#help-28
thorny rapids
Ok I kinda have a qn for 18 part (Ii(
So when they say vessel is 1/4 full I thought of using 1/3piR^2h to subbing in height and radius to find the height when volume is 1/4
But apparently I was wrong when I did that I have to use the formula (pi h^2)25 instead
thorny rapids
But apparently I was wrong when I did that I have to use the formula (pi h^2)25 ...
But cld anyone explain why I had to find height using this volume formula
viral jasper
So when they say vessel is 1/4 full I thought of using 1/3piR^2h to subbing in h...
how did you do this? I'm not seeing it
thorny rapids
how did you do this? I'm not seeing it
Oh no that's my wrong one
So if I did it using this way I wld get height =10
Which is wrong
thorny rapids
But apparently I was wrong when I did that I have to use the formula (pi h^2)25 ...
But using his formula I got bright =20 smth and when I continue solving for rate of change I was right
So I'm not sure why I have to use this formula instead
viral jasper
On top line LHS, what are you dividng by?
viral jasper
,calc 1/38^240/4
glossy valveBOT
Result:
213.33333333333
Uh huh
viral jasper
I mean on the second calculation
thorny rapids
But radius is always constant right so it shldnt be wrong
viral jasper
the radius is not going to be fixed tho
viral jasper
it's a cone
thorny rapids
But when u fill up with water
How does the radius change
Isint it just the height?
thorny rapids
OHHH
viral jasper
that's the new diameter at a given height
thorny rapids
Ohhh no wonder we need to use that formula
Hmm aight tks for the help! I understand now 😁
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ember citrus
Is the following true? Explain your answer.
(a) P(X)-P(Y ) = P(X -Y ) for some sets X and Y , but P(X)- P(Y ) != P(X -Y ) for some
other sets X and Y
Im not sure how to go about proving this
brittle steeple
you need to find sets X and Y for which they're equal and for which they're not
brittle steeple
If you can't find sets where they're equal then you need to show that there's always some element which is in one but both the other
brittle steeple
no
ember citrus
If you can't find sets where they're equal then you need to show that there's al...
i can do this with one example?
brittle steeple
Start by choosing any X,Y and testing them
ember citrus
so ive done that and
what i get is
P(X-Y) always has atleast element {}
but P(X) - P(Y) never has the element {}
so they are never equal
brittle steeple
Oh well there you go
ember citrus
yeah but can i just say "this occurs for every set"
ember citrus
im a bit confused
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ember citrus
is {{},{a}} = {{},{b}} = {{a}}
brittle steeple
no
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raven mauve
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raven mauve
Can i get help with getting started
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raven mauve
@timid iris ahhh sorry didn’t see ur message
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raven mauve
Do you know how to draw scatter plots?
Sort of
Im just confused on what it means put physics on horizontal
Do i put maths on vertical
timid iris
Ohh
Think about this
You just plot points in the form (x, y)
Can you tell me what x and y represent?
timid iris
X is horizontal
timid iris
Lol
raven mauve
Ok so maths on y
timid iris
(x, y)
timid iris
Now plot this point on the graph
raven mauve
Never learnt that
timid iris
Now plot this point on the graph
Any progress?
raven mauve
Now i got to do it 9 more times
raven mauve
Like A (75, 68)
Ye thanks
Relationship ill probably write something along the lines of students physics marks were higher than maths marks, this is due to most of the marks being higher up the y axis
Or something like that
The mean of both is easy ill just use a class pad or sum cause this calc assumed
Then ill plot the coordinates of mean
Then i draw line of best fit
Which is just a straight line on diagonal ??
Then for last question i use my line of best fit
And explain
timid iris
Yup
timid iris
Lmao
raven mauve
Im assuming physics and art have stronger relationship
Right?
