#help-13
cedar kilnBOT
deft prairie
not sure how to do this one
i know partial order relations must be reflexive, antisymmetric and transitive
obsidian coral
You have to wait at least 15 minutes before pinging helpers
deft prairie
oops mb
celest ledge
Clearly 4
b,c,d<=a
For relations between b and c, you can only have no relation
For relation between b and d, you can only have b<=d or no relation ,2 choices
For relation between c and d, you can only have c<=d or no relation , 2 choices
So you have 4 possible partial orders
deft prairie
b,c,d<=a
im really bad at this topic
so basically bRd but d(notrelated)b
why is that a partial order?
my understanding of partial orders is pretty bad
all i know is that
e.g. if i have a set A with elements a,b,c in it
for it to be a partial order relation
each element must be related to itself (reflexivity)
if 2 elements are related, then they must be equal (antisymmetry)
and if we have aRb and bRc, then aRc (transitive)
celest ledge
Yeah
celest ledge
you have 4 possibilities:
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a)}
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a),(b,d)}
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a),(c,d)}
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a),(b,d),(c,d)}
deft prairie
what do these sets represent?
are each of those sets a partial order relation?
if so: can you explain why each set is a partial order relation?
i can see that each element relates back to itself (therefore reflexivity is satisfied)
deft prairie
you have 4 possibilities:
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a)}
{(a,a),(b,...
but i dont understand the rest
celest ledge
{(x,y):xUy}
deft prairie
{(x,y):xUy}
ah so you can represent each partial order relation as an entire set?
celest ledge
As a subset of A times A
deft prairie
you have 4 possibilities:
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a)}
{(a,a),(b,...
how could (d,b) and (d,c) exist though?
i thought d can't be related to b
and d can't be related to c
celest ledge
You can let (b,d) belong to it or not
This gives you 2 choices of constructing this set
celest ledge
Sorry I wrote wrong, editing
deft prairie
oh ok
celest ledge
you have 4 possibilities:
{(a,a),(b,b),(c,c),(d,d),(b,a),(c,a),(d,a)}
{(a,a),(b,...
Correct now
You see the only difference of those 4 sets are in their end, whether they contain (b,d), (c,d) or not
deft prairie
yeahh i see that
because we know
- b can never be related to c and c can never be related to b
- bRd is possible
- cRd is possible
celest ledge
Yeah
deft prairie
so the choices is either
bRd can happen
or bRd doesn't happen
cRd happens
or cRd doesn't happen
celest ledge
Yeah 4 choices
celest ledge
Sure
deft prairie
celest ledge
would this be right?
Correct
celest ledge
Np
deft prairie
oh one more thing
celest ledge
Correct
deft prairie
Correct
thanks man
do u mind if i send you a friend request and dm you questions in the future?
i just liked the way you explained things
all g if not preferred tho
celest ledge
Sure
Any time, no greeting is needed. Directly send me questions any time I will respond when I check my DM
deft prairie
Any time, no greeting is needed. Directly send me questions any time I will resp...
appreciate it man
sent a req, i'll close the thread now
thanks once again
.close
turbid yacht
okay we're trying this again. so I have this math problem and I need help with the second part. I'm not sure if I'm doing it right? it involves finding error using alternating series remainder theorem.
cedar kilnBOT
okay we're trying this again. so I have this math problem and I need help with t...
@turbid yacht Has your question been resolved?
cedar kilnBOT
@turbid yacht Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Please tell me how to solve this sequence.
cedar kilnBOT
Please tell me how to solve this sequence.
celest ledge
You can’t have k appear in both terms and index
crimson sedge
what do you mean?
celest ledge
Use $\sum_{1 \leq j \leq n}j^2=\frac{n(n+1)(2n+1)}{6}$
wraith daggerBOT
Cogwheels of the mind
celest ledge
what do you mean?
Like I said, you can’t have k appear both in terms and under the sigma
lament sonnet
Like I said, you can’t have k appear both in terms and under the sigma
You can though. It's a sum, not an integral. $\sum_{k=1}^n k = 1+2+3+...+n$
wraith daggerBOT
1345631
crimson sedge
I learned about ∑ today, so I don't know much about it. sorry.
celest ledge
You can though. It's a sum, not an integral. $\sum_{k=1}^n k = 1+2+3+...+n$
What? Do you under what I said?
He needs to change the symbol
He can use another symbol like j i whatever
lament sonnet
What? Do you under what I said?
I don't "under" it, but I understand it. Also, in your latex above, you used j as index and j as variable
celest ledge
For his first sum
lament sonnet
Maybe he did a typo, and that k+1 is meant to be k=1. The thing on top is n
Slightly eccentric writing, but we can understand it
crimson sedge
**Cogwheels of the mind**
I solved it using this.
However, I don't know how to solve it from here.
How to factor this
crimson sedge
Slightly eccentric writing, but we can understand it
I just realized that I was making a mistake. sorry.
