#help-0
lone heartBOT
weak tendon
U need to post a question not "who can help me"
abstract shuttle
Ok
weak tendon
read #❓how-to-get-help
echo socket
Send the screenshot of your problem here
weak tendon
send a picture of the question
echo socket
,rotate
ocean sealBOT
echo socket
Are you asked to prove this?
mortal trellis
lets not get confused by all the square roots here
note that this has the form c^2-d^2 <= c^2
weak tendon
is this just mean value theorem?
mortal trellis
no
echo socket
No
abstract shuttle
Nah
echo socket
c^2 - d^2 <= c^2 is true since -d^2 <= 0 for all d
weak tendon
nvm
mortal trellis
wdym with "wrong one"
abstract shuttle
I have To say why this is an inequlity
abstract shuttle
wdym with "wrong one"
Question
mortal trellis
what else should it be?
abstract shuttle
?
echo socket
You sent the wrong question?
mortal trellis
,rotate
ocean sealBOT
mortal trellis
ah you have to prove the other inequality using the circled one?
mortal trellis
well you did all the manipulations
mortal trellis
you found sqrt(ab) <= (a+b)/2
abstract shuttle
Yed
mortal trellis
which is what you wanted
so what's the problem
here you subtracted 2sqrt(ab) one too many times
abstract shuttle
Thx
mortal trellis
make sure to draw your sqrts properly
abstract shuttle
Ok
mortal trellis
the last lines look like $\sqrt{a} b$ instead of $\sqrt{ab}$
ocean sealBOT
Denascite
abstract shuttle
Ok
mortal trellis
actually a lot of the sqrts look like that. which is very different and wrong
abstract shuttle
actually a lot of the sqrts look like that. which is very different and wrong
Its because
@mortal trellis
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lone heartBOT
abstract shuttle
.reopen
lone heartBOT
✅
mortal trellis
I dont see how these formulas have anything to do with how you draw the sqrts
mortal trellis
unless you have more questions
lone heartBOT
slim leaf
so i need to find the values of a and b and I do not really know what is the most effective way to find it
slim leaf
$a^4+2a^2b^2+b^4-8ab^2-8ba^2=0\newline a^2b^2-b^3-ab^2-ba^2-a^3=0$
ocean sealBOT
Filipes
craggy token
slim leaf
yes i know the answer should be a=4,b=4 and a=0,b=0 from wolfram alpha but i have no idea how to find the solution
what would you do to get a and b?
lone heartBOT
@slim leaf Has your question been resolved?
lone heartBOT
@slim leaf Has your question been resolved?
analog bronze
I need help figuring out if i got this right
write the quadratic function in vertex form. then identify the vertex
g(x)=0²+7x+2
g(x)=x²+7x++2+
the spaces equal to 49/2
so g(x)=x²+7x+49/2+2+49/2
(x+7/4)²-45/2
x=(7/4,45/2)
lone heartBOT
analog bronze
.open
lone heartBOT
Available help channel!
honest veldt
If i have $a \equiv b$ (mod $n$), can i say $a^{\frac{1}{k}} \equiv b^{\frac{1}{k}}$ (mod $n$) ?
ocean sealBOT
CBA Honestly
honest veldt
i.e. is it "legal" to take both sides of a modular equation to the $k$'th root?
ocean sealBOT
CBA Honestly
echo socket
**CBA Honestly**
As long as 1/k is a natural number, sure
lone heartBOT
harsh girder
honest veldt
.reopen
lone heartBOT
✅
honest veldt
is it never true where i can do that? or is there some secret world where like if some gcd = 1 then it's possible
honest veldt
like if i have $a^k \equiv 1$ (mod n), gcd$(a,n) = 1$, i can't take both sides to the $\frac{1}{k}$?
ocean sealBOT
CBA Honestly
mortal trellis
well x->x^k is not bijective
so you would need to choose a root
and there is no obvious canonical choice
honest veldt
well in reality its $a^{k\phi(n)} \equiv 1$ (mod n)$
ocean sealBOT
CBA Honestly
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
honest veldt
right, that's what i'm trying to prove
mortal trellis
*nonzero a
honest veldt
please don't provide a proof
i'm just trying to see if i can prove that
by taking both sides to the 1/k
honest veldt
ookay
so not the way to go
thanks i'll try something else
appreciate it
.close
lone heartBOT
mortal trellis
do you want a hint or just do it completely on your own
honest veldt
i'm good let me poke around a bit more - thanks
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
struggling on this
grave matrix
try replacing x with (x-11) (the brackets are important) and see what function you get
boreal verge
just replace x with (x-11) in h(x) and the equation for h(x)
then subtract to get the difference
alpine sable
just replace x with (x-11) in h(x) and the equation for h(x)
then subtract to ge...
