Oh I just found a quora thing on it...
#help-0
knotty sleet
keen wasp
sauce link 😉
knotty sleet
alpine sable
Yes, I recently just learnt linear equations - there's a long way to go
keen wasp
ty
coral pagoda
I like that answer a lot!
alpine sable
Lol, abnormal flex
coral pagoda
I didn't write it goof ball :p
knotty sleet
Ah I see
keen wasp
wait so how do you know which interval to choose
coral pagoda
Haven't read so Idrk if it helps 😅
tldr: it doesn't really matter where you look at the solution set. However, just looking at specific intervals gives us the intrinsic property of connectedness, which has quite a few consequences.
coral pagoda
Well, kind of, but that wasn't what's relevant here
I do see your point though
That is a nother important thing to keep in mind
knotty sleet
Ok thanks😄 I'll think about it some more
keen wasp
wait dackid could you explain how you knew to choose the positive interval
coral pagoda
I didn't
keen wasp
so couldnt the answer also be x<0
coral pagoda
Actually fair point
keen wasp
like on a free response since that wasnt an answer choice
coral pagoda
What is the x value in our initial value problem
coral pagoda
OH UR SO SMART
Thanks for finally noticing 😆
keen wasp
xD
alpine sable
does this have an analytic solution?
if yes, how can i find it
a is a constant
obv
charred flint
is that 0 on the bottom?
coral pagoda
[\int_0^a \int_0^a \frac{dxdy}{a^2+x^2+y^2}\leq \int_0^{2π}\int_0^{a} \frac{rdrd\theta}{a^2+r^2}]
charred flint
doesn't look like it has an analytic solution
coral pagoda
I'm not sure what r_1 is here, but this is a good step
charred flint
yea you're integrating a rotationally symmetric function on a rectangle, soooo
alpine sable
yea you're integrating a rotationally symmetric function on a rectangle, soooo
thats exactly what im doing haha
okok what about r1 -
alpine sable
yea you're integrating a rotationally symmetric function on a rectangle, soooo
also does this mean it should have an analytic solution?
charred flint
I'm implying it probably doesn't since it's "meant" to be integrated on a circle
coral pagoda
My bound is off, but it does have a solution for sure
alpine sable
aaa.
coral pagoda
There, that's good
alpine sable
wait the left integrals should be from 0 to a, not from a to b
coral pagoda
Wait what?
alpine sable
charred flint
r1 is a/cos(theta) [theta 0 to pi/4, multiply by 2 in the end]
and I'd guess when you try the theta integral it gets ugly
ocean sealBOT
dackid
alpine sable
r1 is a/cos(theta) [theta 0 to pi/4, multiply by 2 in the end]
can you explain how you got that? abskdhs
im kinda braindead
charred flint
it's like the radius of a square
coral pagoda
Okay, so if we are just looking for if there is a solution, this will do it for us
The region of our OG integral is bounded by the region of our new one
spare hill
og integral lmao
charred flint
why are you bounding 
coral pagoda
Well, how can the solution of our larger area exist if the area of the smaller region doesn't?🤷
alpine sable
ummmmmmmm.
i am very
very sure that the last integral is zero
and that makes no sense since there is no way the result should be zero
coral pagoda
asec(theta) does not make sense here
alpine sable
well it's a physics problem so i can always approximate
coral pagoda
You're suggesting when $\theta=π/2$ that $r\to \infty$
ocean sealBOT
dackid
alpine sable
but i just wanna see if i can get an exact thing first
coral pagoda
**dackid**
And this is just not true
alpine sable
**dackid**
i think the upper bound on the theta integral should be π/2
since we're on the corner of the square
coral pagoda
Actually, here is something that we can do!
Actually, nevermind, it still deals with an ugly problem
spare hill
how do u guys persevere through long problems like this, jeez
junior blade
Practice builds stamina
coral pagoda
how do u guys persevere through long problems like this, jeez
Part of the deal with math is getting your ass kicked
prime grove
Why isn't the original set a subset of the power set? (discrete math set theory)
coral pagoda
It is
prime grove
isnt the original set only an element
coral pagoda
Wait, I take that back. It is just an element
prime grove
i just watched a video and he said the original set isnt a subset of the power set he said its an element of the power set tho
coral pagoda
i just watched a video and he said the original set isnt a subset of the power s...