It's k=1
celest ledge
There is a general method to calculate $\sum_{1 \leq j \leq n}j^{r}$ this way: let D , E , I be three maps mapping sequences to sequences: $D(f(n))=f(n+1)-f(n)$ $E(f(n))=f(n+1)$, $I(f(n))=f(n)$ then we have $D=E-I$ therefore $\sum_{0 \leq j \leq n}f(j)=\sum_{0 \leq j \leq n}(E^{j}f)(0)=\sum_{0 \leq j \leq n}((D+I)^{j}f)(0)=\sum_{0 \leq j \leq n}\sum_{0 \leq i \leq j}(\binom{j}{i}D^{i}f)(0)= \sum_{0 \leq i\leq n}\binom{n+1}{i+1}D^{i}f(0)= \sum_{0 \leq i\leq r}\binom{n+1}{i+1}D^{i}f(0)$ all you need to do is to make a difference table of order r to calculate all $D^{i}f(0)$ for $0 \leq j \leq r$ because $D^{k}f(0)=0$ for $k>r$ when $f(n)=n^{r}$
wraith daggerBOT
Cogwheels of the mind
celest ledge
Your case r=2 but I will make an example when r=5:
This is your r=2 case also:
I leave proving $D^{k}(j^{r})=0$ when $k>r$ to yourself which isn’t very hard
wraith daggerBOT
Cogwheels of the mind
celest ledge
Break it into two sums: it equals $\sum_{k=1}^{n} k^{2}-\sum_{k=1}^{n} 2k=\frac{n(n+1)(2n+1)}{6}-n(n+1)$
wraith daggerBOT
Cogwheels of the mind
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
I solved it! thanks
sand cradle
cedar kilnBOT
sand cradle
You start on the "X".
What is the probability that you land on "O" when you randomly move up, right, left or down?
whole ember
what are the orange things
celest ledge
He didn’t give the number of steps so it’s impossible to solve anyway. For example the limit of probability of the person stopping at O after n steps is 0 when n approaches infinity
I mean like p(2)=1/12, lim p(n)=0
cedar kilnBOT
@sand cradle Has your question been resolved?
sand cradle
He didn’t give the number of steps so it’s impossible to solve anyway. For examp...
that was exactly my thought, you can infinitely go back and forth, right?
But this is a simplification I made from this problem
sand cradle
He didn’t give the number of steps so it’s impossible to solve anyway. For examp...
It ends if the frog goes on a red square
sand cradle
what are the orange things
It ends if the frog goes on a red square
crimson sedge
It ends if the frog goes on a red square
Oh
crimson sedge
so is it possible to calculate the possibility?
Ig then it is because the frog can't do infinitely back and foruth anymorr
He might land on a red square
sand cradle
Ig then it is because the frog can't do infinitely back and foruth anymorr
it can, lets say it jumps up down up down et.c
oh
crimson sedge
it can, lets say it jumps up down up down et.c
Oh wait
Can't it loop
Like a circle
On one place
crimson sedge
the percentage that he jumps up and down infinitely is infinitely small so 0 <:c...
Lol 
sand cradle
I think I'm approaching this problem wrong with my visualization lol
celest ledge
It ends if the frog goes on a red square
Makes sense now, but I can’t solve😂
sand cradle
Maybe this visualization is better
I thought about using something like a Pascal's triangle
But then again I can't use this because he could always go back so 0 shouldnt be 0 but 1, but then 1 should be 2 etc.
celest ledge
I have an idea:
We denote p(a,b) the probability of the point escaping from the square from two vertical edges starting at point (a,b)
Then one result we know is that p(2,2)=1/2
Now p(1,2)=x which we want to find , p((1,3)=y, p(2,3)=z
We have x=1/4+1/8+y/2
y=1/4+z/4+x/4
z=y/2+1/8
We can solve this system of linear equations
cedar kilnBOT
cedar kilnBOT
Available help channel!
limpid grail
cedar kilnBOT
crimson sedge
how does 2-sqr(x-1) = f(x)
They defined it like that ig but i generally don't see people doing it that way
limpid grail
I think im starting to see it
crimson sedge
However the problem is how $\frac {1}{f(x)}$=$\frac{2+\sqrt{x-1}}{5-x}$
wraith daggerBOT
Frustrated Cat
crimson sedge
but part b is weird
I think I got it
So first what part are you exactly confused with?
crimson sedge
$f(x) = 2-\sqrt{x-1}$
wraith daggerBOT
Frustrated Cat
limpid grail
how
crimson sedge
They defined it ig
crimson sedge
The moment they changed the denominator to f(x)
crimson sedge
if i find the reciprocal of this how does it give 2 - squr(x-1)
$\frac{1}{2-\sqrt{x-1}}$
limpid grail
ohh i see
wraith daggerBOT
Frustrated Cat
wraith daggerBOT
Frustrated Cat
limpid grail
Ok what's been done
I don' think I would ever think of these substitutions in an exam though lol
crimson sedge
Ok what's been done
Just trying to explain why 1/f(x) equals that thing
limpid grail
yeh I understand it now but i didn't even need to know that really
crimson sedge
yeh I understand it now but i didn't even need to know that really
Lol ok
limpid grail
i mean bc it gives you it in the first solution
that you need to use these parts bascially
@crimson sedge Anyway ty ,I understand this now and going to see if i can do it again after a shit
bye
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
hushed valley
how do i do this i got 4950(is it correct?)
cedar kilnBOT
how do i do this i got 4950(is it correct?)
livid hound
translation?
cedar kilnBOT
@hushed valley Has your question been resolved?
