ok
#help-33
dry prawn
prime scroll
nothing
but its more efficent to learn with others
thats what I know
i mean i know some stuff
like basic rules of pemdas i think
dry prawn
but its more efficent to learn with others
this means doing homework problems and such with other people who are also doing those problems
not getting someone who knows them to explain how to do everything
dry prawn
do you know how to add fractions in general?
dry prawn
not necessarily
prime scroll
only i know the same demominator
like 1/4+1/4
is 2/4
i know this
but i dont know
1/32+1/68
dry prawn
prime scroll
i need help not this youtube video
dry prawn
if you don't know how to add fractions, you can't solve the problem
dry prawn
it is
dry prawn
if you know the process for adding two fractions with different denominators, you follow that exact same process when there are variables
civic dove
Dont guess
prime scroll
its not guessing its educated
prime scroll
this one
civic dove
Send your question
dry prawn
question is always in pins for future reference
civic dove
Ok
civic dove
question is always in pins for future reference
Ok ill help him if u want
civic dove
Whats the bottom of fraction called in english?
civic dove
Ok they have to be the same in addition/substraction you know that right?
civic dove
Ok cool
civic dove
how do i make it same
You have to multiply other fractions by whats missing but first you should deal with 3rd one
Do you know how to make x²-16 similar to other two?
civic dove
Ever heard of difference of squares?
prime scroll
no
prime scroll
ok
prime scroll
ok
civic dove
So in your scenario x²-16 would be what
Hint: you have to make 16 as a number squared
prime scroll
um
civic dove
You got this
prime scroll
(x+2)(x-2)
prime scroll
ok
civic dove
But yes x-4 x+4
Goood
So now as you can see 1st fraction is missing x+4 and 2nd one missing x-4
You have to multiply both top and bottom of fraction by that number
prime scroll
it cancel out on both i think
civic dove
1(x+4)/(x+4)(x-4)
prime scroll
what is this
civic dove
it cancel out on both i think
Show me how you cancel it out
civic dove
what is this
Its 1st fraction but how it should look in order to perform substraction
civic dove
Well
One of the fractions is missing x-4
As you can see by the bottom
If its missing something from other fractions you have to multiply by it
exotic ingot
i got x=8
prime scroll
i dont need answer i need learning
prime scroll
ok
exotic ingot
aight wait so just find lcm of the two fractions, in this case, x^2 -16
civic dove
If say you have 1/x - 1/y = 0
exotic ingot
then multiply by missing factors on each fraction top and bottom
civic dove
How would you multiply each one to do substraction?
exotic ingot
you should get like 2x/x^2 -16
its hard to type out
ok so we know the lcm is x^2-16
prime scroll
ok
civic dove
Ok i dont know what is he doing but sure ima just go to my chem
prime scroll
it alr gives u the facotr of it
factor
i think
idk if it does that every time
or if its just lucky
exotic ingot
you need to add them up
prime scroll
add what up
exotic ingot
thinking of them as like fractions without same denominator
exotic ingot
no no no
civic dove
and the x-4 by x-4?
Not by x-4
prime scroll
so what happen to the x-4
prime scroll
what is all that
exotic ingot
alright so the slash is the fraction bar
write it all out
we multiply the top and bottom by the same number, essentialy we multiply by 1, just in a way that we can get it to add up nicely
ie) add 1/3+1/2
exotic ingot
ie) add 1/3+1/2
do this first
prime scroll
where did the 1/3 and 1/2 come from
exotic ingot
where did the 1/3 and 1/2 come from
its an example
do the example
im tryna teach you
exotic ingot
its 1 in the morning and im not studying for chem test for you
prime scroll
o
exotic ingot
alr so what is it
exotic ingot
isnt the same
yea so what would you do
prime scroll
multiply them to make it like better
exotic ingot
whats m for
multiple
prime scroll
whats a multiple
prime scroll
ok
prime scroll
3
prime scroll
its 1/3 tho
exotic ingot
bc 3/3 is one so it stays even
exotic ingot
so then it become
exotic ingot
its 1/3 tho
its different for 3
prime scroll
what
exotic ingot
we want the denominator to be 6, thats the LCM
exotic ingot
what do you multiply 3 by to get 6
prime scroll
2
exotic ingot
but arent we supost to do the same thing on both sides of the equation
no bc when we multiply top and bottom of 1/2 by 3, we're essentialy just multiplying by 1, so it doesnt change anything
prime scroll
no bc when we multiply top and bottom of 1/2 by 3, we're essentialy just multipl...
oh o
ok
exotic ingot
same for 1/3, we multiply yop and bottom by 2
so then that becomes 1/2+1/3=3/6+2/6
=5/6
prime scroll
so if u multiply it by the multiple it just changes the numberator and demonenator to make it easier to add and subtract but it doesnt change its value?
