🥲
#help-27
tired tendon
strange nimbus
OK, what's the compound interest formula?
tired tendon
A = P(1+r)^t
strange nimbus
OK, that's almost right.
A is the amount in total at that time.
So, it includes the starting amount.
So, like at t = 1, A = 400 + P and at t = 2, A = 432 + (400 + P).
Sorry, one mistake.
tired tendon
I see
strange nimbus
Fixed the mistake.
tired tendon
Alright
cerulean tide
gm
tired tendon
Why do we do A = 432 + (400 + p)?
?
strange nimbus
With the t = 2 equation, yes.
tired tendon
With the t = 2 equation, yes.
Yeah.
strange nimbus
So, we have:
A = P(1 + r)^t
P + 400 = P(1 + r)
P + 400 + 432 = P(1 + r)^2
How can we find out r?
tired tendon
I don't know..
strange nimbus
P + 400 = P(1 + r)
OK, first, get rid of the parentheses.
What do you get from that?
strange nimbus
Right.
tired tendon
400/p = r?
strange nimbus
Right.
tired tendon
I still don't understand how A turned into P + 400
tired tendon
Isn't 400 what we have or is it what we earned on the firsty year?
ah
that would make sense.
strange nimbus
It's the interest we got. Interest is the money we get paid that gets added to our balance.
tired tendon
Yeah, right. My bad.
strange nimbus
So, it gets added to the original amount, P (for 'principal').
So, we got r = 400/P.
tired tendon
Then we sub r?
strange nimbus
P + 832 = P(1 + 400/P)^2
400/r + 832 = 400/r(1 + r)^2
Which one do you want to deal with?
Oh, wait.
Fixed it.
strange nimbus
You're welcome.
tired tendon
I think it's right?
strange nimbus
What did you get?
tired tendon
P = 32 and r = 11.5
strange nimbus
OK, let's try that.
A = P(1 + r)^t
32 + 400 = 32(1 + 11.5)^1
32 + 832 = 32(1 + 11.5)^2
Do both of those come out to something = itself?
strange nimbus
P + 832 = P(1 + 400/P)^2
400/r + 832 = 400/r(1 + r)^2
OK, so let's try the first version here ^
tired tendon
Okay
strange nimbus
P + 832 = P(1 + 400/P)^2
P + 832 = P(1 + 800/P + 160000/P^2)
P + 832 = P + 800 + 160000/P
How can we continue from there?
strange nimbus
OK, take your time.
tired tendon
I'm lost on how we got 832
strange nimbus
It's the total interest we got over two years.
P is the original amount. We added 400 and we added 432.
strange nimbus
No problem.
tired tendon
w3ait
How did we end up going from P + 832 = P(1 + 400/P)^2 to P + 832 = P(1 + 800/P + 160000/P^2)
?
we expanded the exponenet
strange nimbus
Oh, I did the squaring.
tired tendon
Yeah, so we squared 1 + 400/p. Wouldn't that get us 1 + 160000/P^2?
strange nimbus
No, you have to do FOIL or something like that.
tired tendon
What does that mean?
strange nimbus
Well, there's something called Freshman's Dream: [(x + y)^n = x^n + y^n].
woven radishBOT
Chai T. Rex
strange nimbus
But Freshman's Dream is incorrect.
tired tendon
oh
strange nimbus
Instead you have to do: [(x + y)^n = (x + y)(x + y)(x + y)\cdots n \text{ times} \cdots (x + y)]
woven radishBOT
Chai T. Rex
strange nimbus
So, ((x + y)^2 = (x + y)(x + y))
woven radishBOT
Chai T. Rex
strange nimbus
Then the best way of doing that is to use the distributive property.
tired tendon
Oh
Yeah
I didn't forget that. I tried it, but got weird values, so I kind of went atgag
strange nimbus
You do something like this:
[(x + y)(x + y)]
[x(x + y) + y(x + y)]
[x^2 + xy + xy + y^2]
[x^2 + 2xy + y^2]
woven radishBOT
Chai T. Rex
strange nimbus
So, what's (\qty(1 + \frac{400}{p})^2) expand to?
woven radishBOT
Chai T. Rex
strange nimbus
No problem.
strange nimbus
Why do you think P would be 0?
tired tendon
P + 832 = P + 800 + 160,000
strange nimbus
Oh, no, it's (P + 832 = P\qty(1 + \frac{800}{P} + \frac{160000}{P^2})).
woven radishBOT
Chai T. Rex
strange nimbus
And then on the right, you get (P + 800 + \frac{160000}{P}).
woven radishBOT
Chai T. Rex
tired tendon
then what?
strange nimbus
OK, now there's no easy way to solve (P + 832 = P + 800 + \frac{160000}{P}) directly.
woven radishBOT
Chai T. Rex
strange nimbus
But you know how to solve quadratic equations, right?
strange nimbus
OK, so that's almost a quadratic, except one of the terms has a P denominator.