edgy hazel
y′′ + by′ + 49y = 0
find value(s) of b where the solution does the ff:
i. as x approaches infinity, rapidly decays to 0
ii. decay while oscillation
iii. oscillates regardless of the value of x
upper abyss
This depends on the roots of the characteristic equation
cedar kilnBOT
@edgy hazel Has your question been resolved?
edgy hazel
This depends on the roots of the characteristic equation
should i start by finding the general solution?
cedar kilnBOT
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cedar kilnBOT
Available help channel!
glossy root
I know the answer is - 1 but how
cedar kilnBOT
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indigo badge
Hey, does anyone know how to do this one? I'm really not sure where to begin, I'm not sure what the "parametrized surface in the natural way" really means...
indigo badge
I thought I'd just use the equation of the tangent plane at a point equation?
cedar kilnBOT
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dire geode
start with the general equation of the tangent plane
cedar kilnBOT
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verbal dove
Is there anyone who can write 5*1²+5*2²+5*3²+5*4²+...+5*(n-1)²+5*n² in the letter n?
mighty drift
That's 5 times the sum of the squares, which you may or may not know the formula for
verbal dove
?
verbal dove
I mean, how can you write like a function of that in the letter n
So if n is 5, the solution is 5*1²+5*2²+5*3²+5*4²+5*5²
glad kestrel
do you know summation/sigma notation?
verbal dove
Yes
glad kestrel
so what trouble are you having exactly
verbal dove
But I don't want to use that
glad kestrel
then good luck
glad kestrel
That's 5 times the sum of the squares, which you may or may not know the formula...
actually this
verbal dove
I don't even know what that shit means he wrote
mighty drift
There's a formula for 1+2+3+...+n
Similarly there's a formula for 1+4+9+...+n^2
verbal dove
And which one is that?
mighty drift
n(n+1)(2n+1)/6, but you'd need to include a proof if it was a test or an exercise
sharp juniper
(3) Two forces of magnitude 80 and 120 pounds are acting on an object at angles of 60° and 30°, respectively.
Find the resultant force exerted on the object
lofty gust
F is the force vector, ||F|| is the norm (length)
lofty gust
norm, length, modulus, size, magnitude
lofty gust
it has multiple names
sharp juniper
ok
so how would I obtain the force vector?
I think I've calculated magnitude
as for that one it should be sqr((80sin60+120sin30)^2+(80cos60+120cos30)^2)
which should be sqr( 129.6^2 + 144.4^2)
which results in 194.03 Pounds
is force vector just the x and y component?
sharp juniper
and how should that be formatted do you think?
x component is 144.95 y component is 127.46?
lofty gust
i haven't calculated it, but it shouldn't be hard
if you can find the x and y components of the two forces you shouldd get it right
lofty gust
that depends on whoever grades your work
sharp juniper
brain fried.
lofty gust
i can't answer questions about notation, everyone likes a different thing
sharp juniper
fair enough, I'm just trynna get an idea of the standard notation
what's it normally formatted as
cedar kilnBOT
cedar kilnBOT
Available help channel!
sudden lance
can someone help me find phi
cedar kilnBOT
can someone help me find phi
bold vine
2phi = θ if you can find a way to represent θ in the circle
sudden lance
if we continue the red line
on the top
we can see that theta is mirrored
but how do i know that this implies phi is half of theta
i assumed it was because of the orthogonal to the tangnet line but
idk if thats the right reasoning
@bold vine
bold vine
Look at the radius that is part of the ray that defines θ
Look at that line’s angle with the horizontal - that is also θ
sudden lance
the radius?
cedar kilnBOT
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lunar yoke
How would i find the arc length from this point?
cedar kilnBOT
How would i find the arc length from this point?
lunar yoke
Im assuming i would get the circumference and the multiply it by 20/360 but im not sure if thats correct
cedar kilnBOT
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meager bear
cedar kilnBOT
meager bear
hi idk what I’m doing wrong
how do I express what I did in step 1 into step 2
in that form
cedar kilnBOT
@meager bear Has your question been resolved?
meager bear
no
bright fiber
Well step one asks you to complete the sqaure
but you tried solving for it right away
meager bear
I completed the square in the second line and went off that
but then -4 is a^2
and a^2 can’t be a negative number so
idk what to do
sleek condor
cedar kilnBOT
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modern valley
hey i have a z score of 2.91388 and i want to find the p value for it how can i do that?
My null hypothesis is P less than 0.5
modern valley
i did
p value = P(Z < 2.91382)
p value = 1 - P(Z ≥ 2.91382)
But after this i dont know what to do
cedar kilnBOT
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sand ether
cedar kilnBOT
rocky garden
Here's the question:
Question->What is your 95% credible interval for the number of people who will be alive in the year 3000 CE (including digital people)(must go through this before attempting- [ https://forum.effectivealtruism.org/posts/AKxKR4CeakyBsGFoH/digital-people-would-be-an-even-bigger-deal ] ? Explain your reasoning by giving a roughly one-sentence justification for each important step of your reasoning.
A 95% credible interval means that you believe there is a 95% chance that thetrue value will fall within your interval. If I were 95% confident that the number of books in a library was between 100 and 500, then my 95% credible interval would be 100-500.
cedar kilnBOT
Here's the question:
Question->What is your 95% credible interval for the numbe...