prime scroll
isnt 1/3 times 2
exotic ingot
x-4 and x+4
exotic ingot
there lcm is x^2 +16
prime scroll
ok
exotic ingot
so then we multiply top and bottom of each fraction by the factor that isnt the numerator
prime scroll
ok
prime scroll
ok
exotic ingot
once the denominators are =, you can multiply each side my the denominator to cancel it
exotic ingot
so i do 1/x-4(x+4)
dont forget to multiply the numerator by x+4 too
to keep equality
exotic ingot
prime scroll
why is there so many numbers
exotic ingot
why is there so many numbers
its all the same numbers thats why
prime scroll
which part is the solving part
prime scroll
the first one u just wrote it i think
exotic ingot
the first one u just wrote it i think
yuh
exotic ingot
prime scroll
did u add 4+1x twice
exotic ingot
do yk how to add fractions
prime scroll
wait no thats 4
exotic ingot
its colledge albregra
ok so pre calc
prime scroll
i have not took calc in high school
exotic ingot
so you should basically know most of the steps already
prime scroll
this is prob why i struggel
exotic ingot
i have not took calc in high school
ik, college algebra is pre calc
how do oyu add 1/2 +1/3
i just explained it,
prime scroll
so you find the least common multiple
exotic ingot
whats a lcm
exotic ingot
i have to wake up at 6, so il give you 5 minutes before i just send you some video links ok
try to work it out on your own
prime scroll
i have to wake up at 6, so il give you 5 minutes before i just send you some vid...
its ok i can watch videos
i think i can visualize it better that way
cause im a bit slow
exotic ingot
yea ok
prime scroll
u can sleep now
exotic ingot
dw abt it
exotic ingot
u can sleep now
no i still need to study for ap chem
prime scroll
chemistry need basic math
exotic ingot
u add the stuff together
what my test is on is an easier version of this at its simplest
exotic ingot
chemistry need basic math
just like this
exotic ingot
i hope you realize im in 10th and im taking the same class as you right now
shoot wait you aint know that
prime scroll
i hope you realize im in 10th and im taking the same class as you right now
i am not take math degree
exotic ingot
i am not take math degree
neither am i
exotic ingot
i used to get 100% in algebra and be top of my class
this is algebra
exotic ingot
algebra 2 ish
prime scroll
this is a bit harder for sure tho
exotic ingot
this is a bit harder for sure tho
i did this last year
prime scroll
like before the hardest thing was factoring stuff
exotic ingot
this is just the opposite 😭
its multiplying things out
yk need to know this to factor gng
prime scroll
yk need to know this to factor gng
ok go study ap chemistry
exotic ingot
prime scroll
i will watch yt videos
and someone else canhelp me if i get stuck
dont worry
u can study
exotic ingot
adding fractions w/ unlike denominators and addding rational equations
thats the two topics
marsh citrusBOT
@prime scroll Has your question been resolved?
marble gazelle
forst of all learn what are ectraneous roots sire
otherwise this question seems pretty vague to a person who doesnt know what it was/is
abstract snow
Can someone help me with number 5b
marsh citrusBOT
Can someone help me with number 5b
abstract snow
The problem im facing is that i cant find the upper and lower bound of d(sinh(x)) / dx
lapis sparrow
aight so the derivative is cosh(x).
Maybe you forgot what the minimum value of cosh(x) is? That's the lower bound you're lookin for.
whole thorn
graph cosh x on desmos
lapis sparrow
aight so the derivative is cosh(x).
Maybe you forgot what the minimum value of ...
is it?
what do u get if u plug in x=0 to cosh(x)?
lapis sparrow
There ya go. So now you know the derivative is always >= 1.
How're you gonna use that with the MVT? You need to pick an interval first.
abstract snow
Nvm im not on to smth
abstract snow
There ya go. So now you know the derivative is always >= 1.
How're you gonna us...
The interval of x for the MVT?
lapis sparrow
Ur work looks solid. You're super close.
You have 1 <= (sinh(b) - sinh(a)) / (b - a).
The goal has sinh(x) and x.
You must pick values for a and b to make your equation look like the goal. What if you try making the interval [0, x]? Sub that in and see what happens.
marsh citrusBOT
@abstract snow Has your question been resolved?
abstract snow
Smth like this?
Gimme a sec im trying to fill in the gaps
Like the domain of x etc.
lapis sparrow
Nice, u basically got the two cases down.
But check ur conclusion at the end. You wrote x <= sinh(x) for all x, but ur second case for x < 0 proves the opposite, right?
You're just one step away. You've proved what happens when x is positive and when x is negative. Now you just gotta combine them to get the absolute values.
lapis sparrow
Wait
abstract snow
Tyt
lapis sparrow
That first case with [0, |x|] is all u need, nice. The rest is redundant.
You've basically proven sinh(|x|) >= |x|.
You must connect this to the final answer with the absolute value around the whole sinh(x). What happens when x < 0?
abstract snow
That first case with [0, |x|] is all u need, nice. The rest is redundant.
You'v...
Wait how come
Dont i need to interval of (-|x| , 0) too?
Cuz i only got the R+ the first time
Also i just realized that i can just let a= -|x| and b = |x| to skip the second half
@lapis sparrow
Also thx a lot for ur help
Appreciate it
marsh citrusBOT
@abstract snow Has your question been resolved?
novel juniper
$p(X=x) \begin{cases} x\in A & p(1)=p \ x \notin A p(0)=1-p \end{cases}$
\
Then the p(Y) $=\sum_{i \in A} p(x=i)$
marsh citrusBOT
$p(X=x) \begin{cases} x\in A & p(1)=p \\ x \notin A p(0)=1-p \end{cases}$
\\
The...
elfin berryBOT
wai
novel juniper
,close
This problem is drivng me mad
Okay, let's start off simple
$Y(\omega)=I_A(X(\omega)) = \begin{cases} 1 & X(\omega) \in A \ 0 & X(\omega) \notin A \end{cases}$
\
We then have $P(Y(\omega)) = P(I_A(X(\omega)) = \begin{cases} p &X( I_A(\omega)) \in A \ 1-p & X(I_A(\omega)) \notin A \end{cases}$
\
\textbf{this feels off}
lethal bridge
wai
novel juniper
like the CDF would make no sense then
The reason this PMF makes no sense is say A is (a,b)
then the CDF is 1-p until a
1 in (a,b)
and 2-p after??
