no
#help-0
lone heartBOT
pale kestrel
huh what?
remote heron
its not special
pale kestrel
if n = 0, x can be anything?
remote heron
2/5 ^ 0 = 1
pale kestrel
x can be anything non-zero
remote heron
eh
lone heartBOT
Available help channel!
austere star
hello
random mica
Hello, how do you find this root from the equation without quadratic formula, just roots extractions
random mica
there is 4 roots it seems, i found the other both
but i don't get how i can find this one
random mica
wil ltry
well it become very odd, there is no way to solve it other way without quadratic equation or else ?
for the first root i did 4th roots on both side to remove the power of 4 and get sqrt(8) on right
.close
alpine sable
Π(a+n-t) from t=1 to b+1
alpine sable
Π(a+n-t) from t=1 to b+1
Calculate what this expression gives yourself
lone heartBOT
@narrow pawn Has your question been resolved?
raw shard
ocean sealBOT
quantum
alpine sable
**quantum**
That's what I said
alpine sable
lone heartBOT
alpine sable
I need to find the determinant of this matrix
the answer I got is -57
but the key says -41
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
My calculator says minus 11
Do it again
Its basic four operator question
Actually instead of doing it again, show me what you multiplied and summed
Maybe your process is wrong idk
We'll see
@alpine sable
3 x |-5 2 3 1| -1 |8 2 -4 1| -2 |8 -5 -4 3|
I don't use that method personally
There is an easier one
Logic is the same but visually it's better
yea ik that method, it's very hard for me
Seriously? I thought people use it more
alpine sable
Seriously? I thought people use it more
yea more ppl do use it, but personally I find the pattern stuff to be kinda hard to remember
But anyways, your process is correct
I think you probably made calculation mistake
It happens to everyone
I'm so stuck on where my calculation mistake is
It's not important
The point is knowing what to do
You are wasting time looking for a simple mistake
Don't you agree?
rich basin
lone heartBOT
rich basin
can someone please explain this
lone heartBOT
@rich basin Has your question been resolved?
rich basin
<@&286206848099549185>
rich basin
this is for (ii)
lone heartBOT
@rich basin Has your question been resolved?
lone heartBOT
@rich basin Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
stable olive
lone heartBOT
buoyant kayak
what exactly is giving you trouble here
don't do people's work for them
...
if you want to
stable olive
thank you here
buoyant kayak
he's already seen it
stable olive
what exactly is giving you trouble here
i couldn't figure out the transposing stuff
from lhs to rhs
ohh yes
.close
alpine sable
what is 0÷0
lone heartBOT
what is 0÷0
buoyant kayak
undefined
alpine sable
oh wait I figured it out imagine that you have zero cookies and you have zero friends to give them to see it doesn’t make sense and you have no cookies and no friends
buoyant kayak
thanks siri
wary stream
oh wait I figured it out imagine that you have zero cookies and you have zero fr...
That's a siri answer
lone heartBOT
@alpine sable Has your question been resolved?
atomic lodge
hi
atomic lodge
can anyone help me with the derivative of ln[In(x)]
gray isle
what have you tried?
gray isle
are those u and v?
its hard to tell them apart
atomic lodge
hold on
strange shale
Your v is too differentiable if you know what I mean thats why it looks like a u
alpine sable
hello guys i need a help with me homework
rough gale
yes?
buoyant kayak
lone heartBOT
Available help channel!
hybrid blade
Hello, why is it that the area under the curve equals the integral of the function?
jagged imp
The integral of a function is pretty much defined as the area under it. What is it that you think an integral is?
hybrid blade
the inverse function of the derivative?
I understand that it is defined as the area under it
but I want to know why that is the case
alpine sable
the inverse function of the derivative?
I think your question was why is the inverse of the derivative the integral
hybrid blade
yes
inland gyro
I understand that it is defined as the area under it
I can send you a very good link for that...may I?
hybrid blade
yes please do
jagged imp
oh... good thing sloct corrected that. I guess i was completely misunderstanding what you were asking..
inland gyro
yes please do
alpine sable
lone heartBOT
alpine sable
the length of the green line = 9.7sin14 = 2.34
@buoyant kayak
bottom angle of triangle = asin(2.34/8.1) = 16.8
so therefor we know the angle z2 makes with the x-axis = 180 - (180 - 14 - 16.8) = 30.84
then the real part of z2 is 8.1cos(30.84) and the Imaginary part is -8.1sin(30.84)
so why is this wrong
lone heartBOT
@alpine sable Has your question been resolved?