so like this? h(x - 11) = -4(x - 11) - 72
boreal verge
then factor
alpine sable
h(x - 11) = -4x - 28
boreal verge
-4x + 44 - 72 => h(x-11) = -4x - 28
then do h(x) - h(x-11) = -4x- 72+4x + 28 = 44
alpine sable
i forgot somethin
so the answer is 28?
boreal verge
yeah
boreal verge
-4x + 44 - 72 => h(x-11) = -4x - 28
then do h(x) - h(x-11) = -4x- 72+4x + 28 = ...
i edited it
alpine sable
-4x + 44 - 72 => h(x-11) = -4x - 28
then do h(x) - h(x-11) = -4x- 72+4x + 28 = ...
ohhhhhhh
okay
grave matrix
then factor
expand*
lunar bolt
This is a mental math question
Slope is -4, so that means that for each decrement in x, y increases 4 times
So if x decreases 11 units, the y increases by 4*11= 44 units
royal token
Find the area between the curve $y=x^{2}-1$ and the x-axis between x=0 and x=3
I have found $\int_0^3x^{2}-1\dd{x}$ to be 6 but the answer is $\frac{22}{3}$
I checked and my integration is correct, so I'm unsure how to find this area?
last ether
Does it want absolute area?
ocean sealBOT
Nail
royal token
Does it want absolute area?
yea
royal token
that makes a difference?
last ether
Yeah because there's area underneath the x axis
So regular integration is gonna cause net-integration
,w Int[|x^2 - 1|, {x, 0, 3}]
ocean sealBOT
royal token
how does that
last ether
,w Int[x^2 - 1, {x, 0, 3}]
ocean sealBOT
last ether
Just to test
royal token
well that's confusing
last ether
So when you do regular integration, you have positive area and negative area
And it adds those up
What the absolute values does is take those negative areas and says "nah, make those positive"
royal token
so its $\int_0^3x^{2}-1\dd{x}+\int_3^0x^{2}-1\dd{x}?$
ocean sealBOT
Nail
royal token
that is ±1
ok so i need to find negative area
and add it to the positive area
which would yield 12
hm
ocean sealBOT
royal token
where did 1 come from
last ether
last ether
Because x^2 - 1, between 0 and 3, has an x intercept at 1. At x = 1, x^2 - 1 changes from - to +
Which means the area from 0 to 1 is negative
We need to make that positive
So $-\int_0^1(x^2-1)dx = \int_0^1(1-x^2)dx$
ocean sealBOT
Umbraleviathan
royal token
wait so you first find x when y is 0 to find the point where its gonna give an negative area?
last ether
Yes
royal token
and then integrate said area and add up?
last ether
Well make each area positive but yes
It also relies on you knowing what the integrand would look like when graphed
alpine sable
lone heartBOT
crisp pine
I think you made a typo and may have meant to write -10 in that box
crisp pine
I think 12 should be 11
alpine sable
oh so i just suck at counting
crisp pine
Hahaha it happens
last ether
Peter, the horse
alpine sable
i have another question
crisp pine
Ok sure
alpine sable
crisp pine
What have you tried so far?
alpine sable
nothing, cause i dont understand what the question is asking
last ether
It's basically asking when is f(x) below g(x)
alpine sable
so, -10 < x < 11, x is not equal to 0?
$-10<x<11,:x\ne 0$ i tried this but it didnt work
ocean sealBOT
InfiniteAxis
alpine sable
It's basically asking when is f(x) below g(x)
$-10<x<0,:x>11$ i got this, but it says its wrong
ocean sealBOT
InfiniteAxis
last ether
Look at how your functions are labeled
lone heartBOT
lone heartBOT
✅
alpine sable
Look at how your functions are labeled
i got a new question
thorny lake
Hi there!
So I have this problem with Sequent calculus, where I need to find the axioms of formulas. I know there are rules that I can apply with these but the problem there is more than 1 formula next to each other, separated by a comma. So how could I apply the rules to get the axioms if there are more than one formula?
Thanks anyone in advance!
lone heartBOT
Hi there!
So I have this problem with Sequent calculus, where I need to find th...
@thorny lake Has your question been resolved?
lone heartBOT
@thorny lake Has your question been resolved?
lone heartBOT
@thorny lake Has your question been resolved?
thorny lake
Please:cc
bitter panther
A 3cm by 3cm by 3cm cube of white wood is painted black all over, and then chopped into 27 cubes, each 1cm by 1cm by 1cm. These smaller cubes are then put into a bag and three are picked (without replacement) at random. What (to 3 s.f.) is the probability of getting exactly four black faces in total? To get your final answer, multiply this by 185 and take the integer part. stuck on how to start
serene junco
Multiply by 185?