elfin berryBOT
wai
novel juniper
well, this is a mess
$Y(\omega)= I_A(X(\omega)) = \begin{cases} 1 & X(\omega) \in A \ 0& X(\omega) \notin A \end{cases}$
\
We then have $P(Y(\omega)) = P(I_A(X(\omega)) = \begin{cases} p& X(\omega) \in A \ 1-p & X(\omega) \notin A \end{cases}$
elfin berryBOT
wai
novel juniper
Which makes no sense to me?
marsh citrusBOT
@novel juniper Has your question been resolved?
still temple
Hello. I am trying to understand this proof
marsh citrusBOT
Hello. I am trying to understand this proof
still temple
I don't understand the second line in the solution
Why is n! multiplied by (n-k+1) ? The numerator to the left is what I am referring to
glass silo
They multiplied both the numerator and denominator by (n - k + 1), in the denominator it gets absorbed into the factorial (n - k)! 
still temple
Oh
still temple
They multiplied both the numerator and denominator by (n - k + 1), in the denomi...
Are you referring to this ?
Is that was used to multiply everything?
glass silo
Well, they wanted to get a common denominator between the terms, for the first term, they achieved that by multiplying numerator and denominator by $(n - k + 1)$, so the first term became
[
\frac{ n! (n - k + 1) }{ k! {\color{green} (n - k + 1) (n - k)!} }
]
but from the fact that the factorial satisfies $(m + 1)m! = (m + 1)!$, the green turns into ${\color{green} (n - k + 1)!}$
still temple
Thank you. I am looking at it now
elfin berryBOT
@glass silo
marsh citrusBOT
marsh citrusBOT
Available help channel!
solid mural
A (30.0 m, 20.0 m), B(60.0 m, 80.0 m), C (10.0 m, 10.0 m), D(40.0 m, 30.0 m), and E(70.0 m, 60.0 m), all measured relative to some origin,
- start at tree A and move toward tree B, but to cover only one-half the distance between A and B.
-then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D.
-finally move toward tree E, covering one-fifth the distance
between you and E, stop.
b) What If? What if you do not really know the way the
pirate labeled the trees? What would happen to the answer
if you rearranged the order of the trees, for instance, to B
(30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m,
30 m), and D (70 m, 60 m)? State reasoning to show that
the answer does not depend on the order in which the trees
are labeled
wispy stump
A (30.0 m, 20.0 m), B(60.0 m, 80.0 m), C (10.0 m, 10.0 m), D(40.0 m, 30.0 m)...
!status
marsh citrusBOT
A (30.0 m, 20.0 m), B(60.0 m, 80.0 m), C (10.0 m, 10.0 m), D(40.0 m, 30.0 m)...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
i don't get how the answer does not depend on the order of the trees
wispy stump
i don't get how the answer does not depend on the order of the trees
Can you post the original question if you have it?
wispy stump
Where P is the position vector and a is the fraction by which you move towards X
wispy stump
i can show my work
Yeah
wispy stump
Its correct
@solid mural
Now find P4
Nvm
You did
So you got the final position
wispy stump
Try to find Pfinal = 1/5*(A+B+C+D+E)
solid mural
wait, why 1/5
wispy stump
For both x and y co-ordinates
wispy stump
wait, why 1/5
How many terms in the bracket?
solid mural
you mean points ?
wispy stump
Yeah
solid mural
sorry, english is my second language
wispy stump
Find it for both x and y co-ordinates
solid mural
and after that ?
solid mural
alright
wispy stump
P = (xa + xb + xc + xd + xe/5) , (ya + yb + yc + yd + ye/5)
xa, xb, etc are x co-ordinates and ya yb, etc are y co-ordinates
solid mural
yes, i'm doing this now
wispy stump
yes, i'm doing this now
Yep
solid mural
so it's the same as P4
wispy stump
so it's the same as P4
Yeah, you see why
Everytime you applied the formula, whether it be 1/2, 1/3
It was arithmetic mean
And sequence of the tree doesn’t matter when we apply arithmetic mean
So even if the order of tree is change, it wont affect the final position
solid mural
so why did i torture myself to do all of that in the first place
i could've done it the first time
wispy stump
Unless and until the position of the trees are same, labelling of the trees wont mattr
wispy stump
so why did i torture myself to do all of that in the first place
Because when you learn it the hard way, you understand it better
wispy stump
thank you very much
No need, it was all you
solid mural
Thats how it is
unfortunately
wispy stump
If you’re satisfied with the answer pls close the ticket and have a nice day ahead
wispy stump
unfortunately
Indeed
solid mural
If you’re satisfied with the answer pls close the ticket and have a nice day ahe...
you too!