What can you do to (\frac{160000}{P}) to get rid of the denominator?
woven radishBOT
Chai T. Rex
strange nimbus
Right, so multiply both sides by P.
tired tendon
P = 5000
strange nimbus
Right.
tired tendon
400/5000?
strange nimbus
Right, what does that fraction simplify to, or, if you want, what's that in decimal?
strange nimbus
You're welcome, but check your work.
tired tendon
yeah, thanks
strange nimbus
If you have time.
tired tendon
There is another one I need help with, if you don't mind
strange nimbus
That's fine.
strange nimbus
OK, how far have you made it?
strange nimbus
OK, what does it look like with those filled in?
tired tendon
10,000 = 4350(1+0.076/4)^4t
tired tendon
Yeah. I try to expand it, but the numbers come out weird
strange nimbus
OK, you won't be able to expand it because you don't know t.
tired tendon
Yeah
strange nimbus
Like if t was 1 or something, you could expand it.
tired tendon
that's hwat we're looking for
strange nimbus
Right.
tired tendon
cubic root 4?
strange nimbus
Well, those are two things. Cubes are 3D, so cube root is the third root. You'd perhaps want the fourth root, but that won't work here.
tired tendon
That's what I meant. My bad.
strange nimbus
[\log\qty(\frac{200}{87}) = \log\qty(\qty(\frac{1019}{1000})^{4t})]
woven radishBOT
Chai T. Rex
strange nimbus
Do you know the log rules?
tired tendon
noi
It's larihht
I don't need to know how to solve this question anyways
thanks for the help
strange nimbus
No problem.
jolly echo
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lunar nimbus
help
lunar nimbus
I solved this identity and I dont think it is accurate, I think the problem might be written wrong
When I simplify I get 2(cosx) / sin^2x which is not = to 2 csc^2x
winter torrent
,w 1/(1-cos3)-1/(1+cos3)
woven radishBOT
winter torrent
,w 2*csc^2(3)
woven radishBOT
winter torrent
,w 1/(1-cos3)+1/(1+cos3)
woven radishBOT
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sweet ridge
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sweet ridge
if i just prove f(xf(x))=2(x(f(x)) for all x
is that enough to say f(x)=2x
like if i substitute k=xf(x) i get f(k)=2k
<@&286206848099549185>
obsidian harbor
Yes because f is R->R
obsidian harbor
x->0: f(yf(y)+f(0))=2yf(y)
So f(x+f(0))=2x
f(x)=2(x-f(0))
x->0: f(0)=-2f(0), f(0)=0
f(x)=2x
obsidian harbor
but rly thats it??
The range of f(x) is R, xf(x) is included in R, so xf(x) can be domain of f(x)
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restive river
can someone explain to me how the relative freq is calculated here in the example
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can someone explain to me how the relative freq is calculated here in the exampl...
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analog zealot
I want to get better at math I’m doing questions like
2x(4-5z-7+18k-22h) for ex
analog zealot
Combining like terms and distribution
I want to do stuff higher than this I feel I understand it pretty well
toxic grove
What exactly are you trying to do with it?
analog zealot
I was giving the question as an example of what level I am on
But I wanna try to go higher
I used to do like derivitives functions anti derivitives and power rules a while ago but I stopped I found it fun though
toxic grove
My best advice for you is to find probably a pre university textbook on algebra and work through that
toxic grove
I'm sure you can!
analog zealot
I'm sure you can!
Ok
toxic grove
Idk any in particular because it's been a long time since I did that stuff but I'm sure there are loads
On a pdf site somewhere if nothing else
analog zealot
Alright
analog zealot
Also I need some help on this
Could you help me with this
toxic grove
https://archive.org/details/Precalc/page/n17/mode/2up or something like that. It doesn't have any calculus in it but it'll give you a good baseline before getting to that stuff
What do you know about limits?