I haven’t done it yet
But it will most likely have a strong correlation
timid iris
Just draw the points again
And get the best fit line
This line will be better than the prev one
timid iris
Im assuming physics and art have stronger relationship
So yeah
raven mauve
It would be negatively skewed basically
If not like negative/symmetrical kinda
But negative is prob better to use
raven mauve
Dw
Ok i have this one
I need help with c and e please
Oh and d too
WAIT nvm d is easy
timid iris
Bro I have to go
Sorry
Open a new channel for this
And ping helpers after 15m
Good luck
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gritty rose
King's identity
coral mountain
pigeonhole principle question:
are the pigeons distributed evenly like n+1 pigeons and n holes and there is 1 pigeon in each hole and 2 pigeons somewhere in one of the holes or can all of the pigeons be put in one hole?
dusky elk
If all you know is that n+1 pigeons are distributed among n holes, then you know that at least one hole contains at least two pigeons. it could be that all are in one hole, or that there is only one hole with two pigeons
polar valve
you know that there is at least one hole with more then one in it. nothing else is known.
coral mountain
ok thanks
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vital ferry
could someone help me solve b and c? I understand parts of it but I would like to see someone else thought process
dusky heath
could someone help me solve b and c? I understand parts of it but I would like t...
are you familiar with the unit circle?
narrow path
sigma circle mentioned
vital ferry
are you familiar with the unit circle?
Some understanding of it yes
vital ferry
our teacher wants us to use the special triangles as well as the unit circle
vital ferry
okay
dusky heath
so make cos(x) the subject
vital ferry
it goes to
dusky heath
make cos(x) by itself
narrow path
wait are you supposed to get two solutions
vital ferry
narrow path
oh okay nice
dusky heath
doesn't state how many. It states find solutions within that domain
vital ferry
this b and c
dusky heath
Yea but you shouldnt look at it like that
just beacuse the answer has 2 solutions
You should find as many solutions as you can that fits the required domain
vital ferry
understood
vital ferry
ill show u what I have for this
it becomes
x = arccos (-0.75)
(i think arc is the word for inverse)
vital ferry
well no, for that we can use the calculator
vital ferry
thats impossible to solve by hand like that
its js the way we were taught
ive heard 1000 times how dumb it is
our teacher sucks lol
anyways
vital ferry
x = arccos (-0.75)
so this is equal to about 2.42
and i know that the triangles live in q1 and q3
now idk where to go
vital ferry
yes, unit circle and special triangles are the first option
dusky heath
but like
vital ferry
if not then we go to calculator
dusky heath
yea
you can tell if you have to use calculator or not
if its not an exact value
are you familiar with this
vital ferry
yes
vital ferry
but its not relevant to the question. the entire solution doesnt actually use those
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narrow path
but its not relevant to the question. the entire solution doesnt actually use th...
what are you confused on ?
rocky loom
yo
rocky loom
i need help
violet bolt
send
torn jolt
Question
viral jasper
!status
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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 need help understanding how to make these expressions
viral jasper
what do you mean?
rocky loom
Could you explain to me how to solve it
viral jasper
I do not know what you are trying to "solve"
You just wrote some expressions with zero context
without further instructions, there is nothing to solve
rocky loom
Sorry if I wasn't clear, I meant to ask if you could help me solve expression 58 by explaining how to do it.
viral jasper
Sorry if I wasn't clear, I meant to ask if you could help me solve expression 58...
Again, "solve" means nothing here. There is nothing to solve. Did you mean simplify?
rocky loom
Again, "solve" means nothing here. There is nothing to solve. Did you mean _simp...
yes
simplify
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rare dragon
Sorry if I wasn't clear, I meant to ask if you could help me solve expression 58...
Are you there?
pallid topaz
Sorry if I wasn't clear, I meant to ask if you could help me solve expression 58...
I'd just end it atp
hot lark
To calculate the area of a figure with double integrals
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To calculate the area of a figure with double integrals
hot lark
I can put the first integral with x domain and then y domain right? But do I put x in the integral?
umbral dome
do you have an example? In general when you are trying to find area you just integrate 1
hot lark
do you have an example? In general when you are trying to find area you just int...
Ok but when polar u integrate Rho righe?
umbral dome
you are still integrating 1, the factor of rho comes from the jacobian
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hot lark
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brisk obsidian
5.34 am I solving it correctly?
No.
brisk obsidian
One moment, let me make a graph that will hopefully explain.
The way the integral is setup, you should be integrating a line vertically and the integrate horizontally across that line.
Because the integral shows dx dy.
hot lark
mh
wait
are u saying the domain must be y simple
wait no its x simple
whats the matter then
brisk obsidian
The outer integral will be the interval 0 <= y <= 2.
The inner integral will be the boundaries created by the slanted lines.
f(y) <= x <= g(y)
brisk obsidian
Is that another question?
hot lark
Is that another question?
no i showed as an example
it says dxdy here too
but its in the order ive written it with
brisk obsidian
The interval for integration is given and not dependent on the other variable so you can swap the order of integration.