.close
marsh citrusBOT
wispy stump
Lmk if you need any help again
solid mural
Lmk if you need any help again
you are good at this so don't tempt me or you won't get rid of me
wispy stump
you are good at this so don't tempt me or you won't get rid of me
From where i come, sharing knowledge is like nurturing a tree
So idc
marsh citrusBOT
Available help channel!
void brook
question 4 is just wrong, right? the professor insisted that we take a hypothetical situation in which it's true, but I didn't know how to go forward with it
marsh citrusBOT
question 4 is just wrong, right? the professor insisted that we take a hypotheti...
void brook
so how do we go on with it, then?
proud ice
"If false, then true" is always true
stoic saddle
so how do we go on with it, then?
to prove the statement false one would have to present an integer(?) n such that 3n+2 is divisible by 3 but n itself is not
agree or disagree?
void brook
yeah, agree
void brook
bleak meadow
can anyone help me with my math homework
please send your problem in an available channel, like #help-42
marsh citrusBOT
@void brook Has your question been resolved?
north otter
how do i do this can someone help
marsh citrusBOT
how do i do this can someone help
pallid tapir
how do i do this can someone help
We're saying that $T(v)=Av$ for some matrix $A=\begin{pmatrix}a&b\c&d\end{pmatrix}$
elfin berryBOT
Flip
pallid tapir
*for all vectors v
buoyant jetty
every linear transformation can be represented as a matrix representation
like, this matrix that you are trying to find is the matrix representation of T wrt standard basis
pallid tapir
so in particular, [\begin{pmatrix}a&b\c&d\end{pmatrix}\begin{pmatrix}2\1\end{pmatrix}=\begin{pmatrix}-11\4\end{pmatrix}] and [\begin{pmatrix}a&b\c&d\end{pmatrix}\begin{pmatrix}-6\-5\end{pmatrix}=\begin{pmatrix}35\-16\end{pmatrix}]
elfin berryBOT
Flip
pallid tapir
this creates a system of 4 equations with 4 unknowns
marsh citrusBOT
@north otter Has your question been resolved?
buoyant jetty
like, if you know that {{(2,1), (-6,-5)} is a basis, call it B = {{(2,1), (-6,-5)}, then we can find [T]_{E->E} like this also, is an alternative route: [T]_{E->E} = [id]_{E->E} * [T]_{B->E} * [id]_{E->B}, which is simplified to [T]_{E->E} = [T]_{B->E} * [id]_{E->B} which is simplified to [T]_{E->E} = [T]_{B->E} * ([id]_{B->E})^(-1)
where E is the standard basis, and [id]_{B->E} is the matrix change of basis from basis B to basis E
namely, the vectors of B placed as columns in a matrix is [id]_{B->E}
and the columns of [T]_{B->E} is just the outputs of evaluating T(b1), T(b2)
but if you guys havent covered change of basis, I wont push this further, since I dont want to confuse
north otter
so in particular, \[\begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}2\\1\end{...
okay i was able to get to this part
but idk what happens after that
buoyant jetty
you get a system of 4 unknowns and 4 equations, no?
north otter
but if you guys havent covered change of basis, I wont push this further, since ...
nope not change of basis
north otter
you get a system of 4 unknowns and 4 equations, no?
idk what happens next
buoyant jetty
do you happen to cover gaussian elimination, try to solve the system
north otter
do you happen to cover gaussian elimination, try to solve the system
idk how to change the equations into a matrix
i think thats where im tripping
buoyant jetty
Flip
wdym? for finding the matrix representation of T we need to find a,b,c,d and place it into a matrix like this
north otter
wdym? for finding the matrix representation of T we need to find a,b,c,d and pla...
uhhhhhhhh
buoyant jetty
sorry I replied to other image
north otter
ok so i got
2a+b = -11
2c+d = 4
-6a-5b = 35
-6c-5d = -16
buoyant jetty
first we solve the system, for a,b,c,d
north otter
am i suppose to add the equations
north otter
first we solve the system, for a,b,c,d
can i not put it into a mrtxi yet
buoyant jetty
ok so i got
2a+b = -11
2c+d = 4
-6a-5b = 35
-6c-5d = -16
this is equivalent to finding x1,x2,x3,x4 such that
i) x1 + x2 + x3 + x4 = something
2) etc
buoyant jetty
ok so i got
2a+b = -11
2c+d = 4
-6a-5b = 35
-6c-5d = -16
for example
first equation is
2a + b + 0c + 0d = -11
buoyant jetty
am i suppose to add the equations
thats one way, there are many ways of solving an system of equations
buoyant jetty
ok so i got
2a+b = -11
2c+d = 4
-6a-5b = 35
-6c-5d = -16
for example, take the second equation and multiply it by 3 then sum it to the fourth equation, we get d as a single value
is equivalent to doing in gaussian elimination like 3R2 + R4
north otter
for example
first equation is
2a + b + 0*c + 0*d = -11
OH
okay i thini
i kinda see it
if i do like
4 euqations w a b c d
pallid tapir
yeah it's however you'd like to solve linear systems
pallid tapir
in this case, you can actually treat it as two systems, with 2 equations and 2 unknowns each
but seriously it's all the same
north otter
in this case, you can actually treat it as two systems, with 2 equations and 2 u...
huh
pallid tapir
{2a+b = -11}
{-6a-5b = 35}
{2c+d = 4}
{-6c-5d = -16}
and even then, they look like the same system, just with different constants at the end
anyway it's whatever
there's a lot of ways to solve linear systems, so just choose any method you'd like
stuff them into a 4x4 matrix, two 2x2 matrices, don't address matrices at all, it's all the same
buoyant jetty
like, geometrically, this system of two equations can be seen as intersection of two planes, so a line (in case both are not the same plane and other edge cases), and then the intersection of two lines being a point (a,b,c,d) in case they are not the same line and assuming this lines have intersection (in case they dont then we get infinitely many solutions to a,b,c,d)
buoyant jetty
i kinda see it
which step are you still confused abt?