And what happens when you expand the denominator?
analog zealot
I know that limits are like a number that approaches the number the the arrow is pointing to idk how to explain
But like in the picture
Like x approaches 0
As x approaches 0 and then other stuff
toxic grove
https://archive.org/details/Precalc/page/n17/mode/2up or something like that. It...
https://archive.org/details/edexcel-a-level-pure-mathematics or this for something slightly more advanced, it's hard to tell where you're at
Expand the demoninator. What do you get?
sorry denominator
queen flare
toxic grove
I know that limits are like a number that approaches the number the the arrow is...
Yeah that's more or less what it is, but you should learn about it from first principles before going right into the deep end, if that makes sense
analog zealot
Is it 3? Or no it feels wrong
analog zealot
Figured
toxic grove
What do you get when you expand the denominator?
toxic grove
No
(3x + 1)^2 + 1
Then you can expand that to get (3x + 1)(3x + 1) - 1
Then cross multiply all the terms
analog zealot
So is that 2 putting what’s in the parentheses in them again?
toxic grove
Yes, the 2 means squared
analog zealot
Ah ok
toxic grove
So for example, $3^2$
woven radishBOT
depression
toxic grove
= 9
analog zealot
Yea
toxic grove
I would start with the precalc book if I were you, that's probably around the level you're at
analog zealot
Alright
toxic grove
But to actually answer your question, (3x + 1)^2 = (3x + 1)(3x + 1), then you cross multiply all the terms and you get 9x^2 + 6x + 1
So when you simplify the whole fraction, it becomes
analog zealot
Wouldn’t you combine like terms though?
toxic grove
Yes, there's also a -1 that cancels with the 1, so you're left with 9x^2 + 6x
analog zealot
15x+2?
toxic grove
So when you simplify the whole fraction, it becomes
${2x\over9x^2+6x}$ (hope I got that right lol
woven radishBOT
depression
toxic grove
Yeah if you try plugging a number in, you can see that x is completely different to x^2
Then you can cancel the xs to get $2\over9x+6$, which then equals ${2\over6}={1\over3}$
woven radishBOT
depression
toxic grove
But you should work through that precalc book first because there's a lot of maths going on in the background here
It's not gonna be helpful for you to work through examples like that
analog zealot
Ok
analog zealot
You’re pretty smart lol
analog zealot
Anyway good luck
Ty
toxic grove
Wasted childhood is what it is 🥲
analog zealot
It's great that you want to get back into it though
I find it fascinating math has always been cool to me but ever since I’ve discovered the other universe of math I’ve just started to enjoy it but it makes me less focused on my actual classes because of how boring they are I feel so ahead of everyone that I get distracted easily
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lunar parcel
Find all such pairs of natural numbers m, n such that 7^m - 3*2^n = 1
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Find all such pairs of natural numbers m, n such that 7^m - 3*2^n = 1
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glacial ether
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@glacial ether Has your question been resolved?
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faint gorge
Not really readable especially dark on dark
glacial ether
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faint gorge
You forgot the factor y
glacial ether
Where?
faint gorge
In your integral
woven radishBOT
anti-algebraist 𝔸dωn𝓲²s
faint gorge
but this doesn't seem to integrate nicely
woven radishBOT
anti-algebraist 𝔸dωn𝓲²s
regal grove
is there somone who understand frensh
glacial ether
**anti\-algebraist 𝔸dωn𝓲²s**
okay i will try that
but what am i supposed to do with that indicato funktion
faint gorge
but what am i supposed to do with that indicato funktion
It's just 1 in [0,2] and else 0
glacial ether
how to integrate it
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severe flicker
Determine the point E(t) on the trigonometric circle if for the number t it holds
a) sin t = -1/2(half) and cos t < 0
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Determine the point E(t) on the trigonometric circle if for the number t it hold...
near trout
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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
spring oasis
severe flicker
thanks ;)
livid geyser
Yes lalo!
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timid blade
hello, I really need to solve this infinite series, I can't help myself for two hours is here somebody willing to help me please
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hello, I really need to solve this infinite series, I can't help myself for two ...
slender mirage
hello, I really need to solve this infinite series, I can't help myself for two ...
n-1 = n + 1 - 2
!show
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Show your work, and if possible, explain where you are stuck.