grave urchin
Is this correct? or does tan theta < 0 make it false?
lone heartBOT
Is this correct? or does tan theta < 0 make it false?
tropic sluice
Is this correct? or does tan theta < 0 make it false?
it seems correct
how is tanΘ < 0?
grave urchin
isn't tan theta= 4/3 which is greater than 0?
vale wigeon
you did not take into account the sign info given to you by the problem
"isn't tan(θ) = 4/3 which is greater than 0? ...wait that means i fucked up didn't i"
notation is a little all over the place too
cos(theta) should be **-**3/5.
precisely because tan(theta) is known to be negative and sin(theta) positive
grave urchin
oh because sin is positive and tan is negative, cos must be negative
orchid sparrow
coz the equation will be quadratic
grave urchin
.close
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
woeful heart
you know the generalised binomial expansion for (1+x)^n is valid for |x| < 1 right?
alpine sable
yh i know it is
but am unsure like why
i know it is simply because it says that it is in my datasheet
woeful heart
so if you have a sequence of numbers and sum them, sometimes you get a convergent sum and sometimes u have a divergent sum
convergent means its finite divergent means its infinite
alpine sable
yh
woeful heart
if you have |x| >= 1, then if you look at your formula
for expanding the binomials
the terms don't eventually "get small", so it's impossible for it to be convergent
as in they don't tend to zero
supple tundra
but am unsure like why
You would need to do some wider reading into convergence of series
woeful heart
just some intuition
yeh im not being formal
like if u see the terms for |x|<1, you can see the factorial terms tend to approximately 1 eventually
so if you look at the series sum its less than a geometric sum
alpine sable
the terms don't eventually "get small", so it's impossible for it to be converge...
oh yh of course i understand that
woeful heart
which we know converges
we know a geometric series converges if and only if the common ratio r < 1
and this formula looks sort of like that when you get to the big numbers
alpine sable
ah alright, thanks
woeful heart
but yeah if u want rigour u need to learn a lot more stuff
u need an actual textbook with all the definitions and build everything up from first principles
frank plover
I can't seperate the concept of vector spaces and a euclidian vector space 4 some reason, i keep trying to think of any vectors (take functions) as points in a R^3 space.. i think it has to do with the coordinates a euclidian vector space has
frank plover
i guess in a way my question is, what are coordinates in terms of the vector space definition of euclidian space and do coordinates have any meaning for non euclidian vector spaces like the space with polynomials of any degree
vale wigeon
coordinates have meaning when you construct a basis
once you have a basis, you can write a vector in your space as a linear combination of your basis vectors
and the coefficients in said linear combination will be the coordinates of your vector in that basis
frank plover
How do you get a basis in R^2 (for example) without first having a coordinate system
I guess it has to do with what i define to be my vectors in my vectorspace/set but i cant seem to put it in words
vale wigeon
(1,0) and (0,1)
these form a basis
they are vectors in R^2 by the definition thereof
frank plover
but (1,0) and (0,1) have no meaning without a coordinate system right?
unless i just see real vectors as a list of numbers and think of euclidian space as a way of representing them
i think thats my issue, i try thinking of vector spaces spacially, in my head vector spaces are R^n but the axis are changed to their respective basis
vale wigeon
but (1,0) and (0,1) have no meaning without a coordinate system right?
they do
R^2 is by definition the set of ordered pairs of real numbers
(1,0) and (0,1) are just as valid pairs of real numbers as (420,69) or (pi,e) or (32.34526435645, -0.4948485)
frank plover
Oohhh okey okey
frank plover
unless i just see real vectors as a list of numbers and think of euclidian space...
so does the latter part of this still hold up?
If R^n is defined that way, is the euclidian space of R^n just a way of visualizing it?
And can i visualise all vector spaces like that if i think of the axis as their basis (for example 3x3 matrices-space) with x-axis =
\begin{pmatrix}
1&0&0\
0&0&0\
0&0&0\
\end{pmatrix}
ocean sealBOT
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frank plover
no wait
the axis should be coefficients and the unit is just 1 basis matrix (3x3-space)
vale wigeon
i think you might be overthinking it
crisp summit
hey
frank plover
Or i just suck at explaining what i mean lol
crisp summit
anyone that can help me?
frank plover
@crisp summit check out #❓how-to-get-help
vale wigeon
@crisp summit please move to an available channel to receive help.
crisp summit
uh okay tho, but what if its urgent
vale wigeon
go get your own channel
it's going to take less time than you're spending here arguing and trying to intrude on another conbo
convo*
crisp summit
go get your own channel
what do you mean?
vale wigeon
read #❓how-to-get-help
frank plover
but anyway, is what i'm saying a correct way of thinking?
vale wigeon
the way it's worded is very wonky
frank plover
(1,0) and (0,1) are just as valid pairs of real numbers as (420,69) or (pi,e) or...