That is not the case for 5.34.
hot lark
im confused wdym?
the interval is that greek letter right?
oh wait maybe you meant that i had to put x^2y all on the outer interval?
e.g from 0 to 2x
?
brisk obsidian
One moment, let me make two graphs to demonstrate how the boundaries change depending on the order of integration.
This is integrating dx dy with the upper and lower boundaries for x given.
hot lark
ok
brisk obsidian
The outer integral iterates from y=0 to y=2. The boundaries of the line segment is given by f(y) and g(y) as shown above.
The latter two graphs integrates dy dx.
You can think of the outer integral as just a line at x =a where a is on the interval of integration with respect to x. The length of that line bounded by the region goes from L(x) <= y <= U(x).
hot lark
But this is same as mine
brisk obsidian
Yes, but that is not the order of integration the problem asked you to solve.
It asked you to solve for dx dy which is a different double integral.
The intervals will need to be changed.
This is what you should be setting up and evaluating.
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viscid ridge
I see
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hollow tide
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hollow tide
so I need to search f(t) such that the right hand side is true
my only concern is, I got 3/4 sqrt(x)
gritty rose
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gritty rose
but shouldnt it be ln(x^2)??
,tex .log rules
glossy valveBOT
riemann
hollow tide
,tex \.log rules
but theres no additional 2 on the left hand side
theres 2x for chainrule on x^2
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brazen scroll
Can someone tell me how I am getting a negative answer? The answer is 0.589, which means that I resolved the horizontal forces wrong, but I don't know how.
wide heath
One quick error I’m seeing is that it should be 4mgcos(40) rather than just 4gcos(40)
brazen scroll
the m is 4kg
wide heath
Oh mb mb
wide heath
I think what might be the issue is that the force of static friction acts opposite to the direction you think it does
If the force S outmatches the portion of the gravitational force going down the slope, then the force of static friction points upwards
torn jolt
Right. Your frictional force (F) has the wrong sign. It points up the incline
Once you change that you get positive 0.589 for mu
torn jolt
The box will naturally slide down the incline, and friction opposes that motion
wide heath
But if the force you push up with is less than the gravitational force downwards, then the force of static friction makes up that slack
brazen scroll
i understand
how do i know that the force up is less than gravitational force downwards
i just calculate it?
wide heath
Yes, they’re both proportional to g, so just see which of cos(40) and sin(40) is lower
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unkempt sparrow
I need a little help finding the intersection between a line and a sphere. Ive got some of it already following https://en.wikipedia.org/wiki/Line–sphere_intersection
But im looking for the 1-2 particular solutions where the point lies on the spheres surface (the point is exactly 1 radius away)
unkempt sparrow
In 2D id just use the quadratic equation solution with a, b, c and d but here im not sure how to proceed
ive got nabla and d calculated
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midnight lotus
hi
midnight lotus
how do i simplify this
i factored x4 plus 1 and 2
out
of the whole thing
then got this
reef moss
then got this
what other factor does the 2nd part share?
blissful mango
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blissful mango
how do i do this?
fast peak
expand, complete the square, trig sub
blissful mango
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foggy holly
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torn jolt
i have not taken calculus yet, only at logarithms, and we are now taking eulers number. So I was playing around with the calculator and searched it up a bit and saw it's a pretty special number. for example i searched and saw e^pi*i + 1 = 0, and when playing with the calculator, the area under the curve of e^x from 0 to 1 is e - 1, and from 0 to ln(e+1) it is e. Why is it so special and what makes it special cuz it lowkey looks like it behaves like a function despite being just another number like pi
weak plover
from what i know
some mathematician who was cooking with maths
noticed that a specific number kept naturally occuring when dealing with a lot of mathematical concepts
like population growth, interest, finance, etc.
and then euler came along a few years later
and standardised the number as 'e'
why is it so special? the fact that it naturally appears in so many different areas of maths
and no its not a function
i dont quite get how it behaves like a function
its a constant
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torn jolt
like population growth, interest, finance, etc.
oohhh
torn jolt
i dont quite get how it behaves like a function
idk it just
from its origin i guess it just appears so much i feel its unordinary for it to be a constant
like u dont find pi on the regular when solving Bht u do find e on the regular
idk how to explain
thank u tho
fierce grail
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rare pine
"Using induction, show that […] for all positive integers a,b
rare pine
my friend told me this uses strong induction, i dont really understand how to do that though
wise gate
"Using induction, show that […] for all positive integers a,b
a-b divides obviously both a^n - ba^{n-1} and ab^{n-1} - b^n, so it remains to show that it divides a^{2n} - b^{2n}
rare pine
a-b divides obviously both a^n - ba^{n-1} and ab^{n-1} - b^n, so it remains to s...
isnt the question asking to purely use induction? cause this is trivial basically
or am i dumb
wise gate
isnt the question asking to purely use induction? cause this is trivial basicall...