@rocky garden Has your question been resolved?
rocky garden
<@&286206848099549185>
cedar kilnBOT
@rocky garden Has your question been resolved?
cedar kilnBOT
@rocky garden Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
✅
rocky garden
<@&286206848099549185>
rocky garden
<@&286206848099549185>
rocky garden
<@&286206848099549185>
cedar kilnBOT
@rocky garden Has your question been resolved?
cedar kilnBOT
rocky garden
.reopen
cedar kilnBOT
✅
random shale
Here's the question:
Question->What is your 95% credible interval for the numbe...
what have u tried so far?
signal stag
h
cedar kilnBOT
@rocky garden Has your question been resolved?
shy garnet
h
jade notch
How can we solve it, where the upper boundary is N 😦
cedar kilnBOT
How can we solve it, where the upper boundary is N 😦
rocky garden
.reopen
rocky garden
what have u tried so far?
Hi!
Yes
I would personally measure an 95 confidence interval, by calculating standard deviation of my data but there's no dataset given
N idk how do i proceed wo that
That's the place that ive been failing at
cedar kilnBOT
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rocky garden
.reopen
crimson sedge
cedar kilnBOT
crimson sedge
can anyone help me here?
crystal raptor
You choose a t, any t you want, and plug it into those equations
That will give you the x and y coordinates of a point on that line
regal torrent
Does anyone know how to calculate the impulse response of a z domain transfer function?
So i have my difference equation, which is y(n) = x(n) +0.3x(n-1) + 0.8y(n-1)
I managed to get the first 5 samples for a step response
But now i'm supposed to get output samples using impulse responses
regal torrent
why?
crimson sedge
idk how to make tiket
regal torrent
ticket is one the side
cedar kilnBOT
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crimson sedge
cedar kilnBOT
eager meadow
Does anyone know how to calculate the impulse response of a z domain transfer fu...
x[n]∗h[n]⟶ZX(z)H(z).x[n]∗h[n]⟶ZX(z)H(z).
In case the system is defined with a difference equation (as you proposed) we could first calculate the impulse response and then calculating the Z-transform. But it is far easier to calculate the Z-transform of both sides of the difference equation.
So let's rearrange the equation,
y*(n)-(x*(n)+(3/10)x(n-1)+(8/10)y(n-1))=0
yn-((nx+((3/10•x)•(n-1)))+((4/5•y)•(n-1))) = 0
yn-((nx+((3/10•x)•(n-1)))+4y•(n-1)/5) = 0
yn-((nx+3x•(n-1)/10))+4y•(n-1)/5) = 0
Adding a fraction to a whole
nx = nx/1 = nx • 10/10
Adding up the two equivalent fractions
nx • 10 + 3x • (n-1)/10 = 13nx - 3x/10
yn - ((13nx - 3x)/10 + 4y • (n - 1)/5)
Pull out like factors :
13nx - 3x = x • (13n - 3)
This is huge process and unfortunately this doesn't have a solution
eager meadow
Does anyone know how to calculate the impulse response of a z domain transfer fu...
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
dire geode
x[n]∗h[n]⟶ZX(z)H(z).x[n]∗h[n]⟶ZX(z)H(z).
In case the system is defined with a d...
this channel's occupied. open your own. #❓how-to-get-help
eager meadow
this channel's occupied. open your own. <#488120190538743810>
My bad 😔
cedar kilnBOT
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real bone
cedar kilnBOT
real bone
I keep getting in a situation where the answer will include i. There must be a mistake because i is never part of our problems
dire geode
,w differentiate 2/(x^2 - 36)
wraith daggerBOT
dire geode
,w differentiate -4x/(x^2-36)^2
wraith daggerBOT
wraith daggerBOT
dire geode
you can easily see where the hyperbola is concave up and down, but the second derivative's numerator is never zero
real bone
Oh
dire geode
,w second derivative 1/x
wraith daggerBOT
real bone
I am a little confused by the term 'non-differentiable'
Because we just did 2 derivatives
dire geode
similarly, this function is not differentiable when the denominator is zero
because it's not even defined there
dire geode
https://encyclopediaofmath.org/wiki/Non-differentiable_function
maybe a bit too advanced. look at this instead
https://socratic.org/questions/what-are-some-examples-of-non-differentiable-functions
real bone
Oh this is awesome thank you
dire geode
real bone
.close
hidden radish
Where do I start this one?
cedar kilnBOT
Where do I start this one?
jovial snow
It might help to rewrite the expression as $3\cdot (sin(\frac{1}{(2-x)}))^4$.
wraith daggerBOT
Goose on a Moose
hidden radish
<@368773186512224256> u know product rule?
yeah i know those, just confused about which order to go about this because this looks more complicated than the ones i've done before
hidden radish
It might help to rewrite the expression as $3\cdot (sin(\frac{1}{(2-x)}))^4$.
oh okay so the 4 applies to the entire thing
hidden radish
sin^n (stuff) implies (sin(stuff))^n
what does the ^-1 do? is that applying to the argument or is it part of the argument itself if that makes sense
jovial snow
typically in math ^(-1) means the inverse.