I don't see any reason to do that, or is this part of a larger problem?
bitter panther
I don't see any reason to do that, or is this part of a larger problem?
its the whole q my teacher gave
idk y either
serene junco
Ok well
for the probability
Can you picture the cube it's talking about?
made of a white material, painted black on the outside. So when you cut it into the 27 unit cubes, the cubes all have varying numbers of white and black faces
bitter panther
yh
serene junco
Can you describe how many cubes have 0, 1, 2, 3, etc black faces?
serene junco
Yeah, exactly
So you put all those cubes into a bag and choose three at random
The question is what's the probability that the cubes you pick have a total of four black faces
So, how could you pick three cubes with a total of four black faces?
There are a few possibilities
serene junco
Okay
bitter panther
or u could have 0,1,3 i think
serene junco
Yeah
I believe that's all
So, now you have to find the probability of each of those combinations, and add them
bitter panther
ok cool
serene junco
I'd think of it in terms of combinations, so you don't have to worry about the order
Like for 1, 1, 2
That's two of a group of six, and one of a group of twelve.
So (6C2)*(12C1) gives the total combinations of that form
serene junco
(6/27 x 5/26) x (12/25) ?
I think you could do this, but this looks like you're choosing them in order, and specifically picking the 2-faced one last, so we'd have to account for that somehow
bitter panther
if its easier we could do the equation u sent
serene junco
nCr means the number of groups of r objects you can form from a set of n
Yeah I think it's much simpler that way
so like 6C2 means, we have six objects, how many combinations of two are possible
Since we have 6 one-face cubes, and we want to get 2 of them
bitter panther
so 3?
serene junco
,w C(6,2)
ocean sealBOT
serene junco
There are 15 possible combinations of 2 you can make. It's not like just dividing it into groups of 2
serene junco
All good lol
So, we said 1,1,2
2,2,0 and 3,1,0
See how we can count all the possibilities?
alpine nacelle
other way to see it: P(total = 4) = P(1, 1, 2)+P(1, 2, 1)+P(2, 1, 1)+P(3, 1, 0)+...+P(0, 1, 3)+P(2, 2, 0)+P(2, 0, 2)+P(0, 2, 2)
= 3P(1, 1, 2)+6P(3, 1, 0)+3P(2, 2, 0)
bitter panther
(6C2)*(12C1), for 0,2,2 it would be (1C1) x (12C2), and for 0,1,3 it would be (1C1) x (6C1) x (8C1)?
serene junco
Yeah!
serene junco
other way to see it: P(total = 4) = P(1, 1, 2)+P(1, 2, 1)+P(2, 1, 1)+P(3, 1, 0)+...
Yeah, this works too. You can consider all the possible orders of each group and add them all
bitter panther
so for 1,1,2 it would be 15x12=180, for 0,2,2 it would be 1x66=66, and for 0,1,3 it would be 1x6x8=48?
bitter panther
Yeah, this works too. You can consider all the possible orders of each group and...
wouldnt that take ages or is there a quick way to do that?
serene junco
so for 1,1,2 it would be 15x12=180, for 0,2,2 it would be 1x66=66, and for 0,1,3...
Yeah this is right
alpine nacelle
it's quite quick actually, 'cause P(0, 1, 3) = P(3, 1, 0) = ...
so you only need P(1, 1, 2), P(3, 1, 0) and P(2, 2, 0)
serene junco
Oh, yeah, you're right
bitter panther
what do i do from here 😭
serene junco
You have the total number of "4-face" combinations
Put it over the total number of possible combinations
serene junco
27C3, the number of possible combinations of 3 out of a group of 27
serene junco
Yep
bitter panther
so 294/2925?
serene junco
I think 0.101
bitter panther
oh yh my bad
crisp halo
quadratic functions on graph help go
bitter panther
18.685 then*
serene junco
Just means round it down
bitter panther
so is 18.685 the final answer?
serene junco
The integer part is 18
serene junco
Yep
serene junco
Lol no problem 👍
bitter panther
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crisp halo
:(
high rapids
Bro
lone heartBOT
blissful temple
maybe you can try to post your question
lone heartBOT
Available help channel!
crisp halo
maybe you can try to post your question
i already did
crisp halo
but didnt respond
blissful temple
well, you had no question
wary stream
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vivid berry
Set theory. I should determine the amount but what does most mean? I get that i is element of {2,6} but everything else.... What does the intersection do in that context?
low lily
is there missing like a top part?