Maybe
But it's weird to ask to prove something using exclusively induction, or any other proof technique
wise gate
You can prove a^{2n} - b^{2n} using induction though
So it you do that then technically you have used induction on n
rare pine
okay, how do i do that😭
rare pine
yeah i do
wise gate
Then you can prove that formula using induction
And substitute n with 2n
Oh but the proof does not use induction over n
rare pine
oh
wise gate
but is there a way to purely do that?
I have no idea sorry
I would say there is not
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woven tusk
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woven tusk
i don’t actually know the steps in order to solve
brave blaze
you know the formula of the standard deviation and the mean
hidden harbor
you have a binomial distribution.
How do you get the standard deviation of a binomial distribution?
woven tusk
uhhhh
woven tusk
you have a binomial distribution.
How do you get the standard deviation of a bin...
i dont know haha
woven tusk
you know the formula of the standard deviation and the mean
its like uhhh
sum of x over n
for mean
and uhhh
for standard dev
its sum of x squared
over n i think
hidden harbor
do you have a textbook to consult for this?
brave blaze
the mean for the binomial distr is E(X) = np
with your p equal to 1/3 here
woven tusk
do you have a textbook to consult for this?
like a formula booklet?
brave blaze
standard deviation is sqrt(E(X²) - (E(X))²) if i remember
hidden harbor
standard deviation is sqrt(E(X²) - (E(X))²) if i remember
much simpler than that, sqrt(npq)
brave blaze
true
hidden harbor
like a formula booklet?
i would expect you to have a textbook with the binomial distribution, or notes from it
anyways, binomial distributions require the number of tries and the probability of success, n and p respectively
and they have the notation B(n, p)
the probability of fail is q=1-p
And like every distribution, it has a mean and std deviation. For the binomial B(n, p), they are:
mean: np
stddev: sqrt(npq)
you're given p, and the standard deviation. Compute n.
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rugged raft
Why is this?
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Why is this?
rugged raft
wdym?
stiff marlin
U was at first integral like three days ago
dusky elk
what are eta and zeta here? just constants such that the equality holds?
rugged raft
what are eta and zeta here? just constants such that the equality holds?
Idk either😿
rugged raft
U was at first integral like three days ago
My learning route is not linear lol
dusky elk
without further info I can't say exactly, but
$\left\vert\int_{x^2+y^2<r^2}cos(x+y)d\sigma\right\vert<\pi{}r^2$
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LayneTheAndroid
umbral dome
is there any further context here?
dusky elk
which tells you that the integral = (something between -1 and 1)*pi*r^2
and anything between -1 and 1 can be represented as cos(theta) for some theta
rugged raft
which tells you that the integral = (something between -1 and 1)*pi*r^2
Wait why?
dusky elk
Like let $I$ be the integral. If you believe the inequality I have above then
$|I|<\pi{}r^2 \Rightarrow{} \frac{|I|}{\pi{}r^2}<1$
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LayneTheAndroid
dusky elk
so I can just write $\frac{|I|}{\pi{r^2}}=\cos(\theta)$ for some theta, i.e this equation has a solution for $\theta$
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LayneTheAndroid
dusky elk
Why is this?
but I don't know if this is what this ^ is getting it or if that is useful for something later
oh it's also just a consequence of the mean value theorem for integrals
actually that would make more sense (although what I did is related to the MVT)
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sharp ruin
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sharp ruin
yes what cpould it be
I had a test
determine if (1,3) (-1,-3) is odd
My answer yes
My teacher's answer
No
He didn't give a graph on the test so I could determine
So I sent him this
He sent me this
And said " if there is one example of disproving your point your point is false"
Note that the given graph wasn't there on the papers
narrow ermine
determine if (1,3) (-1,-3) is odd
What do you mean by (1,3) and (-1,-3) being odd?