The elements of a power set are all the possible subsets of the original set
So the power set is a collection of sets
spare hill
do i ever get to kick Math's ass
coral pagoda
do i ever get to kick Math's ass
Why do you think I wanna be a mathematician? 😎
coral pagoda
my head hurts now
Good. It will for a moment. 😁
spare hill
😏
zealous cairn
alpine sable
it says how to solve it
zealous cairn
I don’t know how to solve it💀
alpine sable
$\int \frac{x^2}{\sqrt{1-4x^2}}dx$
ocean sealBOT
asteris !!
alpine sable
so the problem states that you should use the substitution 2x=sin(θ)
$2x=\sin(\theta) \rightarrow dx=\frac{\cos(\theta)}{2}d\theta$
ocean sealBOT
asteris !!
alpine sable
and also, $2x=\sin(\theta) \rightarrow x^2=\frac{\sin^2(\theta)}{4}$
ocean sealBOT
asteris !!
alpine sable
mhm?
zealous cairn
So I plug in sin^2theta/4 into the integral?
alpine sable
you plug in sin²(θ)/4 into the x²
alpine sable
**asteris !!**
take a look
zealous cairn
Yeah that’s what I meant so it’ll be (sin^2theta/4) dx/(sqrt 1-4x^2) and I just solve that?
alpine sable
$\int \frac{\frac{\sin^2(\theta)}{4}}{\sqrt{1-(2x)^2}}dx$
ocean sealBOT
asteris !!
alpine sable
you have to also plug in dx and (2x)²
the integral should be much simpler after that
night sinew
i have a problem where i have to simplify an equation with trig identities, i finished it and used a calculator online to check it but got a complete different answer. can someone help me verify the answer and if i did something wrong?
glass lichen
$\frac{2(\cos^2{x}-\sin^2{x})}{2\sin{x}\cos{x}}$
ocean sealBOT
moshill1
coral pagoda
What is the answer you are trying to get?
glass lichen
nicer simplification imo
night sinew
trying to have an answer with no quotients
coral pagoda
What is your answer supposed to be?
glass lichen
I mean that's not possible that im aware
night sinew
yeah i tried my best but i'm just not sure if it's wrong or right
do i have to factor it?
glass lichen
That wont do much
coral pagoda
What is your answer supposed to be?
Answer the question please...
night sinew
Write in terms of sine and cosine with only positive angle. State the identity/identities applied on each step. Simplify so that no quotients appear in the final expression.
coral pagoda
I see no quotients here 🤷
night sinew
**moshill1**
what is this exactly?
glass lichen
another simplication
coral pagoda
That simplifies to [ 2\frac{\cos(2\theta)}{\sin(2\theta)}]
ocean sealBOT
dackid
coral pagoda
And that's $2\cot(2\theta)$
ocean sealBOT
dackid
coral pagoda
Which is a really nice expression
night sinew
i see, so thats like another way of better simplifying it then
but is my way of doing it wrong?
glass lichen
Yes, tho relies on knowing double angle
glass lichen
but is my way of doing it wrong?
no, since you removed the quotient
which is what the question asked for
oak zealot
Hello! I was wondering if I could get some help on this calc problem
- Consider the curve (2y+1)3-24x=-3
d) Given the point (16,0)is on the curve, find the value of (y-1)'(0)
<@&286206848099549185>
north escarp
well my question is bit tied to physics but it's dependent on math
so for my pendulum global coords are like this
so to decompose vector of length it should be like this right?
now the thing that is bugging me is this
shouldn't it be - l sin theta
did I understand this wrong ? again sorry because this isn't a directly maths question but again if someone knows I would appreciate it
yc is displacement vector for center mass of sphere body with a mass of m
woeful pulsar
Ax=b has a solution for all b, so, does it look like you should prove or disprove?
well, to prove inpossibility, how would you do it?
that's one way to start, what would 3 linearly independent nonzero solutions give you?
How about the solutions to (1, 0, 0, 0 ... 0), (0, 1, 0, 0 ... 0) ...
can you rigourously show that?
how many linearly independent solutions can you find?
keen wasp
u can use distance formula to find the lengths of the segment from (-18,-1) to (1,2)
and then since it is a right triangle, you can use trig to find the bottom side length
and then the same can be done to find the length of the left side, using the segment from (-18,-1) to (-7,8)
vagrant sphinx
pale river
The above is part b. Not sure how to apply it to with the identities to get the answer for c.