vivid berry
is there missing like a top part?
no. its just this. i should determine the amount (set theory)
its supposedly simple since it's one of the early tasks i have to do but by god i cant make anything out of that
low lily
yes german lmao
vivid berry
yes german lmao
low lily
also eigentlich musst du nur für die i's einsetzen
vivid berry
also eigentlich musst du nur für die i's einsetzen
Das war ja so mäßig meine Frage. Ich weiß nicht wie ich das lesen soll xD
Vereinigung schnittmenge von mengen verstehe ich aber wie das da abgebildet ist nicht. Was soll mir Schnittmenge von i element von intervall 2,6 und der rest dahinter sagen? Ich finde im netzt auch nichts zu
low lily
also so wie ich das verstehe ist einmal 2 einzusetzen und dann 6
und davon dann jeweils der schnitt
bzw es ist alles einmal einzusetzen in alles
vivid berry
also so wie ich das verstehe ist einmal 2 einzusetzen und dann 6
du meinst in die klammer?
low lily
ja weil du brauchst für den allgemeinen Durchschnitt Mengen
vivid berry
ja weil du brauchst für den allgemeinen Durchschnitt Mengen
okay also wenn ich nun bsp: 2 in i einsetzte habe ich da {2/2, 2+1} und für 6 {6/2, 6+1} . was :
{1,3} und {3,7} ist. Folge ich dir noch?
Und dann die schnittmenge berechne was kurz gesagt einfach 3 ist . Wars das?
vivid berry
Super, dann danke für die hilfe ^^
Hätte noch ne andere Frage. In d) habe ich nun nicht mehr was zum einsetzten wie in c) sonder n ist elemnt von allen natürlichen zahlen
low lily
da bin ich auch komplett raus
lapis trout
for some reason, my minimum cost in terms of Q, when i differnetiate it, is not the same as my lagrange multiplier
lone heartBOT
@lapis trout Has your question been resolved?
lapis trout
<@&286206848099549185>
old mirage
r(t)=<3-5t,2-3t> with t going from 1 to 1. I am supposed to identify what this looks like on a graph. I'm confused on the process... and honestly the right questions to ask! I know I am supposed to square both the 3-5t and 2-3t, but why, and what does this info do for me?
old mirage
I apologize if that was confusing
and whatever this looks like, I know it passes through (-5,-3)(?)
<@&286206848099549185>
lone heartBOT
@old mirage Has your question been resolved?
lone heartBOT
@old mirage Has your question been resolved?
alpine sable
r(t)=<3-5t,2-3t> with t going from 1 to 1. I am supposed to identify what this ...
why would you square it
old mirage
Honest? I’m not sure😂 that’s just one of the examples I had before class ended
alpine sable
oh
this would in fact
just be a line
what you can do
is say
x = 3-5t, y = 2-3t
then find y in terms of x
alpine sable
np
old mirage
.close
undone agate
lone heartBOT
undone agate
I think I prove the congruence statements by AAS
But how do i prove ray n contains point X??
serene junco
But how do i prove ray n contains point X??
Maybe you can prove ray CX bisects angle C, and is therefore equivalent to ray n
Consider triangles CXF and CXD
undone agate
Consider triangles CXF and CXD
So they are congruent by AAS
serene junco
No, you need to prove that CX bisects angle C, you can't use that fact
They are congruent, but not by AAS
undone agate
Well, I only see that 2 sides are congruent, and the right angles are congruent
But that would be SSA, which is not a congruence postulate
serene junco
But that would be SSA, which is not a congruence postulate
It is if the angle is a right angle
You might know it as HL
undone agate
They are congruent, but not by AAS
I see FX is congruent to XD, CX congruent to CX, and BFX congruent to ADX
Oh
I think I've got it!
Thank you
serene junco
Sure thing 👍
undone agate
.close
twin jolt
How many different three-digit house numbers can be constructed from six brass numerals 1, 2, 3, 4, 5, 6?
twin jolt
wouldn't you have 6 to choose from the first 6 to choose second and 6 to choose from the third
so i thought it was 6x6x6
how is it 6!/3!
alpine sable
wait can you
twin jolt
why not though
twin jolt
oh yeah
alpine sable
idk
lone heartBOT
prime badge
i think it could expect you to be able to flip 6 into 9
it's reasonable enough
(5×4×3) + 2 × 3 × 5 × 4 = 180
and you said 6!/3! is intended ok
lone heartBOT
Available help channel!
twin jolt
Of the integers from 1000 to 9999, how many have at least one digit a 5 or 7?