so if we have 5^(-1) this means the multiplicative inverse of 5 which is 1/5
sin^(-1) means the inverse of sin, i.e. arcsin
jovial snow
Sorry something came up and I won't be able to help you more. Maybe someone else can chime in
hidden radish
No problem!
cedar kilnBOT
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hidden radish
Im still waiting for help if you don’t mind
cedar kilnBOT
@hidden radish Has your question been resolved?
cedar kilnBOT
@hidden radish Has your question been resolved?
cedar kilnBOT
@hidden radish Has your question been resolved?
sand ether
sand ether
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mint igloo
Could someone please help me understand which of these answers are correct and why? I especially don’t understand D. I think B and C are both correct, but I’m probably wrong. Thank you so much in advance!
mint igloo
crystal raptor
if B was correct, what would happen if we tried to put in x=2?
mint igloo
It would equal 0
I think
Is that right?
So are you saying it can’t be answer B or D?
crystal raptor
Just think about B for a second
if we plug x=2 into $\frac{y-1.3}{x-2}$, what happens?
wraith daggerBOT
iCaird
mint igloo
Denominator becomes 0
And you can’t have that
I’m sorry I’m struggling so much, I’m trying my best to follow
crystal raptor
its okay, you're correct!
our function wouldn't be defined at x=2 because we cant divide by zero
but in the picture tells us that when x=2, y=1.3
(see the point on the right)
so B must be false!
mint igloo
I had no idea that that was a way to figure that part of the problem out
So then I can plug that in to check for D as well?
Which would make that false as well?
crystal raptor
you would need to check a point that is on the curve, like (2,1.3)
mint igloo
How would I go about doing that?
I’m sorry for such basic questions, but this is all new to me
And I also don’t understand A and C. Aren’t those basically saying the same thing?
mint igloo
Ok
crystal raptor
so in the equation in D), try replacing x with 0 and y with 1.8 and seeing if you get a true equation
mint igloo
Ok, let me check
I mean true
No, wait
Ya, not true
I really hope I’m right
Thank you so much for working through this problem with me by the way, it really means a lot
crystal raptor
yep not true! do D cannot be true either
otherwise that equation would be true for any x and y
mint igloo
I can’t believe I didn’t know how to go about doing that
mint igloo
Can we visualize that on the graph or do we need to do that kind of input?
C and A confuse me, because I feel like they are almost saying the same thing
crystal raptor
A it talking about the relationship between points
C is talking about the relationship between changes in coordinates
crystal raptor
Can we visualize that on the graph or do we need to do that kind of input?
lets test an input!
mint igloo
Ok
mint igloo
Yes, sorry about that
crystal raptor
dont worry about it honestly
okay now can you check if A is true with that x and y you just picked?
mint igloo
I feel like I should know what to do based on what you helped me with
But I don’t understand how to put this into an equation to check if true
crystal raptor
if i said to you "b is 5 times as large as a", do you know what kind of equation we could true?
mint igloo
I honestly am trying my best to remember but I can’t
It’s embarrassing to say but my brain is hurting I’m trying so hard lol
crystal raptor
We could say $b = 5a$
wraith daggerBOT
iCaird
crystal raptor
you see? when we put something into a, then b will be 5 times as much as that
so b is 5 times as large as a
mint igloo
Ok, yes I do see that
crystal raptor
so if we are being told that y is 0.25 times as large as x, what could we write?
mint igloo
Let me think
crystal raptor
sure
mint igloo
I can’t believe I don’t get what to do next
The best I can think of is
Ahhh, I just can’t seem to get it even with the equation
wraith daggerBOT
iCaird
crystal raptor
"y is 0.25 times as large as x"
this would read as y = 0.25x
does that make sense?
mint igloo
Yes, so then you would input something for x?
crystal raptor
yes remember your favourite point you chose
plug that x and y into that and see if you get something that is true
crystal raptor
not true right?
mint igloo
Not true
mint igloo
Wait a minute, let me check for c to see if I got this
Hmmm
I don’t think I’m checking for c right
crystal raptor
C) is a bit more tricky, we have to use two points to test this because its talking about the change in x and y
if we go from (0,1.8) to (2,1.3) what is the change in x? (the first coordinate)
mint igloo
The change is 2
crystal raptor
the bottom! because we're decreasing
crystal raptor
so C) is claiming the change in y is -0.25 times as large as the change in x, can you write that as an equation?
mint igloo
Let me try
crystal raptor
very similar to the last one, just now we have change of y and change of x (just changes the words)
mint igloo
crystal raptor
not quite
its just (change in y) = -0.25*(change in x)
so now check that with the values you just found!
crystal raptor
we can just write it in words
if you want a symbol it would be $\Delta y = -0.25\Delta x$
wraith daggerBOT
iCaird
mint igloo
How do I know where to input the values and which ones, I’m sorry I’m trying I’m trying I promise
crystal raptor
we worked out that the change in x was 2 and the change in y was 0.5
mint igloo
Yes
crystal raptor
so put those into our equation we just made
mint igloo
Oh my goodness
crystal raptor
you might now ask, well do we have to check more points? what if another two points makes it not true??
mint igloo
Ya
crystal raptor
the good news is that because this is a straight line, if its true at two particular points, its true at any two points
because lines have constant slope
so the relationship between the change in y and the change in x is the same no matter which points we pick
so we're done!
mint igloo
Wow
I can’t believe you took the time out of your day to help me over such an extended period of time with the little knowledge I have. Is there something I can do or donate or anything??