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 begun many times with 3 different approaches but i don't know it's hard for me to simplify it to get the solution
so
step 1.
slender mirage
Step 1. $\sum_{n=1}^{\infty} \frac{(-1)^{n-2}}{n!} - 2\sum_{n=1}^{\infty} \frac{(-1)^{n-2}}{(n+1)!}$
woven radishBOT
Arya
slender mirage
[= 2 + 3\left(\sum_{n=1}^{\infty} \frac{(-1)^n}{n!}\right)]
woven radishBOT
Arya
slender mirage
Can you figure it now? Paranthesis is well known
timid blade
**Arya**
ooh yeah i've seen this step before on almost same math problem but I can't figure out why is there -2
slender mirage
n-1 = n + 1 - 2
.
timid blade
so the -2 stayed and n+1 is cancelled out with the denominator right?
slender mirage
Yes
slender mirage
Can you show which step you're at now, and where are you stuck?
timid blade
to be honest I don't really understand the first step you sent 
i get the -2 but the second sum i don't know where it came from
slender mirage
The first sum is when you isolate n+1 from n+1-2 and cancel (n+1) from both denom and num , the second sum is due to the (-2) that was left isolated in the numerator, which is written in the second sum with denominator as is
@timid blade
timid blade
The first sum is when you isolate n+1 from n+1-2 and cancel (n+1) from both deno...
Like this?
I still cant uderstand why the second sum has the original denominator even tho it was cancelled out
slender mirage
Because you cannot cancel out things like you did in your work
$\frac{x + y}{x} \neq \frac{\cancel{x} + y}{\cancel{x}}$
woven radishBOT
Arya
timid blade
then what i was supposed to do?
i don't know how only the n! can stay in the first sum
then
Is this right?
timid blade
$\frac{x + y}{x} \neq \frac{\cancel{x} + y}{\cancel{x}}$
or better atleast
slender mirage
HuHhhh
woven radishBOT
Arya
Compile Error! Click the 
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(You may edit your message to recompile.)
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gaunt kestrel
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gaunt kestrel
ive got a discrete math problem I don’t know how to finish the induction proof for (problem 6)
the right side is what i have so far
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gaunt kestrel
<@&286206848099549185>
If k+1 doesnt exist in the subset then there are k elements of the {1,2,…,2k} set in it. Which is just under the requirement for having a sure duo of integers where one divided the other
uneven talon
If k+1 doesnt exist in the subset then there are k elements of the {1,2,…,2k} se...
I don't think that's true
Even if k+1 is not in the subset, that subset can still have k+1 elements
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jovial wing
Please help me
devout snowBOT
Please help me
jovial wing
I don’t know the last 2 digits of this numerical response
Apparently my answer is wrong
supple knot
how did you get your answer
jovial wing
Like it’s 8 units long
supple knot
where does 8 come from
jovial wing
To find b
f(x) compressed into g(x)
Mapping notation:
f(x):(x,y) —> g(x):((6/8) x , y)
Y = a f[(1/b)(x-c)]+d
So 6/8 —> 8/6
8/6 =1.333
supple knot
are you saying b = 1.3, rounded?
supple knot
does the point 12 map to 9 under multiplication by 8/6 ?
because you're saying 12 maps to 9 using these two points
jovial wing
No but that’s cause there’s a horizontal shift
f(x) moves 1 unit left
Then compresses
supple knot
there's no horizontal shifting here
jovial wing
But it didn’t ask for it, so how would it move back by 1 unit left?
supple knot
g(x) is a horizontal compression/stretch and a vertical compression/stretch of f(x)
supple knot
But it didn’t ask for it, so how would it move back by 1 unit left?
i don't know why you're asking this question
jovial wing
What
I’m trying to say that it had a horizontal shift but the question didn’t ask for it
The real answer of this question is 1408
It’s tryna say that b = 0.8, which is rounded from 0.75
0.75 = 6/8
Why is b reciprocated
supple knot
x = 12 gets mapped to 9 under b * x. what's b?
jovial wing
6/8
supple knot
I’m trying to say that it had a horizontal shift but the question didn’t ask for...