If this is how R^n is defined, does that mean that the coordinate system (up to dimension n) is just a way of visualising R^n? If not are they both equivalent definitions of R^n?
vale wigeon
well
i suppose in some sense you could say that
but im apprehensive about going full "yes this is exactly how that works"
frank plover
alright
Well if i assume it to be a way of visualising R^n
Could that visualisation, using axis/coordinates defined by the basis vectors, be applied to any vector space?
For example, in the 3x3-matrix vector space. The basis vectors are
For x:
\begin{pmatrix}
1&0&0\
0&0&0\
0&0&0\
\end{pmatrix}
For y:
\begin{pmatrix}
0&0&0\
0&1&0\
0&0&0\
\end{pmatrix}
and for z:
\begin{pmatrix}
0&0&0\
0&0&0\
0&0&1\
\end{pmatrix}
ocean sealBOT
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vale wigeon
no
frank plover
or for the space of polynomials up to (inclusive) degree 2, the basis vectors would be "1" "x" and "x^2"
vale wigeon
the space of 3x3 matrices has dimension 9, not 3.
you're trying to pass something off as a basis that isn't
the matrix $\bmqty{0&0&0\1&0&0\0&0&0}$ isn't a linear combination of the three matrices you presented
ocean sealBOT
Ann
frank plover
Oh
I guess the basis' are matrices with a 1 in one place and zero's in all the others
vale wigeon
no such thing as "the" basis
every real vector space has infinitely many possible bases
frank plover
I guess the basis' are matrices with a 1 in one place and zero's in all the othe...
is there something special about this basis?
vale wigeon
it's convenient to express matrices in terms of
frank plover
are there any criteria about which basis to use for a vector space?
vale wigeon
no
frank plover
hmm
alright
Thanks for the help! in a way i kindof understand my original question better now haha
.close
vague iris
I got 16 lies on the last question. I don't know how they got 10 or 20?
vague iris
3(12)=2(1.2)^x
this is my equation
ocean sealBOT
Result:
15.853154222255
that... yeah, that sounds like 16
wary plaza
I need to find an equation of the plane passing through the given point and parallel to the indicated plane. (6,5,-2), x + y - z + 1 = 0. I'm not getting the right answer. I tried using the the equation of a plane by getting the normal vector to be (1, 1, -1) from the plane. What am I doing wrong here?
vale wigeon
what equation did you get
wary plaza
$x+y-z=-12$
ocean sealBOT
satoshi
wary plaza
so $x+y-z=13$
ocean sealBOT
satoshi
wary plaza
$(x-6)+(y-5)-(z-2)=-1$
ocean sealBOT
satoshi
pale kestrel
thats not the way
wary plaza
how would I go about it then?
pale kestrel
You have the answer already from what Ann said
but if u want to use vec equation of plane
its r.(1,1,-1) = D
where D is to be determined
wary plaza
D is 13?
wary plaza
yeah, thanks I have one more question
Find an equation of the plane through the given point and witht he specified normal vector. (1,2,3), n = 15i + 9j - 12k. Here I get $15x+9y-12z=-3$, but thats wrong
ocean sealBOT
satoshi
pale kestrel
its probably because you used the same wrong method?
pale kestrel
its r.(1,1,-1) = D
use what i just said
wary plaza
I just plugged in the numbers in the equation of a plane
pale kestrel
what is the plane equation
ocean sealBOT
satoshi
wary plaza
I used it for a similar problem, and I got the right answer
according to my book the answer is 5x+3y-4z+1=0
pale kestrel
well you can quickly check
5+6-12+1 = 0...
but that normal vector is completely wrong
its not 1 2 3
wary plaza
oh wait yeah
sorry
its (15, 9, -12)
(1,2,3) is the point
but I will still not get the right answer
pale kestrel
wait im confused lol let me see
no your answer is correct
you just didnt factor out 3?