twin jolt
hi i just kinda dunno how to calculate the numbers with 5 and 7
i think its the integars subtracted by that
but idk how to calculate that
alpine sable
consider complementary counting
rose sigil
maybe try counting the ones that don't have a 5 or 7
hollow pawn
can someone help me factorise
prime badge
yeah, basically you make numbers that have neither 5,7
rose sigil
can someone help me factorise
see #❓how-to-get-help 🙂
twin jolt
ok ok
prime badge
then subtract from numbers that may have them
karmic solstice
ones tens hundreds and thousands
prime badge
note that "distinct digits" is not a rule anumore
you don't make numbers that have 5 or 7 to solve this, that's the goal
what do you mean
twin jolt
i have to find the total amount of integars
then subtract by the numbers that do have 5 or 7 right?
twin jolt
how do i do that?
prime badge
you subtract numbers that don't
twin jolt
ok ok
prime badge
numbers don;t have 5 or 7 if hey are made from 0,1,2,3,4,6,8,9
there's still a rule about no leading 0, but repeats are ok
twin jolt
oh ok got it
let me try
alright so
the numbers that don't are claculated using 7x8x8x8
7 since you can't start with 0
prime badge
perfect
slate egret
lone heartBOT
alpine sable
i think whast wrong
is when you multiply by 1/x / 1/x
then move the x inside the squareroot
that removes the negative
since x -> -infinity then the 1/x is a -
so moving it into the square root causes problems
cuz sqrt(x^2) not equal to x in this case
slate egret
so how would I solve this limit
lone heartBOT
@slate egret Has your question been resolved?
grave niche
How would this be formated?
Would the square root 3 become a negative or would the 3 just be a negative 3?
karmic solstice
,rccw
vapid ice
How would this be formated?
Would the square root 3 become a negative or would ...
doesn't matter where you place the negative(s) for multiplication-only operations as long as you just keep it outside of everything
ocean sealBOT
vapid ice
the 3s cancel and leave you with a -sqrt(3)
grave niche
oh, im stupid thanks lol
grave niche
the 3s cancel and leave you with a -sqrt(3)
arnt i subtracting?
well anyways, imma hit the hey gn
vapid ice
arnt i subtracting?
Oh oops
meager crypt
lone heartBOT
meager crypt
I’ll cashapp $5 to whoever gets this right for me
inner jungle
lone heartBOT
@meager crypt Has your question been resolved?
karmic solstice
I’ll cashapp $5 to whoever gets this right for me
use the x int
and find factors
then at the end add a +c
then when x is 0
add everything up and ull have smth +c = -7
and solve for c
lone heartBOT
@meager crypt Has your question been resolved?
plucky geyser
I didn't understand exactly what the question was asking. What do they mean by associated homogeneous and particular solutions? Is there a particular solution of first-order differential equations? Where should I start solving the problem?
plucky geyser
lone heartBOT
@plucky geyser Has your question been resolved?
tacit arch
I didn't understand exactly what the question was asking. What do they mean by a...
The 5 makes it nonhomogeneous
lone heartBOT
lone heartBOT
Available help channel!
hardy ermine
lone heartBOT
echo socket
Why does he not write d/dt of pir^2h/3 right away?
hardy ermine
we are finding height, why does he have dv/dt?
echo socket
"Gravel is being dumped from a conveyor belt at a rate of 25ft^3 per minute", so dV/dt = 25
hardy ermine
hardy ermine
okay
he already knows its V=25, why does he do that?
all that extra stuff
because of product rule?
karmic solstice
V is Not 25
echo socket
dV/dt is 25*
karmic solstice
yepp
echo socket
So that he'll write 25 instead of dV/dt later
jade wolf
need help proving
lone heartBOT
need help proving
serene junco
S is a statement, right?
serene junco
The biconditional on the left is always true from left to right
It's equivalent to $$\exists xS(x) \rightarrow \forall xS(x)$$
ocean sealBOT
tatpoj
jade wolf
im trying to proof it via equivilance laws
gusty gorge
The biconditional on the left is always true from left to right
this is not true in the case of vacuous truth
like say your universe is the empty set
serene junco
this is not true in the case of vacuous truth
Oops, you're absolutely right
lone heartBOT
@jade wolf Has your question been resolved?
wheat rampart
If
[1,0,X][cos(Ø),-sin(Ø),0][1,0,-X]
[0,1,Y][sin(Ø),cos(Ø) ,0][0,1,-Y]
[0,0,1][0 ,0 ,1][0,0,1]
Is for 3D Anchored Z Rotation
wheat rampart
Then what will Anchored Y (Or X) Rotation will be?
if
T(x,z) =
[1,0,X]
[0,1,0]
[0,0,Z]
So it will be T(x,y) * R(y) * T(-x,-y) right?