I know I should use the third identity, but I dont know how
elfin hazel
Using the identity $E[X+Y]=E[X] + E[Y]$, we can change $E[X(X-1)]=E[X^2]-E[X]$
ocean sealBOT
PseudoFlash
elfin hazel
o
elfin hazel
i dont know much stats so i cant rlly help sry 😓
pale river
ah dang
elfin hazel
ill try still tho
pale river
I got an answer: 2/P^3
2/P^2 *
alpine sable
how do you find the critical points
the critical points are where the first derivative =0
you're given f(x), so find f'(x), set that equal to 0, and then solve for x
woeful pulsar
the critical points are where the first derivative =0
there's also those places where the derivative is undefined too but that's not in this question
pale river
ill try still tho
how's the checking going?
alpine sable
there's also those places where the derivative is undefined too but that's not i...
oh yeah that's true
supple folio
junior vigil
note that you can write sqrt() as ^(1/2)
cold roost
do you know how to square root 125
blazing rose
can someone confirm/deny that the answer is B
tight locust
alpine sable
can someone confirm/deny that the answer is B
answer would be c
first step find the inverse function
original function, rotated about y axis
alpine sable
inverse function, rotated about the x-axis
alpine sable
graphically the inverse means flipping the function over the line y=x
blazing rose
yeah yeah ik
but
so i was given y = sqrt(100 - 4x^2)
do i solve for X or do i find the inverse
alpine sable
so the volume of the solid when you rotate the original function around the y-axis is the same as the volume of the solid when you rotate the inverse function around the x-axis
blazing rose
are thse not equivalent
'oh wait
whered the sqrt go
can u show me how u did the inverse functin
function
void sphinx
are there any simple ways to find the quotient and remainder for this fraction?
alpine sable
Question: Can someone please explain inner product spaces. I was a bit confused today in class
vale wigeon
informally an inner product space is a space where there's a notion of dot product
i.e. a function which takes two vectors of the space and returns a number, & shares a few key properties with the dot product you're (probably) familiar with in R^2 and R^3
this lets us talk about stuff like lengths and angles and whatnot
@alpine sable does that clear up your confusion in any way?
alpine sable
A bit @vale wigeon lemme look again at my notes
vale wigeon
do you have any more specific things that got you confused?
@alpine sable channel busy, please move
alpine sable
@vale wigeon I do one sec
vale wigeon
also to get this out of the way
vale wigeon
are there any simple ways to find the quotient and remainder for this fraction?
besides long division i dont think theres anything
void sphinx
i'm still trying to manipulate if possible
alpine sable
So its just defining properties of commutativity, and such for a dot product. Which has to be finite and in R2 or R3 as you said (Euclid-an )
alpine sable
Yeah we wrote ( u , cv ) = ( cv, u ) and such
vale wigeon
you take these properties satisfied by the dot product, and you take them as axioms
alpine sable
So because we take them to be axioms thats what allows us to find the length and such as you said. Like the Comsky-shwarts inequality .... whatever that is
I am a newb so excuse my bad math lingo
cinder sundial
guys i had an question
shu askin the age of her teacher, teacher said:when i was in your age, you only 8 year old. when you reached my age, i had 47 year old. then whats the age of shu and teacher?
i cant seem to find a method to get the age of the teacher and shu
small stag
This mf
cinder sundial
just some thought, but i still have no clue bout how to reach the answer
small stag
Nvm message got deleted
cinder sundial
yea i saw the message too lol
proper perch
i had to sorry
small stag
Oh ok
Ok so
Correct me if I’m wrong
But when the teacher was Shu’s age, shu was 8
So that means to get from the teachers age to shu’s age
cinder sundial
it is correct
small stag
$T - x = S$
ocean sealBOT
AyeWaddup
small stag
This models the teachers situation
X represents the age difference in years
But
We need shu’s situation
Solve for x and we get
$x = T - S$
ocean sealBOT
AyeWaddup
cinder sundial
let me try
small stag
If shu goes back that same amount
She is 8
So S - x = 8
Technically the system for shu is
T - x = S
S - x = 8
Solve that how you want
Well you can’t solve it
small stag
Just combine everything
Because this is gonna be a part of a larger system
Actually wait
cinder sundial
the question is askin for them ages, so i think there gonna be a number
small stag
Solve that how you want
You get 2S - T = 8
Solve the the next two
Wair
There
Then for these two
2T - S = 47
Solve that system
Well technically it’s three right
Whoops
small stag
Oh I messed up
It’s three equations
T - x = S
S - x = 8
T + x = 47
There’s 3 unknowns
Eliminate x from the last two equations using the first
cinder sundial
i wanna get an number
cinder sundial
let me try
vale wigeon
shu askin the age of her teacher, teacher said:when i was in your age, you only ...
something got lost in translation
"when i was your age, you were only 8 years old. when you reach my current age, i'll be 47 years old"
is that what it says?