there is no horizontal shift. there's horizontal compression
supple knot
f(x) compressed into g(x)
you even said that here
jovial wing
Ok
Ok
Ik
But what I meant is
In general formula for this you would write it as
Y = a f[(1/b)(x-c)]+d
In mapping coordinates
supple knot
that's completely irrelevant to this problem
supple knot
jovial wing
Previous question had same formula
But my answer is right here, I checked
I did the same thing
jovial wing
Ok but for the question I just showed
The graph f(x) stretches by 3/2 to become g(x)
In mapping notation:
(x,y) —> ( (3/2) x, y)
General mapping notation:
(x,y) —> (bx + c, ay + d)
General term for f(x):
Y = a f[(1/b)(x-c)]+d
So because b turns into 1/b in the general formula
3/2 becomes 2/3 in the equation
g(x) = af( (2/3)x)
b = 2/3
In for p/q, it is 2/3
So p and a respectively are 2 and 3
That’s why it is 1 2 2 3
Same logic applied to the initial question should make b = 8/6 =1.333
supple knot
b=2/3 is incorrect
supple knot
But my answer is right here, I checked
show where it says 1223 is correct
jovial wing
supple knot
-6 gets mapped to -6 * 2 / 3 = -4 so that's wrong
jovial wing
The answer sheet is wrong?
jovial wing
Then I am confused why my teacher made this
supple knot
teachers make mistakes
jovial wing
Yeah I see
supple knot
23 is 32 backwards
livid geyser
Love your Pieck pfp. Here's an image for when you get the right answer.
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solid osprey
bruh
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stable orchid
yoo
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stable orchid
Oh alr
knotty sage
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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
1
knotty sage
how would I do that exactly?
you could multiply (x+1) to both sides does the same thing
latent quarry
Let me write it
latent quarry
So 7 > 7(x+1)
stable orchid
Ok
Alr I'll just use the = sign instead of this >
And then just switch it for the answer at the end
So now what?
7 = 7x + 7?
X = 7/7?
X = 1?
x > 1?
latent quarry
7 = 7x + 7?
It should be 7-7=7x
0>7x
X<0
But
We should remember that there is x+1
Meaning if we plug x =-1
We can't divide 7 by 0
stable orchid
Ahh ok
latent quarry
And if we try to input smaller negative number like -2
7/(-2+1)>7
It doesn't met the equation
stable orchid
Yea true
latent quarry
So the answer is -1 < x <0
latent quarry
Factor the top and bottom first right?
Yep
stable orchid
(x-5)(x+9)/(x-4)(2x+3) < 0
stable orchid
Wdym multiply it with 0?
latent quarry
(X+9)(x-5) < 0
stable orchid
Alr
latent quarry
See now we have (x+9)(x-5) < 0
stable orchid
Mhm so we always get rid of the bottom?
What's the point of even doing it then if we're just gonna get rid of it lmao
latent quarry
See now we have (x+9)(x-5) < 0
Good way to visualize this equation is by drawing a graph
See when -9< x <5 the value was smaller then zero
stable orchid
How is 5 smaller than 0?
latent quarry
Do you understand about quadratic equation
What I mean here is if -9<x<5
When we plug it into (x+9)(x-5)
We will have value less than zero
Try it
If we plug 3 or 2 or -1 the value would be < 0
stable orchid
Ohhh
So if we plug in -9 as x or 5 as x we will have a value less than 0
Or + 9, and -5
What do we do now?
I understand the steps up to here
latent quarry
Alr now we just need to find the restriction with the bottom part
(2x+3)(x-4)
First we can't have -3/2, 4
stable orchid
yea ik that
latent quarry
Not only that if we observer the equation
If -3/2<X<4
The value of the bottom part will be negative
While the value of the upper part will also be negative
Creating a positive number
So we can't have the entire -3/2 < x < 4
latent quarry
So if both top and bottom are negative
Let me recap
The first range of number to meet the equation is
latent quarry
See when -9< x <5 the value was smaller then zero
.
stable orchid
Ok
latent quarry
So we can't have the entire -3/2 < x < 4
Next we discover that we also can't have -3/2 < x < 4 to meet the equation
So we are left with the answer
-9 < x <-3/2
And 4<x<5
stable orchid
That's the final answer
b)
And then I do the same thing for c right?
I multiply it by x+7 and x + 3? Or?
Thanks for ur help tho I really appreciate it
latent quarry
Cross multiply
stable orchid
latent quarry
Alr
stable orchid
Thanks man
latent quarry
First multiply 2x-1)(x+3)
Then multiply x+1)(x+7)
If you do it correctly we will have
(2x-1)(x+3) < (x+1)(x+7)
latent quarry
Then we just expand
Yes
stable orchid
2x² + 6x - 1x etc
latent quarry
2x² + 6x - 1x etc
5x
latent quarry
Yeah
stable orchid
Let's say on the other side we get
3x² + 7 - 3 we'd add 3, -7, and -3x² on that side and the left side
Right?