You mean to determine whether any function going through (1,3) and (-1,-3) is odd?
sharp ruin
What do you mean by (1,3) and (-1,-3) being odd?
You mean to determine whether ...
Yes
Question number 2 what is true in the following ones
a) if f and G are two then f•g = g•f ( false)
b) (1,3) (-1,-3) is odd
C) (-3,4) (-3,5) has a undefined slope
D) B+C are correct
This is the test question
I chose D) since I thought of many functions like x³ or cubic root of x * 3 or any function
narrow ermine
This is either extremely poorly written or not copied right
sharp ruin
This is either extremely poorly written or not copied right
That's just how it was written
narrow ermine
Regardless, your teacher is right if the meaning is what I said above.
If the claim is that it holds for all functions that go through (1,3) and (-1,-3), a single function for which it works like the one you sent is not enough
sharp ruin
I trasnlated it all correctly
sharp ruin
Regardless, your teacher is right if the meaning is what I said above.
If the c...
And he didn't give a graph or anything so I can judge
Just points
sharp ruin
Regardless, your teacher is right if the meaning is what I said above.
If the c...
It didn't say All
It just said they are in one function
Is it odd?
How am I supposed to know what is that ( one ) function
narrow ermine
If f and g are not explicitly defined then the statement should apply to all choices of them ...
sharp ruin
and like when I asked him why wasn't B correct he sent me this
narrow ermine
I guess it's lost in translation because all of the choices you've written are missing words.
It's not correct because there is a counter example
That is one counter example they sent
There are plenty
sharp ruin
I guess it's lost in translation because all of the choices you've written are m...
Nope 100% correct translation
narrow ermine
Then it was simply poorly written idk what to tell you you're literally missing words
sharp ruin
sharp ruin
Then it was simply poorly written idk what to tell you you're literally missing ...
Ronlarson calculus just sucks
sharp ruin
Idk what to say tbh
These test determine my collage
And they trick us with stupid words
sharp ruin
Ok well those are two very different things in English
Tak in my Language means Odd/ one
One to one or odd
narrow ermine
In general, odd means that f(-x) = - f(x). Like sin(x) for instance is an odd function.
A one-to-one / injective function is such that if f(x) = f(y), then x=y (the function never takes the same value twice)
x^3 is odd, so is cbrt(x), so the function you described is odd.
However, the statement is about an arbitrary function, so if that statement is to be true there cannot be a counter example.
And your teacher provided one counterexample, there are others
sharp ruin
x^3 is odd, so is cbrt(x), so the function you described **is** odd.
However, t...
Yeah my book doesn't talk about these things might be out of it
Anyways I don't care let it be
Thanks for you help
I appreciate it
Have a good night/ day ❤️
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maiden cave
|x-1|+|x+3|=a. Find all values of a, a for which the equation has two roots
I don't really understand how I do these types of problems,can anyone explain?
civic bay
|x-1|+|x+3|=a. Find all values of a, a for which the equation has two roots
I d...
try considering three cases: x < -3, -3 <= x <= 1, and x > 1
in each of these three cases, you can rewrite |x-1| + |x+3| into a simpler form
and you might be able to even sketch a nice graph of it
once you get an idea of what that LHS looks like, it's actually surprisingly easy to find the values of a
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maiden cave
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civic bay
What is a LHS?
left hand side, i'm referring to the expression |x-1| + |x+3|
like the left side of the equation
maiden cave
once you get an idea of what that LHS looks like, it's actually surprisingly eas...
The question is meant to know all a for which the equation has two roots
Not just all a
civic bay
The question is meant to know all a for which the equation has two roots
i know, and once you can kind of get an idea for what the graph looks like, you can find those values of a
where there are two roots
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maiden cave
@civic bay is the answer ∅?
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copper shell
how can i represent this in heaveside function form?