buoyant jetty
send your work
buoyant jetty
can yall see if i did it correct
ye
north otter
buoyant jetty
you have a small sign mistake when finding b, it should be b = -1
north otter
-2b = 2 ==> b = -1
my baddd
ahhhhh
thanks
okay so
a = -6
b = -1
c = -2/3
d = 4
is that righr
@buoyant jetty
buoyant jetty
,w 2a + b = -11 , 2c + d = 4, -6a-5b = 35 , -6c - 5d = -16
elfin berryBOT
buoyant jetty
you should get this as the answer
I even checked using matrix change of basis,
,w {{-11, 35},{4,-16}} * {{2, -6},{1,-5}}^(-1)
elfin berryBOT
marsh citrusBOT
@north otter Has your question been resolved?
buoyant jetty
buoyant jetty
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
vague shell
i dont understand the assumption why couldnt it have been n^2 is odd and n is even?
marsh citrusBOT
i dont understand the assumption why couldnt it have been n^2 is odd and n is ev...
vestal sandal
what would you prove in that case? youd end in a contradiction and say "therefore, if n^2 is odd then n is also odd". thats not what youre trying to prove though
stoic saddle
to violate "if A then B" there needs to exist something that satisfies A but violates B
vestal sandal
besides, your starting point is n^2 is even. the only thing you know for certain is that n^2 is even
assuming it to be odd is just not following the exercise
vague shell
what would you prove in that case? youd end in a contradiction and say "therefor...
but i thought i just need to negate the statement to prove by contradiction
but i dont know which part to negate like in this case
it feels like a gamble to me
vestal sandal
its telling you that n^2 is even. it wants you to prove that n is, in that case, also even
well, assume that n^2 is even. then, in hopes of leading to a contradiction, assume that n is not even
vague shell
its telling you that n^2 is even. it wants you to prove that n is, in that case,...
i see ok
viscid pond
Think if the question giving you a rock solid fact that n² is even.
vague shell
right
viscid pond
So for proof of contradiction, we try negate the consequent
vague shell
so im assuming the rock solid fact will be followed after "if" like in this case
viscid pond
unless...there is a type of proof that it is obvious that antecedent is false
vague shell
right
viscid pond
unless...there is a type of proof that it is obvious that antecedent is false
for example:
If 1 + 1 = 3, then 2 + 3 = 6.
obviously this is true because antecedent is false
vague shell
i just gotta clarify the meaning of "proof by contradiction" as its lil fuzzy in my head
viscid pond
But since we have no way to verify n² is actually odd or even, we gonna just accept
vague shell
i just gotta clarify the meaning of "proof by contradiction" as its lil fuzzy in...
so is it just me saying the statement is wrong, i assume the "negation". That negation will lead me to a pit of doom aka its wrong which proves the original statement as correct
viscid pond
It is like
you gonna proof
p -> q
now you try
p -> -q
if it leads to contradiction, then the initial assumption -q is false
viscid pond
yup (hopefully)
viscid pond
if it leads to contradiction, then the initial assumption -q is false
aka -q ≡ F
so q ≡ T
vague shell
i dont know what those 2 lines u sent mean
vague shell
if it leads to contradiction, then the initial assumption -q is false
i understand till here
vague shell
oh ok
got it
lemme skim through these powerpoints to see any concerns i got i think u and the other person solved it!
one minute
viscid pond
ogei
vague shell
ogei
everything i understand is fine apart from this dodgy one.
im assuming i just negate the last word to rational?
viscid pond
yes
So you try to prove
difference between any rational and irrational is rational
then try to get to whatever pit of doom
vague shell
yes
so is:
"the difference between any rational number and any irrational number" the antecedent
viscid pond
yup
viscid pond
yes
vague shell
ok perfect, let me just look at the other book rq and thatll be all
viscid pond
noice
vague shell
noice
final one:
its similar to the very first question,
"n^2 is a multiple of 3", is the solid fact im given aka the antecedent
and "n is a multiple of 3" is the consequence i negate into "n is NOT a multiple of 3"
im pretty confident its that (my answer) as it follows a similar "if" approach in the question
vague shell
thank u so much
viscid pond
np
vague shell
.solved
marsh citrusBOT
vague shell
np
was doing some questions and found a weird one
answer:
im assuming it just negated literally both points after the comma?
at least one -> both
p and q is odd -> are even
im assuming for the consequence u negate everything
vital oracle
this is an if then statement which uses implies
The opposite of P => Q is P true, Q false
so here they have P true and Q false
rotund oriole
The opposite of P => Q is P true, Q false
What's the name of this?
marsh citrusBOT
Available help channel!
distant girder
Can someone just help me get started?
Problem:
A bookstore sells 500 copies of a new novel for $20 each. Market research shows that for every $2 increase in price, they will sell 40 fewer copies. Additionally, they have a fixed cost of $2,000 and a variable cost of $8 per book.
Questions:
- Write a revenue function in terms of the number of $2 price increases.
- Write a profit function (profit = revenue - total cost).
- Find the number of price increases that maximizes profit.
- Determine the optimal price, the number of books sold, and the maximum profit.
marsh citrusBOT
Can someone just help me get started?
Problem:
A bookstore sells 500 copies of ...
dry prawn
distant girder
I assume that I should start off by creating a function for the quantity:
y=500-40x
distant girder
$Revenue = price \cdot quantity$
elfin berryBOT
Elliot Pixel
dry prawn
Indeed
distant girder
I’m not sure how I should connect the fact that for every $2 increased, they sell 40 less and that the variable cost is $8 per book
dry prawn
We don't care about costs yet
distant girder
These types of questions just make my head hurt
dry prawn
How much does a book sell for if you increase the cost x times?
wintry oak
-# I am also interested in this question
distant girder
How much does a book sell for if you increase the cost x times?