This was a tremendous learning experience for me
I just can’t believe you walked through step by step by step by step
crystal raptor
No nothing you need to do! Just pass on the knowledge when you're able to:)
you did great
mint igloo
Thank you so much, I certainly will do just that when I get to that point. Thank you for not giving up on me along the way
It means so much to me
What a great teacher
crystal raptor
Much appreciated! Hope you have fun with maths:D
mint igloo
I will be trying my best to have fun with it, hopefully a lot more fun when I get better and better!!
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cedar kilnBOT
cedar kilnBOT
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tulip shadow
how do I do this
cedar kilnBOT
how do I do this
upper abyss
Can you tell the pattern? How would you get the next digit after -54?
upper abyss
Yeah you'd need the number of terms
tulip shadow
a4=18 a5=6 a6=2 a7= 2/3 a8=2/9 so -486(1-(-1/3)^8)/1+1/3
deft forum
I mean you can do it that way to find the number of terms or you can use the formula: $$T_n = a \cdot r^{(n-1)}$$ where a is the first term
and r is the common ratio
wraith daggerBOT
Deep.
deft forum
…
fervent mason
T_n = nth term
cedar kilnBOT
@tulip shadow Has your question been resolved?
austere silo
MECHANICS QUESTION : moments and ladders
cedar kilnBOT
MECHANICS QUESTION : moments and ladders
wraith daggerBOT
austere silo
this is my working out so far but i feel like im doing something wrong
should i not take a moment around A and try B instead ?
okay the issue is uRb that I labelled in my diagram
its not meant to be there but i dont know why
NVM
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cedar kilnBOT
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little chasm
So I'm doing propositional calculus
cedar kilnBOT
So I'm doing propositional calculus
crystal raptor
what do you mean by "solve"?
little chasm
I'm working on truth tables in propistional calculus
little chasm
what do you mean by "solve"?
So I have this now but I'm unsure if it's correct
crystal raptor
You need to describe what you're trying to do
little chasm
little chasm
You need to describe what you're trying to do
so I'm trying to create a truth table for this
and I just want to confirm that it's correct
crystal raptor
whats the value of $T \wedge F$?
wraith daggerBOT
iCaird
glacial pollen
btw the table is not complete either, you need a column for $\neg q$ as well
wraith daggerBOT
jixana
crystal raptor
$\neg Q$ has the opposite value to $Q$
wraith daggerBOT
iCaird
wraith daggerBOT
iCaird
little chasm
ok ty
so to confirm this is fine?
also I just want to confirm that this question is right
crystal raptor
this is correct
little chasm
can someone please tell me if this is right
cedar kilnBOT
can someone please tell me if this is right
little chasm
like the solution to the last 3 columns
crimson sedge
torn atlas
oh sorry didn't realise this channel was taken
cedar kilnBOT
@little chasm Has your question been resolved?
mint sorrel
cedar kilnBOT
mint sorrel
For the calculation of flux across the sphere, why is it okay to just get rid of the y term
Here is the long way
mint sorrel
Is it just coincidence that setting the y term to zero and multiplying by the volume of the sphere yields the right answer?
<@&286206848099549185>
The volume of the sphere evaluates to be 36pi
why does it appear to be the case in the solution set for this question, that the professor just sets the y term in 4+2y to zero, and instead of performing the triple integral he just multiplies by the volume of the sphere
is there some insight about the volume of the sphere or the function 2+2y that I am missing here? Is this a massive shortcut you can take to avoid performing the full triple integral
<@&286206848099549185>
cedar kilnBOT
@mint sorrel Has your question been resolved?
dire geode
For the calculation of flux across the sphere, why is it okay to just get rid of...
where do they "get rid of the y term" and what does that even mean?
dire geode
that is what I mean by getting rid of the y term
y is odd wrt to its domain in cartesian coordinates.
just check it holds in spherical too
mint sorrel
I'm not sure what you mean.
dire geode
I'm not sure what you mean.
which part
mint sorrel
y is odd wrt to its domain in cartesian coordinates.
what do you mean y is odd wrt its domain in cartesian coordinates
dire geode
what do you mean y is odd wrt its domain in cartesian coordinates
write the integral in cartesian coordinates.
mint sorrel
oh, so since y is odd it is equal to zero
so by the sum rule it is just the triple integral of 4
dire geode
yar
mint sorrel
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little chasm
so I'm just wondering if this truth table is saying since there are no values for p, q , and r when they are all false in the first column
little chasm
I don't understand why the firsst column is false if the last one is also true
I thought when p, q, and r it would be false as well
like what is p ∨ q ∨ r tellling me
west dome
Do you mean row?
glacial pollen
again, when doing truth table, draw each columns
dont skip to final step
draw a column for (q or r)
then a column for p or (q or r)
cedar kilnBOT
@little chasm Has your question been resolved?
little chasm
draw a column for (q or r)
so I just made a column for q or r
is this right?
oh wait does this just say that there's either a true or false?
and then the false has nothing but falses?
empty delta
cedar kilnBOT
empty delta
so for the horizontal stretch about the y-axis, the answer is 1/3
similarly, if the equation should 1/3, the answer would be 3 right?
why is it like this I'm having a hard time understanding why
kindred storm
@empty delta That happens because multiplying x by 3 makes the larger x values happen faster, so it gets scrunched up because the higher values occur earlier on.