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how can i represent this in heaveside function form?
copper shell
i thought something like
t^4(1-u(t-5)) + (t^4 + 3sin(t/10 - 1/2))(u(t-5)) works but that does not account for the case when t=5
kindred grove
t^4(1-u(t-5)) + (t^4 + 3sin(t/10 - 1/2))(u(t-5)) works but that does not account...
so t^4 + 3sin(t/10 - 1/2) u(t-5)
what's the problem with t=5?
copper shell
so t^4 + 3sin(t/10 - 1/2) u(t-5)
because this is how heaveside function is defined
so like idk what its value is at t = 5
its undefined at t=a right
so wont our ans be undefined if i just sub in t=5
keen vector
h(5) = 625
kindred grove
that's a sloppy definition :/
usually it's defined so that u(0) = 1, but there's a lot of different conventions
copper shell
usually it's defined so that u(0) = 1, but there's a lot of different convention...
which one is generally used for laplace transformation? second shifting theorem
kindred grove
most of the time it doesn't matter anyway
and for laplace transforms it doesn't matter yeah
copper shell
so i can assume this?
kindred grove
if the value of your function changes at one point, it doesn't fundamentally change the result of the Laplace integral
yea
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daring elbow
A manufacturer has determined that the demand for its product is given by
[
p = \sqrt{M - q}
]
where ( M ) represents the maximum units demanded by consumers, and ( q ) is the number of units supplied to the market per month. Find the number of units the manufacturer should produce and sell per month to maximize its revenue, assuming ( M = 453 ).
glossy valveBOT
Mittens
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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 know where to begin
I think that in order to find the revenue I need something else
Can someone please explain me how to solve this kind of problems?
south perch
is there any other parts to the queston?
daring elbow
is there any other parts to the queston?
Nop
glad surge
Do you have an answer key for this?
daring elbow
Do you have an answer key for this?
Finding maxima
But p is a function which returns dollars
slate violet
**Mittens**
is it just setting dp/dq = 0
daring elbow
So if I want to find the number of units the manufacturer should produce and sell per month to maximize its revenue, I shouldn't derive p
slate violet
So if I want to find the number of units the manufacturer should produce and sel...
no you should
if you change q to be a little bit more or a little bit less if you have the maximum profit
the maximum profit should be stable
of course, the minimum profit is also stable
wait ah the revenue is the profit per unit * number of units
daring elbow
OHH
slate violet
so you should be setting $\frac{d}{dq} (pq) = \frac{d}{dq} (\sqrt{M - q} \cdot q) = 0$
glossy valveBOT
southlander!
daring elbow
so you should be setting $\frac{d}{dq} (pq) = \frac{d}{dq} (\sqrt{M - q} \cdot q...
And using M = 453?
slate violet
And using M = 453?
yep!
just sub M = 453 first then differentiate
you will need the product rule, and then the power rule and chain rule
(well the chain rule just makes you multiply by -1, cause d/dq (inside) = d/dq (M - q) = -1)
slate violet
Is the answer q=302?
yep!
yeah actually just using Desmos like I did is nice
cause I don't think the question makes you do the differentiation by hand anyways
slate violet
Could you verify another solution I've got for another problem?
okay
daring elbow
okay
We have a rectangle with a perimeter of 100 centimeters; calculate the base and height that give the figure with the largest area
slate violet
We have a rectangle with a perimeter of 100 centimeters; calculate the base and ...
ah okay
so you want to maximise A = bh
daring elbow
Do you have the answer already? So I can show mine
slate violet
now can you write an expression for the perimeter
slate violet
Do you have the answer already? So I can show mine
yes the largest area will always be a square in fact
so 25 * 25 = 625
daring elbow
now can you write an expression for the perimeter
2x + 2y = 100
slate violet
2x + 2y = 100
cool yeah
and then actually you don't need calculus cause this is a quadratic
you just want to maximise x(50 - x)
daring elbow
we get that y = 50 - x and just relace bot x and 50 - x as the area
slate violet
yeah cool
slate violet
np!
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chilly lark
where did the +1/2 come from?
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where did the +1/2 come from?
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azure stream
hi can someone help me with these questions i don't understand when do we make y=0 or x equal zero
azure stream
sharp lagoon
Use the point slope form.
y - y_1 = m(x - x_1)
So, like: Gradient = -4, point = (-3, 4).
y - 4 = -4(x + 3)
azure stream
i haven't learnt that
i only know how to like use the gradient method and plugging in two points
to the equation
sharp lagoon
What forms have you learned?
You seem to have learned slope-intercept form.
Like y = mx + b.
Have you learned other forms?
sharp lagoon
OK, there are two ways of doing this. You can learn a new form or you can work with slope-intercept form.
Which would you like to do?
azure stream
work with the slope intercept form
sharp lagoon
OK, so you need to know the slope and the intercept.