pale kestrel
Find an equation of the plane through the given point and witht he specified nor...
divide thru by 3
my bad, misread
pale kestrel
$(x-6)+(y-5)-(z-2)=-1$
i think your method is fine, but maybe you flipped the signs wrong
i havent seen this way before
back to the 1st one
wary plaza
$15(x-1)+9(y-2)-12(z-3)$
ocean sealBOT
satoshi
wary plaza
$15x-15+9y-18-12z+36$, right?
ocean sealBOT
satoshi
pale kestrel
idk i havent seen this method before, like i said
the one I use is to use vector form
wary plaza
the book wants me to use that method
wary plaza
I havent seen that form. How does that one work?
pale kestrel
you know dot product?
pale kestrel
yes
r is the variable vector
call it (x y z)
and you end up with the same plane equation
wary plaza
so in this case (1,2,3)?
pale kestrel
so in this case (1,2,3)?
yes
r . n = r_0 . n
You can also write it like this
if you have the normal vector n and a specific r_0 you know is on the plane
wary plaza
whats the method called?
pale kestrel
vector equation of plane
If you rearrange the math
you will end up with the aame formula you use
but i find think this is easier to remember
wary plaza
ive only seen people use the equation of a plane
pale kestrel
the intuition of this form comes from r . n = 0 means r and n are perpendicular
then the right side D, translates the plane
wary plaza
alright, cool
runic condor
lone heartBOT
https://tenor.com/view/sucka-dick-gif-20002059
tame falcon
.close
lone heartBOT
frank plover
What do points on a plane in R^3 have in common? I know it's a very simple question but my brain is overworked rn and i cant wrap my mind around it.
frank plover
I know something has to be held constant but idk what? (i think this because in the cases of xy/yz/zx -planes one of the three coordinate values is held at a constant 0)
pale kestrel
ngl theres a lot you can say
you can describe the plane by saying all the points satisfy an equation
severe sluice
well
i guess there's a value of a,b,c,d so that ax+by+cz+d=0 (literally the equation of a plane)
frank plover
oh yeah lol, i forgot about that equation.
So all the points on a plane have a,b,c and d in common, right?
severe sluice
So all the points on a plane have a,b,c and d in common, right?
yep!
thanks!
dire basin
hi, i was doing some simulations for a three sided dice. Assuming i found a dice which has 1/3 probability of landing on each of it sides and i do a 1000 throws. We know that it is almost impossible that all the three sides(up, down, edge) come up 333, 333, 334 times(not particularly in this order). My question is what range of values can i accept so that i can assume that the dice i created is almost completly fair. example say i get 310 ups, 340 downs and 350 edges, can i say that this dice is fair?
dire basin
basically i dont know a lot of stats so i had to ask here
sorry if i phrased this badly
severe sluice
hi, i was doing some simulations for a three sided dice. Assuming i found a dice...
- how can you make a 3 sided die? a cylinder?
- no, there's no telling if the dice is fair for certain. there's always a probability that a fair dice comes up with your result. you might want to look into p-values in statistics though.
vale wigeon
if you want a physical design just do a cube with two sides labeled with each number
dire basin
1. how can you make a 3 sided die? a cylinder?
2. no, there's no telling if the ...
- basically a cylinder but thats not relevant atm
- ik we cant tell for certain but is it like possible to somehow use some stats or smthing to get a range allowing a little error
dire basin
if you want a physical design just do a cube with two sides labeled with each nu...
oh no thats done
severe sluice
1. basically a cylinder but thats not relevant atm
2. ik we cant tell for certai...
yeah, you can certainly do that.
bleak ridge
Hypothesis test gives me ptsd
dire basin
uhhh i have no idea what this is but i guess ill give it a look
pale kestrel
hi, i was doing some simulations for a three sided dice. Assuming i found a dice...