Like at x = 1, you'd usually have only gone 1 to the right, but now you've gone 3 to the right instead, so all the stuff in the graph from 0 to 3 in normal cases instead happens from 0 to 1, and it has to scrunch it up to get it to fit.
empty delta
Like at x = 1, you'd usually have only gone 1 to the right, but now you've gone ...
Ahhhhhh okay I understand now, thanks for the help :^)
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cedar kilnBOT
kindred storm
You're welcome.
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floral jasper
is the answer to this
cedar kilnBOT
is the answer to this
floral jasper
this
cedar kilnBOT
@floral jasper Has your question been resolved?
gaunt trench
cedar kilnBOT
gaunt trench
What did I do wrong
lament sonnet
(8x+5)/(8x) is not 5
gaunt trench
Uh
Oh ya
It would be 5\8x
?
wait i dont get this
would it become thus?
integral sign
cedar kilnBOT
@gaunt trench Has your question been resolved?
dire geode
Don't mix u and x variables in the same integral. You substitute ALL the terms at once
cedar kilnBOT
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crimson sedge
Can there be an infinite collection of sets with an infinite number of elements, such that any two sets in the collection are disjoint and the union of the collection is the set of all natural numbers
crimson sedge
Just asking if anyone happens to know.
I was thinking well it cant just be an enumeration starting from some k and then k+1 etc. Cause i either stop, making the set finite or i dont stop, not leaving much room for any other set
I also thought of this correct me if im wrong
I thought of how you could split N into odd and even. And i thought well what if we make that ‘jump’ larger allowing for more sets(?)
But i think that would terminate when youre at that last one (?) making the collection finite. I dunno if i was gonna get anywhere with it but it seemed like it could get me somewhere
But i dont think so
Im just thinking, in what way could you possibly arrange N into an infinite number of ‘infinite sets’?
With every set disjoint from any other
Any1 here like rn?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
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crimson sedge
thank bot
cedar kilnBOT
@crimson sedge Has your question been resolved?
dire geode
you might want to read
https://cs.uwaterloo.ca/journals/JIS/VOL12/Venkatachala/venkatachala2.pdf
digital raptor
you could probably take all even numbers, then all numbers like 4k+1, then all numbers like 8k+3, then all numbers like 16k+7, and the nth one is $2^n*k+2^{n-1}-1$, and all would be disjoint, and every number would appear once.
wraith daggerBOT
opfromthestart
cedar kilnBOT
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shell cloud
It is a zero which isn't too hard to check
But the only way I can think to check the multiplicity is by just dividing by x-k over and over
And I feel like there's an easier way
cedar kilnBOT
@shell cloud Has your question been resolved?
cedar kilnBOT
shell cloud
.reopen
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shell cloud
<@&286206848099549185>
cedar kilnBOT
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cunning loom
Generally, if $a$ is a root of a polynomial with multiplicity $k$, then it is a root of the derivative with multiplicity $k-1$. That will be faster.
wraith daggerBOT
Kimbomanjaro
cunning loom
@shell cloud
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twin coral
twin coral
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knotty fox
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knotty fox
Hello does anyone know how to implement this on Excel
cedar kilnBOT
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knotty fox
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umbral ravine
sprt x = x^2, that would mean x=0, and 1 right?
cedar kilnBOT
sprt x = x^2, that would mean x=0, and 1 right?
quartz vale
crimson sedge
cedar kilnBOT
crimson sedge
Can someone explain to me 2?
I’ve read through the notes
In the Cambridge book and this was a huge jump@to me
- A)
I know how to do the rest
But if they give you 0<=x<=4 domain in a question how would you find the range
shut jackal
But if they give you 0<=x<=4 domain in a question how would you find the range
plug in x as 0 into the equation and thats the lower bound on the range and then again x as 4 and thats the higher bound, so for this example i believe the range would be 0 <= y <= 2
crimson sedge
Yes that’s correct!
OH WAIT
so basically
You put 0 and 4 in the given f(x)
Root 0 and root 4? < cause the domain idk how to explain this with my mind jumbled
You just basically put the domain in
To find y
shut jackal
ya, for this example the graph of sqrt(x) steadily increases so we can just plug in the domain into the range, if the equation were more complicated then that might not work, and youd have to test other values than just the lower and upper bound of the domain
but for this ya
shut jackal
yaya np😊
distant thorn
Umm Hi
distant thorn
So i solved this question and found the asbolute minimum
but the absolute minimum i found was 0
could anyone try the q and lmk if my ans turned out to be correct
thanks
cedar kilnBOT
@distant thorn Has your question been resolved?
distant thorn
<@&286206848099549185>
cedar kilnBOT
@distant thorn Has your question been resolved?
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@distant thorn Has your question been resolved?
obsidian pine
Hello I am struggling to get to the answer shown in the first picture.
cedar kilnBOT
Hello I am struggling to get to the answer shown in the first picture.