Then after that? Idk what I'd do
latent quarry
Yes
stable orchid
List restrictions or
stable orchid
I see
latent quarry
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fervent terrace
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fervent terrace
for this question how did the calculate the probability distribution? i listed outcome and assigned some probablities but it's not right
outcomes {TTT, TTH, THT, HTT, THH, HHT, HTH, HHH}
so for the outcome where i land zero heads 1/8
vast rain
it's not 1/8
fervent terrace
buts that's clearly not the probability
vast rain
the probability of obtaining a head on any single toss is 0.6
fervent terrace
yeah idk how to factor that in
vast rain
if the probability of obtaining a head on any single toss is 0.99999
what do you think the probability of the outcome where you land zero heads is approximately?
vast rain
so the probability of getting a head on a single toss affects how you calculate the probability for the outcomes, yeah?
well how did you get 1/8
fervent terrace
yeah for sure
i just took the number of outcomes that did have zero head and divided it by the total number of possible outcomes
vast rain
oh yeah that only works if all of the outcomes are equally likely
fervent terrace
yeah thats what i was thinking
vast rain
okay suppose that you repeat 1000 times this experiment of flipping the coin 3 times
how many trials do you expect the first flip to be tails, if the probability of flipping heads is 0.6?
vast rain
first flip to be tails
If I tell you that you flip heads 60% of the time, in how many experiments roughly do you expect to have the first flip be tails?
fervent terrace
oh yeah 60% of them
vast rain
no
fervent terrace
damn
fervent terrace
oh my bad
i thought you asked about heads
i just looked now it was ab tails
soz
vast rain
suppose you continue each of those experiments
how many experiments do you expect to have the second flip be tails after flipping the first as tails
vast rain
suppose we're playing squid game and all of the people who didn't flip tails on the first flip are eliminated
fervent terrace
nice okay
vast rain
now what if I ask you about how many are expected to flip heads the third time after flipping tails the first and second times?
fervent terrace
ohh.... 0.4x0.4x0.6?
fervent terrace
okay cool sorry i was forgetful of the other stuff i learned
thanks for your help and patience!
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tacit horizon
can someone tell me how to calculate this rq
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can someone tell me how to calculate this rq
tacit horizon
can i do it like this just like i calculate other cross products or is this illegal
dense jay
sure
[dy(z)-dz(0) , -(dx(z)-dz(xy^2) , dx(0)-dy(xy^2) ]
only issue might be you could have been missing the - on the second entry
and the end result is also a vector
tacit horizon
sure
[dy(z)-dz(0) , -(dx(z)-dz(xy^2) , dx(0)-dy(xy^2) ]
only issue might be yo...
Minus on the second entry?
My result would be (0, 0, -2xy)
Is that wrong or
dense jay
thats fine, im just saying the middle entry would have a minus on it, which i couldnt tell if you would do or not because 0-0 =-(0-0)=0, so i have no way of knowing
tacit horizon
thats fine, im just saying the middle entry would have a minus on it, which i co...
Okay i see
I think we used to build a whole damn matrix to calculate this
But if that works too? Thats much easier
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hollow flare
integrate J4(x) wrt x
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integrate J4(x) wrt x
frozen aurora
what is J4(x) ?
frozen aurora
,w integral J_4(x)
woven radishBOT
hollow flare
whats F?
frozen aurora
$_1 F_2$ is the hypergeometric function
woven radishBOT
artemetra
hollow flare
?
i dont understand
could someone help me manually?
i am sorry to ping you but could you explain further
@frozen aurora
<@&286206848099549185>
tardy edge
it probably stands for the generalized hypergeometric function in the form of $_pF_q$
woven radishBOT
alex <3
hollow flare
what is hyper geometric function
tardy edge
i think you could also try without that function
wolfram alpha likes to go extra
Integral of Bessel Function is usually in the form like this.
hollow flare
The answer is supposed to be in terms of bessels
our teacher ain't responding after looking at the question
hollow flare
tried it
doesnt work
The question is
Integrate J4(x) wrt x
where Jn(x) is bessels function
<@&286206848099549185>
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hollow flare
,w integral J_4(x)
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unborn atlas
Can anyone explain what the Chirp Z-Transform is? I'm pretty confued and don't get its connection to the Z-Transform
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unborn atlas
@dire forge (if youre available)
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dire forge
Can anyone explain what the Chirp Z-Transform is? I'm pretty confued and don't g...