Slope is just another word for gradient, so you know that.
azure stream
yep
sharp lagoon
So, for intercept, you need to know where it crosses the y axis.
If you look at a graph, the y axis is where x = 0.
azure stream
ohhh okay
sharp lagoon
So, we have gradient = 2 and point = (5, -3).
sharp lagoon
No, we want to make x = 0 because we're looking at the y axis, which is at x = 0.
So, we look at the point.
We have x = 5 and y = -3.
So, we want to move from x = 5 to x = 0.
Does that make sense so far?
azure stream
not rly
sharp lagoon
Which part?
sharp lagoon
No problem.
azure stream
.close
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hard willow
Is there a way to use the law of sines here if there is no perfect match-up with the given sides and angles?
hard willow
all the examples i can find online show a given side and it's corresponding angle, like b and B, unlike this problem where i have to work with three disconnected sides/angles
and since it isn't a right triangle, no pythagorean's theorem
all i can deduce is that A + C = 180 - 75.05
help pls thx
umbral dome
you can use the law of cosines
hard willow
hm ok i'll look into it
should i ping you if i'm still stuck
nvm i can probably take it from here, thx for the pointer
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zenith jacinth
Let (\sim) be an equivalence relation on a set (X.) Show that the equivalence classes (\sim) has the following property: For every (x, y \in X, ; [x] = [y] \iff x \sim y.)
\begin{proof}
Let's prove the forward implication first. We just showed (y \in [y]) but it's given that ([x] = [y],) so (y \in [x].) This means (x \sim y ; \forall ; y \in X) for any given (x.) For the backward implication, take any element (z \in [x].) This implies that (x \sim z) but it's given that (x \sim y \equiv y \sim x.) Using transitivity, (y \sim z.) Therefore (z \in [y]) as well. Similarly, you can show that any element in ([y]) also belongs to ([x].)
\end{proof}
glossy valveBOT
usopper.
zenith jacinth
Does my proof work?
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zenith jacinth
@thick hedge
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eternal stone
Does my proof work?
yes
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slender totem
help me
slender totem
i have no idea where to start learning math
like ik some stuff but how do i learn more stuff?
gritty flax
where did you stop ?
gritty flax
take a look into khan academy
wide wind
Follow the schedule a university in your country goes.
slender totem
take a look into khan academy
what abt for free?
gritty flax
cuz here is not a topic discussion / course, its mostly answering specific questions
gritty flax
what abt for free?
it is
slender totem
Follow the schedule a university in your country goes.
im way too early for a university
wide wind
Then follow a high school, junior high school.
slender totem
got it
gritty flax
you can type .close if you done with this channel
lofty linden
a using namespace std; user
gritty flax
a using namespace std; user
no
slender totem
a using namespace std; user
whats dat
slender totem
do yall mind if i close the chat?
gritty flax
nah close it
slender totem
alr
lofty linden
yeah its resolved
copper shell
for the second part of this question
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for the second part of this question
copper shell
why does the solution set z=0?
proven mango
because the boundary of that hemisphere sphere is just a circle with radius a on the xy plane
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half owl
How would you go about doing this question? when i try it i keep getting stuck on the telescoping sum.
i've already separated the original fraction using partial fractions
gritty rose
try partial fractions
half owl
that's the correct method, but when i tried it i ran into trouble. However I found the solution though. thanks!
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scarlet kiln
i need help in this
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scarlet kiln
well its a limit n goes to infinity
i tried squeez theorm but it didn't work
<@&286206848099549185>
uneven canyon
What was your first step?
scarlet kiln
$\sqrt{2n^4+n^2 } \leq \sqrt{2n^4+k^2\cdot n^2} \leq \sqrt{3n^4}$
glossy valveBOT
AN-602
uneven canyon
Can you see a factor that you can rip out and get on the other side of the summand?
uneven canyon
If you factor out n^4 from the denominator
Sqrt{n^4(2+\frac{k^2}{n^2}}
Then you can pull out n^4 from the square root
Gives 1/n^2 Sum (rest of the equation)
uneven canyon
Perfect exactly
Just need to use transforms to get this into a form we can work with
From there simple u-sub and solve
uneven canyon
No worries! Anything else?