'impossible' is a strong term
it is possible, but just very unlikely
pale kestrel
in the end, what range if values is kindof up to you
in stats you choose your confidence interval
but you choose it first, then run your experiment
dire basin
ok so umm a lil context here. this is basically for a physics competition. so i thought that maybe we have to find the range through some mathematical means but if i understand correctly u mean that i can just say that if the results are all in the range 310-340 the dice can be deemed fair(kinda)
the range means the number of times each of the three sides pops up after a total of 1000 throws*
pale kestrel
kindof, and you should justify your choice of confidence interval before doing the experiment
you need to work out the probability of this happening 310-340
if you choose that
dire basin
you need to work out the probability of this happening 310-340
and how do we do that?
pale kestrel
find the distribution
dire basin
i dont know stats that's why i asked here 😥
vestal aspen
lone heartBOT
teal turtle
Do you have graph paper?
merry iris
Graph it
vestal aspen
Yes I do
vestal aspen
I just got done with my break and I forgot how to find slope
merry iris
Slope is the coefficient of x
teal turtle
Equation of line is y = mx + c, m is the slope and c is the y intercept
how did you do 15 without knowing how to find slope though?
vestal aspen
15 isn’t circled
merry iris
Lol
lone heartBOT
@vestal aspen Has your question been resolved?
weak snow
It's possible to integrate a matrix?
I have an formula that gives to me an integrate but the integrator will be a matrix.
pale kestrel
I think by convention, thats what you do (I'm not 100% sure)
frank plover
I think you're supposed to integrate component wise (not sure either lol)
Check out this link: https://math.stackexchange.com/questions/450560/integrating-a-matrix/450565
pale kestrel
Don't think any other interpretation makes sense
weak snow
I can show more details of the problem if you want
Sure, one second
I have this sequence where f(x)=x'
weak snow
and this EDO problem
I already find the solution which is x(t)=acos(t)+bsin(t); y(t)=x'
now I must to show that the sequence converges to the solution.
But i dont know how i can evaluate this sh*t
lone heartBOT
@weak snow Has your question been resolved?
lone heartBOT
@weak snow Has your question been resolved?
weak snow
<@&286206848099549185>
lone heartBOT
@weak snow Has your question been resolved?
karmic quail
lone heartBOT
@weak snow Has your question been resolved?
acoustic spire
hi
orchid pulsar
Is this correct?
lone heartBOT
Is this correct?
bleak ridge
Did it just ask to set up the sum and integral?
orchid pulsar
Yes
bleak ridge
I mean it looks right to me
timid jewel
lone heartBOT
glass lichen
You already did part i.
timid jewel
yeah U x V
timid jewel
ii
lone heartBOT
@timid jewel Has your question been resolved?
pale kestrel
without reading the material
you're not gonna be able to do it
these questions are getting deeper and deeper into the subject
better to read the material or watch videos to understand
lone heartBOT
@timid jewel Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
bold mantle
lone heartBOT
bold mantle
help
vivid charm
what have u tried
bold mantle
i want to do the think where it goes, what 2 numbers multiply to get -4 but also add/subtract to get 11 and i dont think thats possible
and i dont know another way
placid zinc
You're ignoring the 3, which changes how you'd think about the problem
vivid charm
well actually let's write out (3x .........)(x ........) for now
vivid charm
You're ignoring the 3, which changes how you'd think about the problem
ya most likely
bold mantle
yep
bold mantle
yeah foil
vivid charm
i dun call it foil but ik ppl do
bold mantle
i call it foil
bold mantle
ok
@vivid charm lol sorry im stuck
i remember today learning about how i need to split the 11x
but i dont remember how to do ot
it
vivid charm
<@!247713300115226625> lol sorry im stuck
why split 11?
u shud be splitting 4
how would u split 4
gray isle
applying the ac method
i.e. consider a pair of numbers that multiply to ac = 3 * -4 = -12
and sum to b = 11
use that to determine how to split the 11x and continue with factorisation by grouping
paper coral
lone heartBOT
swift harbor
side note is dat baki in ur pfp
paper coral
so the largest positive integer m for which 2^m is a divisor of 9!
yes
baki is epic
not cap
so isn't this saying (2^m)/9! where m is a integer and where that number is a integer
i cannot read nvm
.close
lone heartBOT
lone heartBOT
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nimble bane
How do I do this question
lone heartBOT
How do I do this question
@nimble bane Has your question been resolved?