small stag
It’s all good i managed
small stag
I believe so
cinder sundial
yes it should be what ann just said
small stag
The system works I just tried it
vale wigeon
can i suggest a non algebraic way of solving this particular problem
small stag
Ok while ann does that which I would prefer cause you can’t really see what’s happening with just a system, I’ll explain how
Solve any one of the equations for x
Then substitute that value of x into the other equations
Now you have two equations with two variables
And solve that like a normal system
vale wigeon
cinder sundial
ohh its looks like 8:x=x:47
vale wigeon
you take three equal steps to get from 8 to 47, so each step has size (47-8)/3 = 13
thus shu's current age is 8+13 = 21 and teacher's current age is 21+13 = 34
"when i was your age" is thirteen years ago
"when you reach my age" is thirteen years from now
small stag
That’s a really ingenious solution
cinder sundial
it is, its fkin amazing
vale wigeon
thank you
cinder sundial
what is the method called @vale wigeon
cinder sundial
its looks like sth i mean
small stag
Amazing application of arithmetic sequences imo
It’s a matter of understanding the question well
cinder sundial
but i will also do the one you'd gave me @small stag since its linear equation with one unknown
let me try
i got t-s=x
winter bay
yes
cinder sundial
s-(t-s)=8
small stag
Correct
vale wigeon
channel occupied, please move
mossy kettle
please answer this
vale wigeon
so you boiled it down to $\begin{cases} 2S - T = 8 \ -S + 2T = 47 \end{cases}$
ocean sealBOT
Ann
cinder sundial
yes, but i thought we were doing linear equation with one unknown
vale wigeon
well there are two unknowns here so ¯_(ツ)_/¯
cinder sundial
ok
cinder sundial
vale wigeon
ah wonderful
that's exactly what i was going to suggest
congrats
(and i mean i spent time just now, writing up this exact line of work)
cinder sundial
really, now i just have to bring the result (t=34) to the very first line 2s-t=8
vale wigeon
yes
you could also plug it in the second equation (-S + 2T = 47) if you wanted. it doesn't matter which one
cinder sundial
interesting. even i got all of this, i still dont know the current age of the teacher and shu
think i have to re-read the question
vale wigeon
i still dont know the current age of the teacher and shu
but you do
didn't you give the names S and T to shu and teacher's current ages respectively?
and now you found them
cinder sundial
i cant understand, so shu's current age is 21 and 34 is the teacher's age
cinder sundial
i think the method of yours is much better, more efficient
do you think its linear equation with one unknown
vale wigeon
any problem with two unknowns can be solved through sleight of hand as a problem with one unknown
the issue is that sometimes the sleight of hand required is harder and takes more work and explanation than doing it with two unknowns
cinder sundial
i got u, but how you convert the question to that
vale wigeon
i have a very active imagination, i guess
vale wigeon
i imagined shu and teacher's ages on a number line
going into the past means shifting them both to the left the same amount
going into the future means shifting to the right
past teacher aligns with current shu because of the "when i was your age"
future shu aligns with current teacher because of the "when you reach my age"
cinder sundial
god, its amazin. i will try apply it to question in future
i didnt even know i can use number line to solve question like this
solid orchid
im genuinely trying to understand this question
its a tiny screenshot so i'll type it out: A group of 40 students from your school is part of the audience for a TV game show. the total number of people in the audience is 150. What is the theoretical probability of 4 students from your school being selected as contestants out of 8 possible contestant spots?
alpine sable
Selecting without replacement right
solid orchid
and before anyone says It would be cheating, I already failed the question i just wanna know how I can solve this on my test
alpine sable
So we need #possible ways / #total ways
First lets find #total
Total # is 150C8
From the whole group of 150 we choose 8 contestants
Order does not matter
Now for #possible ways
First we need to choose 4 of the 40 students from your school to be contestants
Then we need to choose 4 of the other 150-40=110 people to be contestants
(40C4)(110C4) =#possible ways
Does that make sense?
solid orchid
imma be honest im in algebra 2 idk half of what you're talking about
solid orchid
yea
alpine sable
So the probability of success is the number of ways we can succeed divided by the total number of ways
Are you good there?
solid orchid
ok understood
alpine sable
So the probability of success is the number of ways we can succeed divided by th...
(Assuming each outcome is equally likely)
So the total number of ways to choose 8 contestants out of an audience of 150 is (150 choose 8)
Do you follow?
solid orchid
yessir
alpine sable
Great
Now to succeed, we need 4 people from the school and 4 people not from the school to be contestants
So there is a group of 40 people and we need 4 of them to be chosen so that we can get what we want
So this can happen in (40 choose 4) ways
There are 150 people in all
40 are from your school
So the other 110 are not from your school
And we want the other 4 people on the team to be people that are not from your school
So for the other 4, you need to choose 4 out of the 110 people not in your school
Which can be done in (110 choose 4 ) ways
So the total number of ways is (40 choose 4) * (110 choose 4)
solid orchid
so then what is 40 choose 4 and 110 choose 4, im not entirely sure i understand what choose means in this context
alpine sable
Ok i can go over the choose function with you
N choose k is the number of ways you can select a team of k people from a group of N people
Where order does not matter
So lets consider a specific case, where we have 6 different people A B C D E F and we want to choose 3 of them to be on a team
So we have 6 choices for who the first person can be, 5 choices for who the second person can be, and 4 choices for who the 3rd person can be
But this would mean that A B then C would be counted as a different conbination from A C then B
Which is not what we want
Notice for every choice of 3 people, there are 3! ways to order them
So # groups where order doesnt matter = #groups where order does matter /3!
