector V would just be the normal of the first plane right?
Because that normal is perpindicular to plane 1
mossy canopy
v is the vector from P to Q
and since n2 is perpendicular to plane 2, n2 is perpendicular to any vector in plane 2
therefore n2 is perpendicular to v
the other thing is, that plane 1 and plane 2 are perpendicular
therefore their normal vectors are perpendicular
bronze linden
Wait I'm lost
bronze linden
We need a second plane that is perpindicular to plane 1
and passes through 2 points
mossy canopy
yes
bronze linden
Ok so v is perpindicular normal
mossy canopy
yes
bronze linden
I was thinking though
mossy canopy
v is the vector from P to Q in plane 2
therefore v is perpendicular to n2, the normal vector in plane 2
and n2 is perpendicular to n1 since their planes are perpendicular
bronze linden
I was thinking I could just use the normal of P1
as the direction for the second equaation aas it would make it perpindicular
to plane 1?
mossy canopy
im not sure
i would use something else
my idea would be to use the cross product
the cross product takes two vectors and outputs a vector that is perpendicular to both
notice that n2 is perpendicular to n1 and v
therefore the crossproduct of n1 and v will give a multiple of n2
but since we deal with planes/normal vectors here, the magnitude of the output vector doesn't really matter
this will give us the plane
-3x-3y+6z=0
which is the same plane as
-x-y+2z=0
mossy canopy
crossproduct gives a vector that is perpendicular to both input vectors
bronze linden
find PQ though
by getting PQ you get a vector that lies on the plane?
I think I get what you did
mossy canopy
btw, the solution is not right it seems
at least not quite
-x-y+2z=0 is wrong
-x-y+2z=something
mossy canopy
yep
oh
wait
it is easy
so
we got:
-x-y+2z=C
where C is some number
now just put in one of our points
bronze linden
Wait so how do you do it?
mossy canopy
if we put this point in, we get
-2-1-6=-9
so in total
-x-y+2z=-9
which equals
x+y-2z=9
mossy canopy
i assumed that
if you have a plane
like
x+y+z=C
where C is a number
then the normal vector here would be (1,1,1)
bronze linden
ye it would
mossy canopy
we know the normal vector
the only thing we dont know is that C
this is the whole solution now
i am sure there is another way to do this all, but this is what i would do intuitively
haven't touched that stuff in a long time
mossy canopy
uni
but we dont do that stuff in uni
in uni it gets real crazy
this is called geometry in our uni
and we did that for like 2 weeks at the end of linear algebra 2
linear algebra here is all about vector spaces
and weird transformations from one space into another
then spaces that are not so nice
and the main idea is to write some functions in the form of matrices
and then find prettier forms of this matrices
bronze linden
but we dont do that stuff in uni
I'm in first year uni rn doing linear algebraa
mossy canopy
by changing basis
linear algebra is nice
but real weird at times haha
im in second year third semester now
mossy canopy
oof
btw
this is where i wrote my stuff
if you click on the graph at the bottom, i think you should be able to move it around(if you click on the cogwheel at the top left of the graph)
bronze linden
How'd you get so good at linear algebra?
mossy canopy
really nice to check your solutions to these things
i think the most important thing is intuition
intuition leads you into the direction of the solution
btw
there is a nice playlist about linear algebra intuition
bronze linden
Where?
mossy canopy
really nice videos
bronze linden
Ah I see thanks
mossy canopy
generally a really great channel
bronze linden
this probably will help
I'm trying to just do a ton of homework
It's not hard when I get the hang of it it's just the word problems tend to make me haave a hard time cause idk how to appraaoch it
mossy canopy
as for exams, i always do the exams of previous years
bronze linden
that's what i'm doing rn
the question i asaked is from a mock mid term
anyway thanks, I'm gonna look at the playlist
hopefully will help me visualize everything a little better
mossy canopy
have a good day^^
jaunty fable
pearl pondBOT
jaunty fable
how would i start this
wind wigeon
is it not just subbing in?
well yes but good luck evaluating that series
jaunty fable
do you have any idea what that is
wind wigeon
i do not
pearl pondBOT
wind wigeon
@jaunty fable it seems theres a pattern
you can use that 3^k is always odd
idk why they overcomplicated the function
seems to me the numerator is just to scare you
pearl pondBOT
Available help channel!
sharp belfry
I need a quick help guys
pearl pondBOT
I need a quick help guys
sharp belfry
How many surjections can be formed with f : {1, 3, 5, 7, 9}→{2, 4, 6}?
I somehow got 540 ways which is wrong
What I did was, think 5 distinct balls in 3 distinct boxes which I still think is correct and then what I did was
P(5,3)* 3^2= 345*(3^2)= 540
Since it is surjections I need to make sure that there will be no empty boxes, and so how many ways can I choose three balls from 5 and that is P(5,3). Then I will have 2 balls left, and there is 3 choice for the remaining 2 balls so 3^2 .
midnight haven
one way you can do this is with complementary counting and principle of inclusion-exclusion
so first off the total number of functions from the first set to the second set is 3^5
and then you'd want to subtract off the number of non-surjective functions
so we want the number of functions where at least one element in the second set has 0 elements that get mapped to it
we can let A be the event where nothing gets mapped to 2, B be the event where nothing gets mapped to 4, and C be the event where nothing gets mapped to 6
and we want at least one of those to happen
the size of the union is given by |A|+|B|+|C|-|AnB|-|AnC|-|BnC|+|AnBnC|
and by symmetry we can write this as 3*|A|-3*|AnB|+|AnBnC|
note that the last term is 0 since at least one term has to get mapped to
|A| is 2^5, |AnB| is 1^5
sharp belfry
Yes that could work but it is too long
midnight haven
Since it is surjections I need to make sure that there will be no empty boxes, a...