Do you have any specific questions about it? It's basically just a discrete-frequency version of the z-transform
Instead of having a function of continuous z, you have a vector, and each entry of the vector corresponds to a specific value of z (the frequency/growth variable)
unborn atlas
Could you give an example maybe? I don’t see how I’m descritizing an already discrete transform
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hollow glacier
Are these correct?
unreal stone
<@&286206848099549185>
I’d be dammed if I can read ur writing
This wrong
+3
Also wrong
3 x 1 = 3
Not 1
unreal stone
Isn’t it +6-3?
Yeas
Yes..
Thats positive 3
Not negative 3
You wrote negative
I think you know how to do it but just some minora alegbra things
hollow glacier
Ya I tend to make some careless mistakes here and there
That’s why I get it checked
unreal stone
It’s fine just have a look over it again.. I’ve only checked two of the photos you’ve sent
hollow glacier
Which two photos did you check so that I can check the other two
hollow glacier
So you’ve checked the last two photos?
unreal stone
Yeah
zenith whale
if f(x)=-5+x^2 what is f(x+1)? ive got -5(x+1)^2 so far
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if f(x)=-5+x^2 what is f(x+1)? ive got -5(x+1)^2 so far
drifting hearth
if f(x)=-5+x^2 what is f(x+1)? ive got -5(x+1)^2 so far
you mean -5+(x+1)^2?
zenith whale
you mean -5+(x+1)^2?
yeah
drifting hearth
that’s technically correct
you could simplify by expanding (x+1)^2
but that’s about it
zenith whale
yeah thats what im wondering idk how to simplify that
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silk flicker
question: glenn is basketballer, she scores 7 out of 10 shots arthur questions if she is right and is saying she wont even hit 60% of shots, they take a bet and out of 21 shots ans she wins if she hits more then 60%. question a solved: what percentage of bets does she win. answer 84% question B UNSOLVED : now they play a bet in which glenn takes 84 shots. calculate how much more probable it is that glenn wins instead of arthur
silk flicker
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misty granite
indigo horizon
The following image appeared in a newspaper in 1979. What is missing from the image from a statistical perspective?
Title of the chart: “Purchasing Power of Wage Rates Compared to 100 in September 1978.”
X-axis labels; months.
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lethal pollen
*The following image appeared in a newspaper in 1979. What is missing from the i...
I think it's the fact it doesn't start from 0
indigo horizon
Nah
lethal pollen
Rip
indigo horizon
This server is so trash
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carmine hollow
(this is roughly translated) Two slanted lines come out from a point that is 2 sqrt(6) away from the plane. Two slanted lines make 90 degrees with each other, and 45, 30 degrees with the plane. find x
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(this is roughly translated) Two slanted lines come out from a point that is 2 s...
carmine hollow
I came up with something like this
polar chasm
I came up with something like this
notice that x is a hypotenuse of the right triangle lying in the plane
polar chasm
this one
polar chasm
So we can draw a right triangle right
carmine hollow
oh yea
polar chasm
and yeah, you could think of it seperately
but firstly, you'll need to compute its other sides
(the legs)
and then you can compute x using pythagorean theorem
polar chasm
yeah, in the blue one we know that there is 30° angle, 90° angle and so the last one must surely be 60°
because they have to sum up to 180°
carmine hollow
yea that makes sense, got kind of confused since it's the first time i'm dealing with such figure
I get something like this for some reason
on the left triangle
k/2 = 2 sqrt(6)
k = 4 sqrt(6)
then I solve for k * sqrt(3)
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mystic flicker
I need to find the area of this ..
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I need to find the area of this ..
misty crest
granite kayak
Integration ?
mystic flicker
Integration ?
yes
granite kayak
Isnt it the same as integration-1 to 0 of the same fonction
mystic flicker
my brain does not understand this so i don’t even know how to start trying it
ebon sage
mystic flicker
whats that?
mystic flicker
haha its okay
ancient sluice
haha its okay
Find the area by integration !
Area of rect - area of the curve x³+1 from 0 to 1 along x axis
mystic flicker
i read the problem a bit more and it is asking which of those variants below is the right way to find the area
um what..?
ancient sluice
I mean you can just integrate and find out, which matches the answer !
granite kayak
One by one
And compare
granite kayak
3/4
ancient sluice
= 3/4
ebon sage
None of the above !