Available help channel!
alpine sable
is the correct answer none of the above? i got x = 848.5 and y = 1697
wary stream
is the correct answer none of the above? i got x = 848.5 and y = 1697
You might have 2y = 1697
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
nimble bane
how i do this
lone heartBOT
how i do this
nimble bane
lone heartBOT
@nimble bane Has your question been resolved?
tranquil kestrel
anyone can solve 2b)?
hybrid blade
have you done 2A?
if so, can i see what you put
i may be able to help
A->W>or equal to 20
where w is the amount william drinks
B->W<20
C->W>or equal to 5
W<20 is logically equavelant to ~(W>or equal to 20)
therefore A and B are contradictories
If C is true, then either A or B is true
C-> A V B
C-> ~(A & B)
ok im not gonna use w
A -> ~B
B -> ~A
therefore ~B -> A
therefore A iff ~B
and B iff ~A
A -> C
tranquil kestrel
sure let me show you mine 2A
tranquil kestrel
My 2a) is Just the lines as given. A= He drinks at least 20 cups a day, B=, William drinks less than 20 cups a day and C= at least 5 cups a day. Basically wrote these.
tranquil kestrel
so my working is wrong right?
hybrid blade
i see
A -> ~B & C
B -> ~A
C -> A V B
If A is true, then ~B & C
the question wants to find who specifically (as in one person?) is right
therefore A cannot be true, for it implies that C is true and therefore two propositions are true
C implies that either A or B is true, which also implies that at least 2 propositions are true
therefore C cannot be true
thus, it is only possible for B to be true?
idk
If B is true, then we know that A is false
but C may be either true or false
B is necessarily true only if ~A & ~C
~C-> ~(A VB)
if B is necessarily true then B -> ~(A V B)
I think the answer is B
im thinking too mich
Just take it like so:
A -> ~B & C
B -> ~A
C -> A V B
If A is true, then ~B & C
the question wants to find who specifically (as in one person?) is right
therefore A cannot be true, for it implies that C is true and therefore two propositions are true
C implies that either A or B is true, which also implies that at least 2 propositions are true
therefore C cannot be true
thus, it is only possible for B to be true?
lmk if u still want help
opaque inlet
Hi
opaque inlet
I’ve got a series of questions related to combinations and permutations
We’ll start off with question 12.
Can anyone help me on this pls
opaque inlet
how many outcomes are there in first case ?
The first roll?
orchid sparrow
yes
opaque inlet
6 outcomes
orchid sparrow
ok in 2nd?
opaque inlet
6 outcomes? I think?
opaque inlet
I meant 36 outcomes
orchid sparrow
yes
pale kestrel
Thats not the answer btw.
pure wasp
It would be easiest to just count them out tbh
And if you roll 0 either time it will be 0
pale kestrel
half of them will be reapeated
more
pure wasp
Are you sure you’re in the right class?
orchid sparrow
and then you have to subtract 4 more as
opaque inlet
Are you sure you’re in the right class?
Who? Me?
opaque inlet
Oh ok
pale kestrel
imo a better way to count this is to notice you have 5 primes
and 0
a slow but sure way is to draw a 6x6 table
and write down all the possibilities
and count the different ones by putting them in order
orchid sparrow
half of the results will be when the digits will be reversed. and you will get 0 five time so u have to subtract 4 also
so the answer imo will be 14
opaque inlet
Ok
orchid sparrow
hm
opaque inlet
Is there a quicker method than doing the table method you suggested?
pale kestrel
so the answer imo will be 14
I get 16 🤔
pure wasp
I got 16 too
pure wasp
Is there a quicker method than doing the table method you suggested?
I just did table took like 1 min
opaque inlet
I just did table took like 1 min
Damn
pale kestrel
so the 'quick' method
opaque inlet
Let me check my textbook
pale kestrel
you have 5 primes
You can choose 2 different ones to make a product
thats 5 choose 2 = 10
you can choose the same one (squares)
thats 5
then theres also 0
so a total of 10+5+1 = 16
orchid sparrow
if u choose 5 and 5 then wont the product be 25
orchid sparrow
you can choose the same one (squares)
.
hybrid blade
oh
orchid sparrow
is there any answer key?
opaque inlet
Yes
pure wasp
Nah it has to be 16 unless they didn’t count 0
opaque inlet
Just 15
pure wasp
How
pure wasp
??
opaque inlet
then how do u know?