I just dont know what T(x,z) will be actualy
gusty gorge
If
```
[1,0,X][cos(Ø),-sin(Ø),0][1,0,-X]
[0,1,Y][sin(Ø),cos(Ø) ,0][0,1,-Y]
[0,0,...
do you mean rotation around the axis parallel to the Z axis that goes through (X, Y)?
wheat rampart
do you mean rotation around the axis parallel to the Z axis that goes through (X...
Idk i just want to rotate Anchored Y
Rotate Anchored Z with this
[1,0,X]
[0,1,Y]
[0,0,1]
But idk how to rotate the other 2 because idk where to put the Z
wheat rampart
Rotate Anchored Z with this
[1,0,X]
[0,1,Y]
[0,0,1]
This is called T(x,y) i think
gusty gorge
the matrix you've given describes a rotation about points in 2D space
wheat rampart
the matrix you've given describes a rotation about points in 2D space
It work in 3D tho
I mean for the Z only
gusty gorge
in general, people represent affine transformations (linear transformations + translations) with (n+1)-dimensional vectors and matrices
wheat rampart
in general, people represent affine transformations (linear transformations + tr...
Hmmmmm
gusty gorge
If
```
[1,0,X][cos(Ø),-sin(Ø),0][1,0,-X]
[0,1,Y][sin(Ø),cos(Ø) ,0][0,1,-Y]
[0,0,...
the three matrices you've written here
first translate the point by (-X, -Y)
rotate counterclockwise by theta
and then translate by (X, Y)
wheat rampart
in general, people represent affine transformations (linear transformations + tr...
Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
Ok
gusty gorge
So T(x,z) would be
[1,0,0,X]
[0,1,0,0]
[0,0,1,Z]
[0,0,0,1]
yeah
wheat rampart
yeah
So R(y) (rotation y)
Is
[cos(Ø) -sin(Ø) 0 0]
[sin(Ø) cos(Ø) 0 0]
[0 0 1 0]
[0 0 0 1]
Dude these things is hard
wheat rampart
what is rotation y?
The rotation matrix
gusty gorge
The rotation matrix
not helpful
wheat rampart
This
Omg finding that image was hard
Ry thingy
Uhmmmmm
[cos(Ø) 0 sin(Ø) 0]
[0 1 0 0]
[-sin(Ø) 0 cos(Ø) 0]
[0 0 0 1]
Sorry for usaly stay silent for 5 mins, customer keep buy thing for 1 or 2 $ but keep GIVING ME A FEW HUNDREDS BUCKS and im out of money to return
gusty gorge
This
these are linear transformations describing rotations in 3d space around the axes
affine transformations in 3d space are represented by 4-dimensional matrices
strange herald
An airplane is flying horizontally with a speed of 119.23 m/s at an altitude of 4667 m. The plane releases a package which falls to the level terrain below. At what distance (measured horizontally from the point of release) does the package strike the ground?
lone heartBOT
@strange herald Has your question been resolved?
strange herald
No
vale wigeon
@strange herald have you made any progress thus far
vale wigeon
the package starts out moving horizontally with the same speed as the plane, and the horizontal component of its velocity is unchanged throughout (assuming we ignore air resistance, which we probably do)
considering only its vertical motion, the package starts at rest at the same height as the plane, and accelerates under gravity
strange herald
sorry but whats altitude btw?
vale wigeon
height above the ground
if there are words in the problem you do not know the meaning of, you would do better to be upfront about it
so that your vocabulary issues can be addressed directly
strange herald
height above the ground
ohh thanks
strange herald
if there are words in the problem you do not know the meaning of, you would do b...
alr
vale wigeon
you might want to find the time it takes the package to fall to the ground.
and to this end, you ought to know that the distance fallen by an object in freefall starting from rest is given by s = gt^2/2, where t is the time of its fall and g is the acceleration due to gravity
strange herald
g is 9.8 right?
strange herald
alr now what do i do next?
golden canyon
and to this end, you ought to know that the distance fallen by an object in free...
use this equation
vale wigeon
9.8 is probably good enough unless you have been explicitly instructed to use a different value
vale wigeon
alr now what do i do next?
if the package falls from 4,667 m altitude down to the ground, how far did it travel vertically
strange herald
alr but the time wasnt given so should i substitute it with 0 or nah?
vale wigeon
if that's the word you've been taught to use for equation-solving, then sure.
strange herald
i still dont get it
vale wigeon
answer my question
if the package falls from 4,667 m altitude down to the ground, how far did it travel vertically
strange herald
uhmm 119.23 m?
vale wigeon
?????
do you hear yourself?