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scarlet kiln
Wait isnt 1/n times the integral
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visual oar
Not sure if this is correct, could someone double check for me
torn jolt
Thats correct
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tardy epoch
idk how to ss on pc but i neeeeeeeeeeeeeeeeeeeeeeeeeeeed help help me
tardy epoch
im doing apex and its having me do geometry instead of personal finance so ive never been taught it
ima take a pic
I need to do 70 questions 😭😭😭😭😭😭
I don’t even know the first one I need explanation
gentle totem
its a vector directed from Q to P, it'll be option A
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limpid scarab
Hi there im insanely confused and need help
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@limpid scarab Has your question been resolved?
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fickle hemlock
i=\log_{b}\left(\int_{r_{1}}^{r_{2}}\int_{r_{1}}^{r_{2}}p\left(x_{1},x_{2}\right)^{2}\ dx_{1}\ dx_{2}\right)
I made an equation that determines the amount of information you can store in a continuous variable (ranged between r1 to r2) with added uncertainty/noise that is determined by the probability distribution p(x1,x2) (p(x1,x2) is equal to the probability density of x1 being the result of the initial x2 after the noise), b is the base (b=2 for bits, b=256 for bytes, b=e for nats, etc.)
Can someone please help check that I did it right?
fickle hemlock
Any information theorists here?
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.reopen
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fickle hemlock
<@&286206848099549185>
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e
fickle hemlock
```i=\log_{b}\left(\int_{r_{1}}^{r_{2}}\int_{r_{1}}^{r_{2}}p\left(x_{1},x_{2}\ri...
question here
It seems to work quite well for the test cases I gave it.
Even used it for silly things.
My friend's pen with a twisty lid can store 5.6 bits according to the equation <:D
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fickle hemlock
e
fickle hemlock
```i=\log_{b}\left(\int_{r_{1}}^{r_{2}}\int_{r_{1}}^{r_{2}}p\left(x_{1},x_{2}\ri...
Question here (again)
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<@&286206848099549185>
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fickle hemlock
<@&286206848099549185>
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fickle hemlock
@winged geyser You're a genius, pls help lol
slate violet
<@207092805644845057> You're a genius, pls help lol
PLEASE don't ping specific people for help
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calm nacelle
If you don't get an answer here, you might try #advanced-stats or #modeling
fickle hemlock
If you don't get an answer here, you might try <#1230103376373743636> or <#10555...
Thanks!
I'm not a uni student though
or someone of that calibre
fickle hemlock
Worth a shot
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austere cove
@fickle hemlock I've not heard of this information measurement before, but it doesn't seem scale invariant. That is to say if you double your measurement numerically, but don't change anything else the information of the variable should not change, yet, if I didn't make a mental math mistake, your information measurement seems to
My understanding is typically the KL divergence is used to measure entropy between continuous variables (and other functions)
fickle hemlock
<@760368177460019240> I've not heard of this information measurement before, but...
No, I tested it, and I don't think it changes with scale
If you mean by changing the range of the continuous variable, it shouldn't.
The probability distribution is normalised, so it cancels out with scale quite nicely.
It's more of a measurement of maximum capacity for information, rather than anything directly related to entropy.
I've given it a few test cases, and it worked nicely!
for me, at least.
austere cove
@fickle hemlock I see, so based on the way you stated it originally, my understanding is each p(x1, c) was normalized and therefore a probability distribution, but there was no reason to believe that the entire function was, as this would require a prior distribution for x2.
Well, if it works empirically, that's certainly not bad.
fickle hemlock
<@760368177460019240> I see, so based on the way you stated it originally, my un...
Yes
gleaming flower
Helo
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fickle hemlock
hello
cedar flint
is your question resolved?
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pure cipher
you'll probably want to use law of cosines
viral jasper
Or just sohcahtoa
pure cipher
oh yeah didnt notice theyd be right triangles lol
gilded apex
Or just sohcahtoa
we didnt learn that yet :
obsidian geode
The distance traveled by bith flights is the same, the second parameter with the direction gives the answer
gilded apex
The distance traveled by bith flights is the same, the second parameter with the...
what is parameter 
viral jasper
we didnt learn that yet :
Do know anything about the terms "sine", "cosine", and "tangent"?
viral jasper
Do you know what an angle is?
gilded apex
yea
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torn jolt
draw a diagram and show us
gilded apex
draw a diagram and show us
how would i draw diagram abt this ? also i dont have any drawing apps on pc :/
torn jolt
how would i draw diagram abt this ? also i dont have any drawing apps on pc :/
ok so
they start at a same point
agree?
gilded apex
ye