Wait sorry let me think
dry prawn
distant girder
Oh if you increase the cost
wintry oak
Sorry I should be more precise with my language
distant girder
Idk 😭
distant girder
Sorry I should be more precise with my language
No it’s not your fault
distant girder
Idk this just hurts my brain ngl
wintry oak
If the company doesn’t increase the price at all, how much do I have to pay to buy the book from them?
wintry oak
Idk this just hurts my brain ngl
I’m also a little curious why
distant girder
I’m back
distant girder
If the company doesn’t increase the price at all, how much do I have to pay to b...
Let me see
distant girder
If the company doesn’t increase the price at all, how much do I have to pay to b...
20 bucks
I’m not sure what it means that they have a fixed cost of $2000 and a variable cost of $8
distant girder
I’m not sure what it means that they have a fixed cost of $2000 and a variable c...
Does that mean that they won’t sell the books for more than a total of $2000?
wintry oak
I’m not sure what it means that they have a fixed cost of $2000 and a variable c...
It means that at a base they need to spend $2000 (e.g. for salaries and machinery), and then every book on top of that they need to spend $8
wintry oak
Even if they didn’t sell any books, they’d still need to spend $2000
distant girder
So the function for their total spent is 2000-8x
wintry oak
To pay the bills etc
With a +, actually
So if they sold one book, they’d spend $2008
wintry oak
If they sold two, they’d spend $2016
wintry oak
And get 20 back
Yeah which would be a pretty bad loss
distant girder
There’s so many variables in this questions I just don’t know where to start
wintry oak
I see, so you feel overwhelmed by all the data?
distant girder
Yes
wintry oak
That’s understandable
Are you writing any of this down, for one?
Keeping it all in your head can be difficult
wintry oak
It might help to give names to the different quantities involved in the question
Like “total spent by company”, or “number of books sold”
distant girder
The function for every $2 increased is 500-40x?
wintry oak
Yes, if x represents the number of times it increases the price
If they don’t increase the price at all, they sell 500 copies
If they increase the price once, by $2, they sell 500-40 = 460 copies
If they increase the price twice, by a total of $4, they sell 500 - 40*2 = 420 copies
wintry oak
The function just gives a compact way of representing the pattern
distant girder
So again, revenue=price*quantity
wintry oak
Yep
distant girder
Quantity is given by 500-40x
wintry oak
Yep!!
distant girder
Price is 2000+8x..?
wintry oak
Remember, price is what the customer pays
If the company doesn’t increase the price at all, the customer pays $20
If they increase the price once, the customer pays $22
If they increase the price twice, the customer pays $24
distant girder
20+2x?
wintry oak
Yeah, that’s the general pattern 
Again, x here represents the number of times the company increases the price
distant girder
So it’s (500-4x)(20+2x)
distant girder
Now for question two
Write a profit function
Don’t say anything I’ll think
Total cost is given by 2000+8x
Not sure if the x would be the same as it is in the revenue function I gave tho
wintry oak
-# can I say anything yet
distant girder
In that case, it’s be 2000+8x-(500-40x)(20+2x)
distant girder
-# can I say anything yet
Sure
wintry oak
Not sure if the x would be the same as it is in the revenue function I gave tho
So, it wouldn’t be
distant girder
So the function is -16(500+12x-5x^2)
wintry oak
I think it would be helpful to give more descriptive names than “x” here
distant girder
I think it would be helpful to give more descriptive names than “x” here
For sure
x=books sold
wintry oak
In the first question, what does “x” represent?
distant girder
Books sold
wintry oak
Are you sure?
wintry oak
The function for every $2 increased is 500-40x?
How about here
wintry oak
It might help to give names to the different quantities involved in the question
Did you do this?
distant girder
Okay so the function for the quantity of books per every $2 increased in price is given by 500-40x, where x is the amount of books sold
wintry oak
That’s not right either
If the company doesn’t increase the price at all, how many books do they sell?
distant girder
500
wintry oak
So, if x is the amount of books sold, wouldn’t x be 500?
distant girder
Right
wintry oak
This is why I suggested giving actual names to the relevant quantities involved in the problem
If you just use single letter names like “x”, you’ll run into confusions like these
distant girder
So for 500-40x, x is the amount of times the price has been increased by $2, f(x) is a function of the quantity of books left
distant girder
If you just use single letter names like “x”, you’ll run into confusions like th...
What should I use then
wintry oak
How about we let “INC” denote how many times the price has been increased?
Or you can choose another name if you’d prefer
distant girder
How do I determine the function for every time the price has increased by 1?
distant girder
Or you can choose another name if you’d prefer
Sure
wintry oak
How do I determine the function for every time the price has increased by 1?