Thank you
ancient sluice
I need to find the area of this ..
ancient sluice
Area of rectangle - shaded area
ebon sage
Hey did you understand why?
Because of 5,5?
granite kayak
Isnt it the same as integration-1 to 0 of the same fonction
Or this
@ancient sluice
potent tusk
you integrate this part than you subtract the other part
ancient sluice
Because of 5,5?
It's not transitive because, we have (1,3) and (3,1) but not (1,1)
Clearly not reflexive, because its missing (1,1)(3,3)(7,7)
And it's neither symmetric because it has (5,7) but not (7,5)
ebon sage
It's not transitive because, we have (1,3) and (3,1) but not (1,1)
Clearly not r...
Okay, you’re explaining it well
I understand it so much better now
ancient sluice
you integrate this part than you subtract the other part
Else you can also just integrate along y axis !
granite kayak
you integrate this part than you subtract the other part
Or -1 to 0
potent tusk
-1 to 0 is clever
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quick peak
$\ddot \theta + 2 \beta \dot \theta + \beta^2 \theta = 0
\ \theta (t) = (A+Bt) e^{-\beta t}$
woven radishBOT
Hamdy Hisham
quick peak
This solution is wrong ?
mystic goblet
I can’t figure this out, the answer key said 5, but I got 5.18 and there’s nothing about rounding
quick peak
hey
quick peak
np
quick peak
<@&268886789983436800>
quick peak
idk why this channel isnt opening
all of them are this way
solar goblet
because HGF and FGE are similar triangles, you can easily calculate GF
that's a place to start
mystic goblet
I been trying to find GF but it’s hard missing other sides and angles
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lavish canopy
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restive river
if the formula for population variance is related to the parallel axis theorem, and varience is the second moment about the mean, then does the variance have anything to do with reimann sums and normalpdf?
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restive river
if the formula for population variance is related to the parallel axis theorem, and varience is the second moment about the mean, then does the variance have anything to do with reimann sums and normalpdf?
lucid idol
Variance, Riemann sums, and the normal probability density function (normalpdf) are all related concepts in statistics and calculus, but they connect in different ways. Let's break it down:
-
Variance and Moments:
- Variance is indeed the second moment about the mean. It measures how much the values in a dataset deviate from the mean.
- The formula for population variance is σ² = Σ(xᵢ - μ)² / N, where xᵢ are the data points, μ is the mean, and N is the number of data points.
-
Parallel Axis Theorem:
- The parallel axis theorem is used in physics to compute the moment of inertia of a body about any axis, given the moment of inertia about a parallel axis through the center of mass and the distance between the axes. In statistics, this is analogous to shifting the origin to the mean when calculating variance.
-
Riemann Sums:
- Riemann sums are used to approximate the area under a curve, which is fundamental in integral calculus. When calculating variance for a continuous random variable, integrals (which can be approximated by Riemann sums) are used to find the expected value (mean) and the expected value of the squared deviations from the mean.
-
Normalpdf:
- The normal probability density function (normalpdf) describes the distribution of a continuous random variable that follows a normal distribution. The variance (σ²) is a key parameter of the normal distribution, influencing its spread.
To summarize, variance connects to Riemann sums when dealing with continuous data, as integrals (approximated by Riemann sums) are used to calculate it. Variance is also a critical parameter in the normalpdf, determining the spread of the normal distribution. While these concepts are interconnected in the broader context of statistics and calculus, they serve different purposes in their specific applications.
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high knot
I don't understand how I can prove these 3 rules
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I don't understand how I can prove these 3 rules
fossil locust
I don't understand how I can prove these 3 rules
try simplifying $b^{\log_b (RS)}$ and $b^{\log_b R + \log_b S}$
woven radishBOT
south
fossil locust
and then showing these will be equal
(if b is not equal to 1, b^x will be a one-to-one function, so b^x = b^y implies x = y)
high knot
**south**
so b^logb will cancel so basically (RS) = R + S
is that enough to prove the rule?
fossil locust
so b^logb will cancel so basically (RS) = R + S
yes, RS = R * S
fossil locust
(if b is not equal to 1, b^x will be a one-to-one function, so b^x = b^y implies...
this is sufficient due to this
high knot
yes, RS = R * S
so we can say x = logbR and y = logbS
And if we do B^x = R (cuz the b and logb will cancel) and B^y = S (for the same rzn)
We get Rs = b^x + b^y