The answer is in the textbook
It doesn’t provide a working out nor explanation tho
orchid sparrow
lol
pure wasp
That’s an answer key
orchid sparrow
yea
pale kestrel
why dont we list all 16 😢
orchid sparrow
yes
pale kestrel
meh this is IB textbook
there are typos everywhere in those
especially in the answers
opaque inlet
meh this is IB textbook
What’s a IB textbook
pale kestrel
is this not IB textbook
pure wasp
0,4,6,10,14,22,9,15,21,33,25,35,55,49,77,121
opaque inlet
What is that
jagged imp
This is an australian textbook
jagged imp
oi oi oi
pure wasp
Math works differently there
opaque inlet
Math works differently there
No it doesn’t lol
jagged imp
ye
pure wasp
Are you caught up donta
opaque inlet
Are you caught up donta
No
pure wasp
Wya
pure wasp
Where are you at
opaque inlet
I don’t understand the question?
pure wasp
WHERE ARE YOU AT IN ONE PIECE
jagged imp
And ur a fan of one piece?
yeah im caught up to the manga, but not the anime.
opaque inlet
WHERE ARE YOU AT IN ONE PIECE
Oh. You have to tell me that you’re a one piece fan
I’m an anime only
jagged imp
i wonder how you figured i was a op fan
pure wasp
Zoro dies
pure wasp
Doesn’t really make sense to me what do they mean by rotated
Like the squares or
Or is it just factorial
pale kestrel
means you have 3 types of floor tiles
that are 2x2
and find how many floor patterns you have that are 2x6
jagged imp
first find out how many ways you can rotate those in one order and multiply that by the total number of ways you could arrange the tiles
pale kestrel
first find out how many ways you can rotate those in one order and multiply that...
hmm.
opaque inlet
Damn
pale kestrel
each of the tiles, how many ways to rotate
no
take the 1st tile
how many possibilities
opaque inlet
4 possibilities?
opaque inlet
4
opaque inlet
Yes
opaque inlet
Yes
pale kestrel
so you multiply the possibilities
opaque inlet
64?
opaque inlet
6 ways
opaque inlet
Calculate the other tiles?
pale kestrel
no..
there are 2 things that are important here
how the tiles are oriented
and how they are ordered
do these 2 things affect each other?
opaque inlet
Of course not
pale kestrel
so you multiply again
the key is, you have no repeats in counting like this
since the tiles all look different
opaque inlet
So 216
opaque inlet
Oh
pale kestrel
i said 3! above, not 3
opaque inlet
i said 3! above, not 3
Yes sorry for the mistake
pale kestrel
,w 6*64
ocean sealBOT
pale kestrel
ok
jagged imp
pale kestrel
think u got it
pale kestrel
any ideas
pale kestrel
hint: try it for 24, first
opaque inlet
hint: try it for 24, first
Wdym 24
opaque inlet
any ideas
I was thinking about making n! = n(n-1) * (n-2)!
The same thing applies for m
But I can’t do anything with it
I don’t think
opaque inlet
But why 24?
opaque inlet
Ok god
Lol
m! * n! = 24
Now trial and error?
m = 4 and n = 1
m = 1 and n = 4
opaque inlet
I don’t get it
pale kestrel
24 = 4!
the person who wrote the question
didnt randomly choose 720
i also didnt randomly choose 24
opaque inlet
720=6!
pale kestrel
yh
opaque inlet
Oh ok
pale kestrel
also be careful
it says in q
m > n
anyways, so you have 1 easy solution for starters
pale kestrel
ok
opaque inlet
Bcuz m>n
pale kestrel
that is a solution
ah actually i think u missed something both times
for 24 and 720
opaque inlet
What I miss?
pale kestrel
0!
pale kestrel
🙂
pale kestrel
there arent
pale kestrel
in the positive integers at least
opaque inlet
in the positive integers at least
Nah we’re only working with positives here
No negatives
opaque inlet
pale kestrel
lol i gotta go off
opaque inlet
lol i gotta go off
Bye
opaque inlet
<@536452419219882004> I can help
Yes pls
alpine sable
Sure which one
opaque inlet
6e.
alpine sable
What u need to do is to treat the three people aka the two parents and youngest child as one entity
And permute it with the rest
And then permute the people in the entity
alpine sable
There is initially 4! Ways to permute the entity along with the 3 remaining kids
And then 2! Ways to permute the parents within the entity
So answer is 2! x 4!
alpine sable
Sure lemme see
Hmm this is a good one
U need to treat the 5 digits as separate empty spots
U can permute the first digit in 9 ways , ( not 10 because 0 will make it a 4 digit number)
Then 9 ways for second digit
And 8 for middle
opaque inlet
Ahhh ok
alpine sable
The last two digits will be fixed as the number is palindromic
So 9 x 9 x 8 x 1 x 1
opaque inlet
Wait so
opaque inlet
Hm
alpine sable
Since the 3rd and 4th digit are same
alpine sable
128821
opaque inlet
Ok I get that