I don’t understand this question
distant girder
Wait so if the company increases the price by $1.99, the amount of books sold remains unchanged?
wintry oak
Ah I think I see what you mean
There are two ways I can see this being interpreted:
- We assume for simplicity that the company can only increase the book price in $2 amounts
So the possible prices are $20, $22, $24, $26, …
So a price of $21.99 just wouldn’t be possible
- We interpolate their results to other price increases
If they increase the price by $2, they sell 40 fewer books
So perhaps if they increase the price by only $1, they’d sell 20 fewer books
distant girder
2) We interpolate their results to other price increases
This is what is not stated in the question
wintry oak
And if they increased it by $3, they sell 60 fewer books
distant girder
Yeah idk myself 🤷
wintry oak
This is what is not stated in the question
If we let the price of the book be 20 + 2 * INC, where INC is the number of price increases, this accounts for both situations
We can say that increasing the price by $1 would be like INC = 0.5
distant girder
Right
wintry oak
Just as a check, if they increase the price of the book 10 times, what’s the new price?
distant girder
40
distant girder
100
wintry oak
That’s correct
How about we let “SOLD” denote how many books they sell
Then we have SOLD = 500 - 40*INC
This is the quantity of books sold
distant girder
And PRICE=20+2*INC
wintry oak
Yep
As you said, revenue = price * quantity
So we get revenue = (20 + 2 * INC)(500 - 40*INC)
distant girder
For the total cost, it’s 2000+8(20+2*INC)?
wintry oak
Which is what we got the first time, except now with more descriptive names
wintry oak
For the total cost, it’s 2000+8(20+2*INC)?
Well, from the fixed-variable stuff, I would think the total cost is 2000 + 8 * SOLD?
$2000 base, and then $8 for each book they sell
distant girder
Right right right
Because once again, 8 is the price and SOLD is the quantity so it’s fixed cost+revenue
I’m totally lost idk
wintry oak
I’m totally lost idk
Well, the total cost is fixed cost + variable cost
The fixed cost is always $2000
That’s why it’s fixed
The variable cost depends on how many books they sell
If they sell 1 book, the variable cost is $8
If they sell 2 books, the variable cost is $16
distant girder
Variable cost means that for every book sold, they’ve spent eight bucks
wintry oak
The name for the number of books sold is “SOLD”, so the variable cost is 8 * SOLD
wintry oak
Variable cost means that for every book sold, they’ve spent eight bucks
Yeah
We then add that to the fixed cost to get the total cost
2000 + 8 * SOLD
distant girder
Wait can I go and eat and I’ll ping you when I’m done? Food might make me think clearer
wintry oak
I’ll probably be asleep by the time you get back
But you can ping other helpers
My advice would be to:
- Write down things instead of trying to keep it all in your head
- Give descriptive names rather than single-letter ones like “x”
- Always go back to specific values (what if they increase the price 3 times?) and see if you get sensible results
marsh citrusBOT
@distant girder Has your question been resolved?
distant girder
My advice would be to:
- Write down things instead of trying to keep it all in y...
Thank you so much
blazing dew
Prove that a quadrilateral with two opposing angles add up to 180 is cyclic.
marsh citrusBOT
Prove that a quadrilateral with two opposing angles add up to 180 is cyclic.
@blazing dew Has your question been resolved?
blazing dew
<@&286206848099549185>
rapid raptor
marsh citrusBOT
marsh citrusBOT
Available help channel!
finite forum
marsh citrusBOT
finite forum
stoic saddle
first step looks incorrect to me
even in boolean algebra * has higher precedence...
so you cannot just simplify that A' + A into 1.
marsh citrusBOT
marsh citrusBOT
Available help channel!
mossy kettle
marsh citrusBOT
mossy kettle
got to 3x^2)+3y^2)+3z^2)-38x -16y +28z +107
but i am not quite sure how to get to center, r in this situation
harsh scroll
Just complete the square 3 times
mossy kettle
Just complete the square 3 times
that's where i take half and then square the number in front x,y,z?
Something like this?
harsh scroll
Something like this?
Well yeah, but I'm not getting the same result
mossy kettle
hmm
mossy kettle
blah blach = -33 1/3?
i think i forgot to / by 3
so center should be (19/3 , 8/3, -14/3) with r -33 1/3
harsh scroll
,calc 38/2
elfin berryBOT
Result:
19
Why did you add the first time by 40/9?
Can you write down more details on how you complete the square?
mossy kettle
Can you write down more details on how you complete the square?
i could try
just not sure where the 38/2 came from
harsh scroll
just not sure where the 38/2 came from
Yeah just show me how you completed the square and I'll explain that later
mossy kettle
Yeah just show me how you completed the square and I'll explain that later
This is what I came up with, now gotta factor
,rcw
elfin berryBOT
mossy kettle
tbh now im even more lost
elfin berryBOT
harsh scroll
,w 12*2/3
elfin berryBOT
mossy kettle
How can half of 38/3 be 12•2/3
huge mistake
harsh scroll
what's this?
My calculation to show that half of 38/3 is not 12*2/3
Well not mine but wolfram alpha
mossy kettle
i did not write that?
bleak meadow
OP said 40 1/9, which is 361/9
though if the number wasn't a mixed number to begin with, I think you may just leave it as an improper fraction next time, OP
harsh scroll
Wut, man who uses that thing....
mossy kettle
i do
harsh scroll
Alright so what's the radius you got
mossy kettle
so center should be (19/3 , 8/3, -14/3) with r -33 1/3
i guess it was just the negative that was off? since 33 1/3 is 100/3
harsh scroll
r^2
mossy kettle
oh
harsh scroll
i guess it was just the negative that was off? since 33 1/3 is 100/3
Yeahh, but you used mixed number so I got confused bit
But 100/3 is r^2
Not r
mossy kettle
it is?
marsh citrusBOT
marsh citrusBOT
Available help channel!
rugged venture
Hi, I Want To Learn About Rotation Matrices And Also How To Get A Rotated Vector In Y Direction By Multiplying The Normal Vector With The Rotation Matrix of the y direction
marsh citrusBOT
Hi, I Want To Learn About Rotation Matrices And Also How To Get A Rotated Vector...
rugged venture
And for getting the rotated vec could you add also how to get it in other directions? X, Z
elfin cairn
The main thing about rotations around the origin is that they are linear transformations, and hence they can be represented by a matrix
so there is some matrix A that for any vector v, Av is the rotated vector
to find what matrix is this we take some basis of R^n (usually the standard basis) and see to what vectors this basis is mapped to
rugged venture
to find what matrix is this we take some basis of R^n (usually the standard bas...