this overcounts cases
sharp belfry
What my professor did was sterling number
and then he multiplied it by 3! and I get what he is doing but I don't really understand it well
IS it because
Sterling number gives us how many ways we can put the balls in the boxes so no boxes are empty but since the boxs are identical in sterling number. He multiplied it by 3! to make up for the other cases where the boxes are different
Is that so?
midnight haven
Since it is surjections I need to make sure that there will be no empty boxes, a...
suppose you have 1,3 ->2, 5,7->4, and 9->6
then that is counted by preplacing (1,5,9) and then 3,6 would be free
and also counted by preplacing (3,7,9) and then 1,5 would be free
so with that method the same case gets counted multiple times
midnight haven
Is that so?
yeah that would work
sharp belfry
yeah that would work
But is that what he did? I mean is my speculation correct or is there another reason he multiplied S(5,3) by 3!?
midnight haven
But is that what he did? I mean is my speculation correct or is there another re...
no you're correct
pearl pondBOT
@sharp belfry Has your question been resolved?
opaque hearth
[sin(9.5) \approx -0.751511205]
[\frac{11,000}{sin(9.5} \approx -14,6371.73]
jolly parrotBOT
dopediscorduser
opaque hearth
Where did they get 66,647 from?
stark barn
calculator
opaque hearth
Right
stark barn
classic blunder
pearl pondBOT
pearl pondBOT
Available help channel!
fathom pumice
Prove that
pearl pondBOT
Prove that
fathom pumice
Don't really have much of an ideia of how to start
<@&286206848099549185> Any clue?
late sedge
maybe take the log of both sides
late sedge
np
fathom pumice
.close
grand forum
pearl pondBOT
grand forum
need help
pearl pondBOT
@grand forum Has your question been resolved?
pearl pondBOT
@grand forum Has your question been resolved?
craggy sigil
Hey, I'm having a problem with something which should be very simple. But for some reason my brain is just not getting or something. I'm doing a calc 2 problem, finding the sum of a geometric series, so i'm doing a/(1-r) and I am getting a = 2 and r = 2/11
craggy sigil
so I get 2/9/11
so I multiple 2/9 by the reciprocal of 11, and i get 2/99
however, the actual answer im seeing in the book is 22/9
can someone clear up my mistake?
craggy sigil
Oh ok I see, sorry for the dumb question
I have one more problem if I can ask it here
I am struggling to figure out this limit, can anyone point me where to start?
I'm thinking it might the indeterminant form, would L'Hospitales rule work here?
real scarab
do you have a feeling for what this does?
pearl pondBOT
@craggy sigil Has your question been resolved?
naive musk
pearl pondBOT
naive musk
I'm thinking that the coin is thrown from 960 ft, and will reach the ground by t=6
Is that correct?
sharp quest
yes
faint onyx
pearl pondBOT
faint onyx
hi this is a pretty trivial question but for some reason i dont get the vector substraction and the workings here lol
.close
pearl pondBOT
faint onyx
.reopen
pearl pondBOT
✅
real scarab
its pythagoras theorem
real scarab
do you get whats coming after the first line?
faint onyx
one sec
real scarab
or was it just the first statement?
real scarab
yeah they are actually calculating the norms
with the cordinates
RHS?
right side
yueah ok
faint onyx
um this
real scarab
its exactly
faint onyx
ah okay
real scarab
yep
real scarab
its proving pythagoras
faint onyx
sorry i asked a dumb question lmao
real scarab
the formula holds
if and only if
u and v are orthogonal
here you have a vector based proof of the pythagoras theorem
faint onyx
pearl pondBOT
faint onyx
so these 3 theorems
hm
- states that the dot product of two vectors can only be less than them multiplied?
- the length of the sum of 2 vectors is less than the length when both are calculated separately
- dont get
little swan
All three are essentially different ways of saying the hypotenuse of a triangle is shorter than the length of the opposite and the adjacent
faint onyx
is there an intuitive understanding tho?
little swan
You can write Cauchy Schwarz in terms of a projection onto another vector and multiply or prove it using determinants, I don't think it's that far a leap, but I don't want to get into it.
faint onyx
hm wut
real scarab
so for the triangle inequality
litterally , when in a triangle
its shorter to go through one side rather than 2
real scarab
real scarab
look into the actual proof of cauchy schwarz
faint onyx
equation of a line squared?
real scarab
faint onyx
okay so this is how u derive the inequality
pearl pondBOT
pearl pondBOT
Available help channel!
primal breach
hii
abstract locust
with what
primal breach
abstract locust
yeah I can help you
abstract locust
you have 2 equations and 2 unknowns, so the method to do this is to get x in terms of y using one of the equations and then substitute that into x of the other equation
sorry if that's a bit unclear, want me to illustratr?
abstract locust
ok
3y - x = -4, our goal is to isolate x, so we would get 3y + 4 = x
now we substitute this value of x, into the first equation
abstract locust
yess, I added x to both sides, and I added 4 to both sides