And we know #groups where order does matter, which is 654
So what we want is 6*5*4/(3*2*1)
So we can use this same logic for any group of n people to find the number of ways to choose a team of k of them
N!/[(N-k)!*k!]
Idk if i explained it particularly well there are also videos explaining the choose function on khan academy and yt
alpine sable
40 choose 4 = 40!/[36!*4!]
solid orchid
so 40 choose 4 is 52,640,640?
scenic crystal
x - (-y) = x + y ? Why?
Can anybody explain this in simple language?
alpine sable
Two negatives cancel each other out
Think of the number line
Multiplying by negative 1 is the same as flipping across the 0 point
Do that twice and you end up back where you started
-(-5)=5 for example
thorn kindle
A multiplication by -1 is a rotation of 180°
latent thistle
vale wigeon
how familiar are you with power reduction identities
golden arch
Im not familiar
vale wigeon
$\cos^2(x) = \frac{1+\cos(2x)}{2}$
ocean sealBOT
Ann
vale wigeon
im talking about this one in particular
this identity, plus some algebraic cleanup, can let you reduce the stuff inside your integral to a linear combination of 1, cos(2x) and cos(4x)
all of which are fairly easy to integrate
golden arch
ill give it a go thanks
latent thistle
its $\phi (x,y,z)$ not $\phi (x,y,x)$
ocean sealBOT
Elmo_AK47
latent thistle
<@&286206848099549185>
sour cypress
does the b cancel out in this formula ?
((a / b) * 0.05) * b
latent thistle
does the b cancel out in this formula ?
` ((a / b) * 0.05) * b `
yes
0.05a
is final ans
sour cypress
yea ty
alpine sable
Use quotient identities
vale wigeon
writing it all in terms of sin and cos would be a good start
alpine sable
Cot=cosine/sine
alpine sable
I did (1/tanθ)(1/sinθ)sin
The (1/sin)(sin) cancels out
You are left with cot theta
=cos theta / sin theta
latent thistle
its $\phi (x,y,z)$ not $\phi (x,y,x)$
ocean sealBOT
Elmo_AK47
ocean sealBOT
iamjohn
cunning finch
If I use indices to find the values, but I can only leave them in index form, what would 2^8÷4^2 be
alpine sable
change $2^8$ to have a base of 4 or $4^2$ to have a base of 2, so that then they have the same base
ocean sealBOT
sxkura
alpine sable
then you can use laws of indices and have an answer in index form
dark umbra
can someone help me set the constraints for this question?
I don't know how to put the passengers into the constraint cus the quesiton wants to set x and y for no. of flights
vale wigeon
these are just greek letters, so without context its impossible to say what they mean
vale wigeon
I don't know how to put the passengers into the constraint cus the quesiton want...
assume all planes are filled to capacity, i guess?
gray isle
c^2 + s^2 = 1
night sinew
AH, i see now! thank you
dark umbra
assume all planes are filled to capacity, i guess?
Ive figured it now thank you
alpine sable
For a bijection, the image is equal to the codomain right?
vale wigeon
yes
alpine sable
Is it saying that both of the points are equally distant from the Y axis?
or is it saying that the distance between the point A and Y axis and the distance between point A and the later as in (k,4) are equal?
vale wigeon
distance from A to y-axis = distance from A to (k,4)
thats what it seems to be saying
vale wigeon
wow
what an incredibly specific, detailed question!
(/s)
@alpine sable youre gonna have to provide more details on this mysterious "something" before anyone can help you
alpine sable
<@456226577798135808> youre gonna have to provide more details on this mysteriou...
I see I was just asking before presenting my question
alpine sable
http://dontasktoask.com/
Faie point
vale wigeon
16 or 17?
alpine sable
No 16
alpine sable
No I wasn't sure how to tackle it tbh
vale wigeon
there are many ways to do it
one approach that doesn't involve too much symbol-pushing is to first ask yourself, "Harry worked 12 hours, but his rate is 4/3 times that of Tom and Samia. How many hours would he need to work at Tom's rate to earn the same pay?"
alpine sable
Ah that actually helps
vale wigeon
then use that to find the equivalent work time done by all 3 people
to find tom's hourly rate
alpine sable
Thank you kindly
alpine sable
Does anyone know how different the books “elementary linear algebra by Howard Anton” and “elementary linear algebra - applications version by Howard Anton” are?
drowsy scroll
Can you send the links to the books?