What Is The Basis Of $/R^n/
elfin cairn
the standard basis of R^3 is (1,0,0), (0,1,0), (0,0,1)
you can see how this generalizes to R^n
rugged venture
So if I want to get a rotated vector that is in [x, y, z] and I want him to rotate in y by 45° using rotation matrix of the y direction
elfin cairn
so think what happens to (1,0,0), (0,1,0), (0,0,1) under this rotation.
the y coordinate stays fixed
rugged venture
See what I mean by
elfin cairn
yeah this would be the result of the calculation I described
rugged venture
Is there is any resources I can get into these
elfin cairn
just linear algebra? its not much of a deep concept from my experience
rugged venture
Because in the image I can for example multiply this with V-> = [1, 0, 2]
So I get back R^v-> = [?, ?, ?]
elfin cairn
I don't understand
rugged venture
Wait a second I'll show you what I mean
rugged venture
I don't understand
Because in the image I can, for example, multiply this with
$$\vec{v} = \begin{bmatrix}1 \ 0 \ 2\end{bmatrix}$$
So I get back
$$R\vec{v} = \begin{bmatrix}? \ ? \ ?\end{bmatrix}$$
elfin berryBOT
Ben Coder
elfin cairn
if R is the rotation matrix the product with v will give the rotated vector
rugged venture
/tex
R = \begin{bmatrix}
1 & 0 & 0 \
0 & \cos\theta & -\sin\theta \
0 & \sin\theta & \cos\theta
\end{bmatrix}, \quad
\vec{v} = \begin{bmatrix}1 \ 0 \ 2\end{bmatrix}
\Rightarrow \quad
R\vec{v} = \begin{bmatrix}? \ ? \ ?\end{bmatrix}
elfin berryBOT
Ben Coder
/tex
R = \begin{bmatrix}
1 & 0 & 0 \\
0 & \cos\theta & -\sin\theta \\
0 & \sin\theta & \cos\theta
\end{bmatrix}, \quad
\vec{v} = \begin{bmatrix}1 \\ 0 \\ 2\end{bmatrix}
\Rightarrow \quad
R\vec{v} = \begin{bmatrix}? \\ ? \\ ?\end{bmatrix}
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.50 R = \begin{bmatrix}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.
LaTeX Font Info: Trying to load font information for OT1+lmr on input line 5
0.
(/usr/local/texlive/2023/texmf-dist/tex/latex/lm/ot1lmr.fd```
rugged venture
do you know how matrix vector multiplication works
This is what I want to understand: /tex
R = \begin{bmatrix}
1 & 0 & 0 \
0 & \cos\theta & -\sin\theta \
0 & \sin\theta & \cos\theta
\end{bmatrix}, \quad
\vec{v} = \begin{bmatrix}1 \ 0 \ 2\end{bmatrix}
\Rightarrow \quad
R\vec{v} = \begin{bmatrix}? \ ? \ ?\end{bmatrix}
elfin berryBOT
Ben Coder
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rugged venture
i have a rotation matrix called R , and so I want to understand how it works and especially how it outputs the rotated vector R*V if I had a vec3 V
devout mauve
that still does not answer my question
rugged venture
do you know how matrix vector multiplication works
Ahhh, I get it Nope
elfin cairn
i have a rotation matrix called R , and so I want to understand how it works and...
the rotated vector is the result of matrix-vector multiplication with the rotation matrix
devout mauve
ok
rugged venture
Let's try to calculate the new rotated vector by the examples I gave
devout mauve
frankly I dont really wanna explain matrix vector multiplication on discord
its a bit painful
maybe esquie wants to
but there are good resources on the internet
devout mauve
google matrix vector multiplication and you will find approximately 1 million websites and videos
marsh citrusBOT
elfin cairn
@rugged venture also you can watch the entire series of 3blue1brown on linear algebra
its very good for begginners
elfin cairn
<@1370497524342718494> also you can watch the entire series of 3blue1brown on li...
well not the entire series if you don't want to
marsh citrusBOT
Available help channel!
unreal spade
GNA HOW TO DO THIS
marsh citrusBOT
GNA HOW TO DO THIS
spark otter
if log_4(y) = a, then y = ?
same question with log_8(2y) = b (start by asking "2y = ?")
unreal spade
same question with log_8(2y) = b (start by asking "2y = ?")
i tink i got it
so like
y = 4^a
2y = 8
y = 8/2
wait no uhh
unreal spade
like this?
bleak meadow
anything else you would like to ask?
humble osprey
marsh citrusBOT
humble osprey
if we have this, where A,B,C are sets
then is "=>" correct?
or can it be "<=>" ?
and why
<@&286206848099549185>
I suck at logic pls help
bleak meadow
it can, via the distributive law
in fact, after applying the distributive law, you'll notice that the two sides are very uncanny
humble osprey
it can, via the distributive law
im kinda trying to prove that the distributive law holds
bleak meadow
ah
humble osprey
its prolly got to do with logic but I cannot think of the idea behind it
bleak meadow
I guess you can use the elementwise argument to prove this