if a package falls from 4667m to 0m
how far did it fall
strange herald
4667 m????
vale wigeon
yes!
so now if you read my message and recall the formula i gave you
s = gt^2/2
you now know everything here except for t
so solve for t
gusty gorge
,w solve 4667 = (9.8 x^2)/2
gusty gorge
yeah seems about right
gusty gorge
you have the correct value for the time of flight
(the time the object spends in the air before hitting the ground)
now you need to figure out the horizontal distance traveled in that time
strange herald
what should i do next?
gusty gorge
you are free to do whatever you want next, as long as it makes mathematical sense
gusty gorge
I told you that t = 31 is approximately correct
strange herald
Just like the the given y
gusty gorge
I told you that probably the most useful thing is to figure out the horizontal distance traveled in tha ttime
strange herald
Oh okay
lone heartBOT
@strange herald Has your question been resolved?
covert sonnet
What is the algebraic expression of “Perimeter of the land whose width is twice as its length”?
covert sonnet
I forgot😭
covert sonnet
Oh yea
covert sonnet
What is the algebraic expression of “Perimeter of the land whose width is twice ...
But can you give me the algebraic expression of this statement? :D
covert sonnet
Nothing
ornate condor
wow
covert sonnet
P for perimeter L for length and W for width
covert sonnet
covert sonnet
so whats P in terms of L and W
I don’t know. That’s what our prof gave us :(
covert sonnet
I believe it’s a rectangle so like a rectangle with the variables?
ornate condor
yes
covert sonnet
covert sonnet
Idk 😭
What if I’ll just use examples ok so if W is 6m and L is 3m what is it in algebraic expression
covert sonnet
Oh
covert sonnet
No they want the expression
lone heartBOT
@covert sonnet Has your question been resolved?
proper bramble
lone heartBOT
proper bramble
hello i tried to prove this by induction but I was only able to do one part and then I got stuck
the expression at the top is where I stopped
<@&286206848099549185>
alpine sable
induction should work here i think
alpine sable
hmm i did reach $n!(n+1) \leq (\frac{n+2}{n})^{n} \cdot \frac{n+2}{n}$ myself
ocean sealBOT
♡LexQa♡
proper bramble
if possible can you do the demonstration on paper ?
alpine sable
any further proof is kind of hard though
alpine sable
if possible can you do the demonstration on paper ?
sure
proper bramble
okey thank you
someone in my class said to use a function to prove it but I have no idea how
alpine sable
a function?
i mean u r doing induction here which is what u should be caring about so dw
proper bramble
a function?
I didn’t get it either 😭
proper bramble
ouii
proper bramble
hehee also I m studying this math in french so translating it to english might seem a bit confusing
alpine sable
hehee also I m studying this math in french so translating it to english might s...
ohh yeah i get that haha
proper bramble
Yess this is the final proof
proper bramble
and no matter how much I tried I couldn’t reach it
proper bramble
i did that yes
alpine sable
and then take P(k+1)
i think u use induction hypothesis afterwards and u should get the proof
my brain is kind of poof tho so im not connecting the dots
proper bramble
wait I’ll show my demonstration because I did what you’re saying but I got stuck in one part
alpine sable
its hypothèse d'induction i think
alpine sable
wait I’ll show my demonstration because I did what you’re saying but I got stuck...
oh sure sure!
proper bramble
démonstration par récurrence that’s what it’s called
proper bramble
lmao a tiny bit
alpine sable
yep anyways i have my own homework due in like an hour actually so i have to speedrun that, but can u hit me up with the answer if u managed to get it tho?
if u havent gotten an answer by an hour i think i will be able to help u
proper bramble
alpine sable
,rotate
ocean sealBOT
proper bramble
alrighttt if i find anything I’ll text you and good luck with your hw !
alpine sable
oh you could have just taken P(k+1) and made ur life easier tho i think
proper bramble
Reallyy 😭
alpine sable
yuhh
also
is this from a uni class or
because this is the same stuff im taking rn lmaoo
alpine sable
nicee discrete maths gang
alpine sable
i m in my first year of comp sci
samee
proper bramble
and this is analysis idk if it’s correct in english
alpine sable
actually kind of two things since im double majoring in cs and ee but yess
alpine sable
and this is analysis idk if it’s correct in english
discrete maths/logic and proofs whatever
proper bramble
Thats pretty cool ! we don’t have double majors here
alpine sable
i hate the sets stuff
proper bramble
samee
alpine sable
Thats pretty cool ! we don’t have double majors here
france thank you for your great consideration
that makes the life of all of you so much better lmaoo
proper bramble
i m not french but yehh 😭 but it seems fun to do double majors like u can choose
alpine sable
oh SORRY 😭 forgot like most of north africa and Quebec are french-speaking still haha
proper bramble
also can this question I sent you be proven if I start from p(k+1) ?
alpine sable
well morocco and algeria i guess
proper bramble
oh SORRY 😭 forgot like most of north africa and Quebec are french-speaking stil...