I am guessing the second book allows you to apply your knowledge in problems
I’m probably wrong but /shrug
alpine sable
@drowsy scroll yeah I inferred that as well. They’re pretty popular linear algebra books so I’m just wondering if anyone in here has read either
drowsy scroll
<@571711697115414575> yeah I inferred that as well. They’re pretty popular linea...
Well, not me. Try reading the reviews to see what is different
drowsy scroll
Hey
limber ledge
can I please have some help with this problem?
drowsy scroll
That's why you're here
drowsy scroll
Well, I gotta head out ( have class soon ) Someone else will help sorry :(
limber ledge
oh ok
<@&286206848099549185> can I please get some assistance
looks like no one is available
alpine sable
limber ledge
yes that is 360
alpine sable
6x+7x+7x+4x=360
rustic barn
Would the change of basis matrix from B2 to B1 be this?
Ofc the bases are for a polynomial space with real components
Or did I mess up the order of bases
alpine sable
graphing a rational function?
crystal needle
you don't gotta make me feel bad bro :( im doing online school and i have covid
alpine sable
ok well is that all the info they give you
rational function just means one polynomial divided by another polynomial
alpine sable
ok so lets say our function is f(x)/g(x) where f(x) and g(x) are polynomials
crystal needle
okay
alpine sable
horizontal asymptote is 0, so as x gets bigger and bigger and approaches infinity, our function is going to approach 0
crystal needle
alpine sable
that means the degree of the bottom polynomial will be greater than the degree of the top polynomial
crystal needle
okay so what do i plot
alpine sable
horizontal asymptote is x=5
so we need g(x) to have a factor of (x-5)
and f(x) can't have a factor of (x-5)
y-intercept =(0, -3/5)
so this means f(0) = -3/5
from here we can figure out a sinple rational function that will meet all these requirements
keep in mind this wont be the only one that works
try -3/(x-5)
there are no x-intercepts, so that means the top polynomial has no real zeroes
alpine sable
i suggest you use desmos to get a visual for -3/(x-5) and verify that it does meet all the conditions
crystal needle
kk thanks
alpine sable
oh whoops the function would be 3/(x-5)
@crystal needle
i made a mistake
f(0) should be -3/5 so 3/(0-5)=-3/5
crystal needle
kk
clear venture
x2 − (x+2) (x−3) in a situation like this, what would be the step by step to do it?
alpine sable
x2 − (x+2) (x−3) in a situation like this, what would be the step by step to do ...
you want to solve for x in this equation?
whoops typo
this one ^
clear venture
i just want to shorten it
alpine sable
oh you want to simplify
clear venture
yes
alpine sable
ok first expand the parenthesis
then distribute the negative
then collect like terms
clear venture
thanks!
does the - change the + and - in both brackets or just first bracket?
im a total noob btw
alpine sable
so after you expand (x+2)(x-3) you will get something with 3 terms
so distribute the negative to each term
clear venture
this helps alot, thanks
spring harbor
Maggy and Theo run a 1 km course around a park every week. Both run at a constant speed that is the same every week. The first week Maggy walks clockwise and Theo runs counterclockwise. After every 250 m that Maggy runs, she meets Theo. The following week, both run clockwise and start at the same place.
How many meters has Maggy ran when Theo catches up with her for the first time?
I feel like it's a simple question but I am confused by it. Based on what's given I know that the speed of Theo is 3 times the speed of Maggy
noble sinew
So how far is Maggy when Theo have made his first lap?
spring harbor
Uh theo would've ran 1km thus Maggy would've ran 1000/3?
noble sinew
yeah so now we can set up an equation
for when he catches up
with (x being Maggy's speed and 3x being Theos speed)
spring harbor
So 3 * the distance maggy ran = distance of theo
noble sinew
well was thinking
Theo is now 333m behind
We know how fast he runs compared to maggy
so we have ||3x-1000/3=x right?||
noble sinew
yes
spring harbor
So the speed of theo - 333.33 = speed of maggy?
spring harbor
x being..?
noble sinew
1000/6+1000/3=?
noble sinew
because Maggy is 1000/3 ahead hence we minus by 1000/3
and Theo is 3 times as fast hence 3x
spring harbor
So x is the distance not speed
noble sinew
si
crystal needle
what would the function be?