@obsidian pine Has your question been resolved?
obsidian pine
<@&286206848099549185>
cedar kilnBOT
@obsidian pine Has your question been resolved?
cedar kilnBOT
@obsidian pine Has your question been resolved?
loud anchor
hi your work can better organized if Feynman's formula for differentiation is used
obsidian pine
I don’t think I can use that method because I have not been taught it in school
I need to find a way using what I have been taught in maths this year but everything I’ve tried hasn’t worked for me.
loud anchor
I don’t think I can use that method because I have not been taught it in school
i think you can. i'm referring to this method to organize your work
Using Feynman's trick
,,\begin{aligned}
\left. \frac{\dd{V}}{\dd{t}}\right\rvert_{\substack{r = 0.6 \ h = 2}} &= \left. \pi r^2 h \left( \frac{2r}{r^2} \frac{\dd{r}}{\dd{t}} + \frac1h \frac{\dd{h}}{\dd{t}} \right) \right\rvert_{\substack{r = 0.6 \ h = 2}} \
&= \pi r^2 h \left. \left( \frac2r \frac{\dd{r}}{\dd{t}} + \frac1h \frac{\dd{h}}{\dd{t}} \right) \right \rvert_{\substack{r = 0.6 \ h = 2}} \
&= \pi (0.6)^2 (2) \left[\frac{2}{0.6} (-0.02) + \frac12 (0.01) \right] \
&= -\frac{111}{2500} \pi
\end{aligned}
wraith daggerBOT
vin100
obsidian pine
I know what feynmans thing is but I have to use methods I was taught in school
This is what I mean
so v=h^3
dv/dh=3h^2
dh/dt=5
then (dv/dh)(dh/dt)=dv/dt
so dv/dt=15h^2
This is the method we are taught
loud anchor
I know what feynmans thing is but I have to use methods I was taught in school
\in public exams i think if you can cite the name of a well-known method like this, you'd be fine. i suggest asking your teacher to clarify though.
loud anchor
hi guys, i am urgently requesting assistance for the below
i suggest opening a new channel for another question
obsidian pine
I could do that but it's not worth it since my teacher is not the one who marks my exam
it goes to a company called SQA who manage all exams
loud anchor
i think that you can even write the steps of feynman's trick without even citing his name
obsidian pine
I don't want to chance it and loose marks I would have tried this if it's a class exam
I'll try one thing to see if it works
loud anchor
this nicely organizes your work, so that it's easier to get your final answer correct. when the marker sees that correct answer probably you'd get the marks
obsidian pine
They have a strict marking scheme I don't want to use anything too complex for my level
This is a past paper question anyway
Maybe the answer on it is wrong because sometimes that happens
loud anchor
They have a strict marking scheme I don't want to use anything too complex for m...
sorry that never interests me. when you get the problem solved respecting the question's instructions, normally you'd get a good mark.
obsidian pine
Thanks for your help anyway 👍
cedar kilnBOT
@obsidian pine Has your question been resolved?
dusk roost
whats :
cedar kilnBOT
@obsidian pine Has your question been resolved?
dense solstice
You can write ratios as fractions then use algebra to solve. 5/7 = x/(x+10)
5x+50=7x
2x=50
x=25
25/35=5/7
sinful geyser
You can write ratios as fractions then use algebra to solve. 5/7 = x/(x+10)
5x+...
Don't write the answer for them please
obsidian coral
You can write ratios as fractions then use algebra to solve. 5/7 = x/(x+10)
5x+...
Don't solve the problem for the user
Also, it wasn't even their channel to start with
dense solstice
Don't solve the problem for the user
sorry, my bad. ill keep that in mind for next time
wary flower
Hi, my question is quite interpretational as well as it is mathematical. I have been plotting autocorrelation functions of time series data (See image attached) and am now wondering: a) what is the best way to quantify the extent of autocorrelation in my samples (is it by doing some kind of calculation for the plot's regression perhaps?)? So what exact measure or process should I calculate from these graphs that will allow me to plot my "assessment of autocorrelation" data into a simple column graph and/or table?
cedar kilnBOT
Hi, my question is quite interpretational as well as it is mathematical. I have ...
@wary flower Has your question been resolved?
dire geode
Hi, my question is quite interpretational as well as it is mathematical. I have ...
what is assessment
wary flower
By "assessment" I mean a mathematical or graphical interpretation of the data present in the graph that "summarise" it if you like.
dire geode
By "assessment" I mean a mathematical or graphical interpretation of the data pr...
I guess you can start with the usual, period, amplitude (damping in this case) and shift if any
Probably not what you're looking for though. Go back and find what exactly about the graph is important to you
cedar kilnBOT
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upper swallow
I need a hand finding the absolute minimum and maximum for this equation with the range -1, 1
upper swallow
I've found the derivative being
f'(x) = (-x^2 - 8x - 3) / (x^2 - 3)^2
but I'm stuck on what to do next
cedar kilnBOT
@upper swallow Has your question been resolved?
upper swallow
<@&286206848099549185>
magic spire
f'(x) = 0
upper swallow
yeah but I'm confused how to get the values for that, normally I would just factor it but the fraction is throwing me off
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dusky plume
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ashen plume
crimson sedge
crimson sedge
Where AB=K