It’s finee and I m from Algeria
alpine sable
also can this question I sent you be proven if I start from p(k+1) ?
i think its a good start yeah
proper bramble
alright I’ll try do it that way
alpine sable
u will end up
with the image i made up there
but i am not sure how to work with that either
induction hypothesis something something
alpine sable
It’s finee and I m from Algeria
thats cool!
hit me up with the answer if u do get one!!
proper bramble
Alrighttt will do
blissful meadow
can you help me in this problem
echo socket
Can you show the previous question?
blissful meadow
blissful meadow
Can you show the previous question?
this one
echo socket
$A_n = 5A_{n-1} - A_{n-2} \$
$5A_{n+1} = 25A_n - 5A_{n-1}$
ocean sealBOT
A Lonely Bean
echo socket
Summing the equations yields $5A_{n+1} + A_n = 25A_n - A_{n-2}$
ocean sealBOT
A Lonely Bean
echo socket
So $5A_{n+1}=24A_n-A_{n-2}$
ocean sealBOT
A Lonely Bean
blissful meadow
So $5A_{n+1}=24A_n-A_{n-2}$
what is this?
echo socket
The result
blissful meadow
is this the answer?
echo socket
The entire proof is the answer
blissful meadow
i don't understand
echo socket
Just look at all the equations I sent in order
blissful meadow
Just look at all the equations I sent in order
what question is the answer?
blissful meadow
can you help me in this problem
is the answer you give is for this question? or for both?
echo socket
can you help me in this problem
It's for this
blissful meadow
It's for this
okay
blissful meadow
It's for this
thanks
alpine sable
has it been proved that odd number can be written as 3 primes?
alpine sable
Go to another channel if u can @hexed dagger
hexed dagger
Go to another channel if u can <@899067003673903116>
Why?
small panther
it's not yours
lone heartBOT
alpine sable
has it been proved that odd number can be written as 3 primes?
What is your set of numbers?
golden canyon
pretty sure it's proven, looked it up on wikipedia
if you mean sum of three primes btw
goldbach's weak conjecture
alpine sable
Why?
Truly a gigachad moment
i just heard from numberphile that it has been proved but cant find
golden canyon
hexed dagger
Truly a gigachad moment
Oopsie i didn't seen the tag tittle fully hahaha
alpine sable
https://arxiv.org/abs/1312.7748
ok so it has been proved, thank you so much ❤️
Also this channel is going to close any second now so just open a new channel @hexed dagger
hexed dagger
Okai!
golden canyon
.reopen
hexed dagger
Thank you 😉
lone heartBOT
Available help channel!
alpine sable
I'm generating a list of n numbers and assigning to each a value uniformly chosen randomly from [0,1).
Then I'm choosing a threshold ~k/n and selecting all the numbers below this threshold and getting about ~k values back.
I'd much rather just generate ~k numbers from the range 0 to n with the exact same distribution as above but I'm not sure how.
hexed dagger
.reopen
alpine sable
I'm guessing I need to generate a single value from [0,1) and compare it with the threshold to get a value for ~k then choose k values from 0 to n
Just not sure how to compare.
mortal trellis
just multiply the numbers you generate by n?
alpine sable
The issue is that my current method is really slow and inefficient for a computer generating 100s of values then removing most of them.
I know that there is an equivalent much faster method but I can't figure out what it is.
It needs to have the exact same distribution as well.
mortal trellis
so essentially for each value 1...n you take it with probability k/n, yes?
alpine sable
Yes
Typically k<<n
It looks like the amount of values returned is normally distributed about k.
Any guesses for what standard deviation might be here? I can probably figure out the rest with a lead to follow.
lone heartBOT
@alpine sable Has your question been resolved?
mortal trellis
I mean isn't the picking part just a binomial distribution?
you either take it or you don't
with probability k/n
see this
mortal trellis
can anyone help me?
read #❓how-to-get-help
mortal trellis
actually read it. and then get your own channel
alpine sable
i dont have one
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
lone heartBOT
alpine sable
.reopen
lone heartBOT
✅
alpine sable
yea
last ether
\frac
golden canyon
the bot didn't even give an error, so doesn't matter
alpine sable
jelle where you from?
golden canyon
Netherlands, why?
alpine sable
same
golden canyon
toevallig
alpine sable
haha idd