alpine sable
horizontal asymptote is y=2
so our function will be a(x)/b(x)
and a(x) and b(x) will be polynomials of the same degree
and the leading coefficient of a will be twice as big as the leading coefficient of b
we have horizontal asymptotes of x=2 and x=-2
so (x-2) and (x+2) are factors of b(x)
x-intercept is (0,0)
so a(x) has a factor of (x-0)=x
alpine sable
so (x-2) and (x+2) are factors of b(x)
so we can set b(x)=(x-2)(x+2)=x^2-4
a(x) and b(x) have to be the same degree
so a(x) is quadratic, and it has a factor of x
and the leading coefficient has to be two times the leading coefficient of b(x)
leading coefficient of b(x)=1
so we can set a(x)=2x^2
tepid jungle
If 6% of the male population have the flu and there’s a flu test that is correct 81% of the time, whilst incorrect 20% of the time. If someone is randomly selected and they are tested to have the flu, what is the probability that they actually have the flu
alpine sable
draw a tree diagram
tepid jungle
Ohhh
So it’s 2 branches of flu & no flu
And then 2 branches off that correct incorrect diagnosis
alpine sable
yes exactly
alpine sable
how can i integrate something over a closed curve?
tepid jungle
0.06*0.8
alpine sable
in this case, the unity circle?
tepid jungle
What is the function
alpine sable
What is the function
find (probability you actually have the flu) / (probability the test says you have the flu)
probability you actually have the flu = 6%
tepid jungle
0.81?
alpine sable
probability the test says you have the flu = probability you have the flu and the test was right + probability you don't have the flu but the test incorrectly says you do
tepid jungle
You've got the Pr have flu * Pr correct result
but also
Pr no flu * Pr incorrect result
add them togehter?
alpine sable
wait a minute
Hi guys, could someone help me with an exercise on mathematical methods for physicists?
flu test that is correct 81% of the time, whilst incorrect 20% of the time
this adds to 101% @tepid jungle
tepid jungle
oh yes
alpine sable
Hi guys, could someone help me with an exercise on mathematical methods for phys...
ask in an unoccupied channel please
tepid jungle
make 80%
alpine sable
k
alpine sable
ask in an unoccupied channel please
😦 ty
alpine sable
0.06*0.8 + 0.94 * 0.20
yes correct
alpine sable
alpine sable
If someone is randomly selected and they are tested to have the flu, what is the probability that they actually have the flu
we want probability they actually have the flu given that the test says they have the flu
oh whoops i made a mistake here
that is bayes (?)
so we want
alpine sable
that is bayes (?)
yeah this is bayes rule
alpine sable
on the top you want P(A and B), the probability that you have the flu and the test says you have the flu
cool
noble sinew
Thats just definition of conditional prob
noble sinew
Bayes is P(A|B)=P(B|A)*P(A)/P(B)
alpine sable
I got a math related question
Jonah has a 95.00 average. She got a quiz worth 20 percent of her grade. If she got a 95 on that quiz will her average go up or down, and what will her new average be.
?
<@&286206848099549185>
radiant pasture
i'm guessing this is based on grading from 0-100
as in 100 is perfect score
either way
you know what her grade is, and that the quiz is 20%
wouldn't it make sense to figure how many points the quiz added to her final grade?
alpine sable
O wait
There is a chart
It says how many quizzes she took and tests and hw
Wait let me show you
420
Ok she has a 100 in hw
Which counts as
radiant pasture
please post all the elements of this problem first
alpine sable
Jonah has a 95.00 average. She got a quiz worth 20 percent of her grade. If she got a 95 on that quiz will her average go up or down, and what will her new average be. She has 100 in classwork that is worth 30 percent of her grade. She has a 92 in tests which is worth 50 percent of her grade. As of now she has a 95 average in quizzes.
radiant pasture
first of all
you need to separate your data from what you're looking for
aka
If she got a 95 on that quiz will her average go up or down, and what will her new average be
alpine sable
Yes
radiant pasture
these are what you're looking for
alpine sable
Mhm
radiant pasture
everything else is data
alpine sable
Mhm
Would her average stay the same?
Since she already has a 95 average in quiz grades
radiant pasture
not percentages, values
alpine sable
Like how many are there?
radiant pasture
no
radiant pasture
give me 2 minutes and i'll be back to you
radiant pasture
were you looking just for the answer?
or how to actually solve the problem step by step
i mean, i'm not your teacher so take this with a grain of salt but just copying the workbook answers won't get you far much
maiden carbon
https://i.kawaii.sh/N3nrVPB.png how does this work
i know the answer but confused on how it works
radiant pasture
i mean
it's a paralellogram
you know 2 sides
what can you deduct about the other 2
maiden carbon
well yeah they are equal but its also not a square
so i need to split it into 3
how do i find the height tho
radiant pasture
i mean
can't you split the shape into more easy to work with ones?
hint: you have that 120degree angle
radiant pasture
that's the idea
radiant pasture
if you know an angle and the 2 sides that make that angle (they have a name sorry my english math terminology isn't the best)
you can figure out everything about the triangle
incl area
radiant pasture
np
alpine sable
I need to mark these points on a graph
I’m stuck on d and e
I don’t know how to mark them
cold monolith
what does the value of the derivative tell you about the function? @alpine sable
alpine sable
That derivative of x is greater than zero?
cold monolith
right, but what does that tell you about the graph of the function?
alpine sable
It’s increasing
alpine sable
Yes
cold monolith
so in the interval (2,6) on the x-axis, your function should be increasing
and it should be decreasing on (0,2) and (6,10) on the x-axis
What does the value of the second derivative tell you about the graph of the function?
alpine sable
so in the interval (2,6) on the x-axis, your function should be increasing
I know all these parts , but I’m confused on how to draw the graph
Never mind
Thank you!
frail grove
No 4 books in 3 drawers
radiant pasture
uuh
frail grove
A drawer can hold up to 4 books
radiant pasture
don't you think that was a piece of crucial information
frail grove
Any drawer can hold multiple books
frail grove
Can u solve it? 👀
alpine sable
How many ways can you store 4 books in 3 drawers?
Are the books/cabinets distinguishable
alpine sable
If the books and cabinets are distinguishable, there are 3 choices of cabinet for each of the 4 books
So we’d have 3^4 = 81
If the books are indistinguishable but the cabinets aren’t, we can use Stars and Bars to get an answer of 6 choose 2, or 15
vale wigeon
this equation is not polynomial in x, y and y' as-is so i would not say it even has a degree
golden arch
huh that's weird the answer sheet says its 4
but it was polynomial what degree would u say it is?
velvet pelican
Probably 4
vale wigeon
it's not a polynomial
if you changed something in the equation to make it polynomial it'd be a different equation
velvet pelican
I guess he means after you multiply by (y-xy')^3
vale wigeon
well yeah then that'll get you an equation which is quartic in y' i guess
if thats what youre looking for
golden arch
so (y' + x) * (y-xy')³ = 0?
vale wigeon
why 0
golden arch
Because i apparently i forgot how to math
I cant even write proper sentences
its time to catch some sleep thanks guys!
alpine sable
i tried writing out the individual terms and stuff cancels out but uh
it looks like nearly everything should cancel
i don't really see how one arrives at the answer
well take a shot at what the answer is
cos(0) - cos(pi/2) = 1 - 0 = 1
because once you telescope out the sum
wrong
it becomes cos(pi/2(n + 2)) - cos(pi/2)
no?
well let me give you the full deal then
ah right
sorry i forgot that odd numbers exist
the answer should be cos(0) + cos(0) - cos(pi/2) - cos(pi/4)
the first term is easy to see
but the way you get the first term's limits don't for reason work on the second one
which is 2 - 0 - sqrt2/2
or 2 - (sqrt(2)/2)
oh lol
i think that should be right
nice
okay what the hell did i miss
this feels dumb
oh lol is it the terms at the last
and since n tends to infinity they both tend to 1
is that it?
at the very end
like when you take the sum
you should get cos(pi/2(n + 2)) + cos(pi/2(n - 1 + 2)) - cos(pi/2) - cos(pi/4)
yeah okay i get it
thanks a lot
np
ban?
vale wigeon
<@&268886789983436800> we got a multipost-spammer here
alpine sable
thanks ann
gray gorge
Taken care of
errant bear
please help im so confused
alpine sable
uhmm
alpine sable
please help im so confused
im confused too
nocturne swift
cap
alpine sable
👀
errant bear
all of it
alpine sable
could someone help me with this
errant bear
which part are you confused on
all of it
ionic jewel
okay lets do the first one
its a cube
whats the formula for the volume of a cube @errant bear
errant bear
100 i think
ionic jewel
no
whats the generic formula for volume of a cube
ignore the 10 in the problem for now
ionic jewel
ill just give it to you, but you should know it
V = s^3
where s is the side length
ionic jewel
could someone help me with this
similar triangles
ionic jewel
im so confused still
whats the side length of your cube?
alpine sable
similar triangles
hm?
ionic jewel
the triangles are similar
errant bear
ive never learned any of this im in sixth grade i havent learned this letter stuff
ionic jewel
the volume of a cube is equal to the side length cubed
errant bear
all the sides are 10 inches