/sci/ - Science & Math

>>7541036
Yes

>>7541036
No

>>7541036
Depends

So, PhD students, how does it feel to be a hivemind?

>>7541036
How do I get my website to appear first or closer to first on google?

>>7541394
Search algorithm optimization. Do not pay anyone or for any service that claims they can help you. It is never worth the cost or is a straight up scam/lie/over exaggeration.

>>7541394
create lots of pages that link to your website.
Or pay google.

>>7541394
Damn, Germany really got cucked over the years.

>>7541036
Yes

I think I'm addicted to massage parlors. I essentially can't stop going and I have to go at least once a month. How do I stop? I don't want to waste 160 a month with a chance of getting caught by the police. Plus, I went today and the condom broke while I was fucking her, so I may even have a disease now.

>>7541036
"Show that it is valid to refute a disjunction p ∨ q by separately refuting p and q provided p and q have no free variables in common."

Isn't the proof for this at the basic level just showing that (∀x, y. P(x) ∨ Q(y)) ↔ ((∀x. P(x)) ∨ (∀y. Q(y)))? Or am I understanding something wrong?

Am I right in thinking the answer is d?

>>7542967
Scratch that, there's a lot of context which is needed to answer if I think about it a bit more.

>>7542975
you are right.
they're not even homogeneous to a distance.
a) is homoegeneous to d*t
b) is hom. to d^2/t
c) is hom. to t*d

>>7541036

can someone explain OP's picture?

>>7542979
Yea, I was thinking the correct answer would be <div class="math">\int_{t1}^{t2} v(t)dt</div>

>>7542982
It was a joke reply to some pathetic thread of someone who couldn't do their own high school homework.
The red in the numerator disguises a minus to look like a plus and trivialize the problem and the text mocks the tried-and-true clickbait banner ads that were rampant before adblock.

>>7542985
this is one of the correct possibilities indeed.

Can someone here prove B identity?
I'm having trouble with it

>>7543013
Great handwriting, anon

>>7543013
https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities

>>7543013
develop everything in term of sin(theta) and cos(theta)
then use t= tan(theta/2)
sin(theta) = (2t)/(1+t^2)
cos(theta) = (1-t^2)/(1+t^2).

the whole thing will simplify to 1/t = cot(theta/2).

>>7543084
I know all these by heart man, I've twisted and turned it in every form I could but couldn't do it. The teacher also said it's supposed to be a five step answer, so maybe it's a very simple concept that I'm overlooking

>>7543094
Did you use the sum-to-product formulas? That's literally all there is to the problem.

>>7543091
Thanks for the hint, trying it out right now

>>7543102
I did. It expands to a humongous expression, but it does not simplify to cot(theta/2)

>>7543013
>tfw my handwriting is so bad I can't read it sometimes
You make me jealous

>>7542975
Same anon again, can anybody help me understand the answer to this question? I thought it would've been a, because when h is much smaller than x <div class="math">\frac{1}{x-h}- \frac{1}{x+h} \approx \frac{1}{x}- \frac{1}{x}=0</div>

I don't know what the correct answer is, just that the answer I chose based on that logic was wrong. It's really bugging me because it's the only question I got wrong

>>7543033
>>7543159
thanks fam. have to have clear hand writing when solving identities.

post yours

>>7543185
It's c.
Zero might be a decent approximation, but c is better. Try expanding the expression in h, then discard all terms h^2 or higher, since the square of a very small thing is so small it's as good as dead.

>>7543216
Ah, that makes sense. Should have spent more time finding other ways to approximate the value rather than just going for the first I thought of.

HEEELP
Can someone explain me how this came to be by solving it step by step?

>>7543125
did it work anon ?

>>7543252

>>7543216
>Zero might be a decent approximation
zero is a horrendous approximation to anything non zero

Argh, just told me that I couldn't say that I liked her more than math or math more than her and now she's being a damn pain...
Not a stupid question, I just have no one to rant about this shit with. If I really need a question... is this normal?

>>7543809
me=my girlfriend...
Oh well...

>>7541036
What is the difference between courses titled "modern analysis" and "real analysis"?

>>7543185
I saw the expression and immediately thought of the definition of the derivative.

>>7543252
Using a strong base on a tertiary amine leads to an E2 reaction. Removal of the proton will from a double bond and "kick out" chloride. The Zaitzev product will be the more substituted product that is possible.

>>7543809
That's some serious love for mathematics, I'd say it's better than normal.

>>7543809
>>7544065
pic related

>>7544018
>What is the difference between courses titled "modern analysis" and "real analysis"?
Whatever the course catalog for your university and the professor teaching the course says.

A class called "real analysis" can be anything from a sophomore/junior class that introduces undergrads to proofs to a graduate-level measure theory class. So there isn't really a quick-and-easy answer to your question.

>>7544040
Okay. This makes sense.
Can you explain me pic related, too?

>tfw I have an exam on Thursday, not on next week tuesday.
;_;

Does a helicopter rising at a constant rate exert more force on the air than one hovering in place?

>>7544120
Yes, and as a result winds will be stronger below a rising helicopter than winds below a hovering helicopter.

>>7543809
Its fine to love one more than the other - but you gotta pick one. Tell her that both of you are a part of who you are. Losing her would devastate you. Same with losing math. But if you had to pick one, it would be her.

>>7543013

First, note the angle addition and subtraction formulas for sine:

sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
sin(a-b) = sin(a)cos(b) - sin(b)cos(a)

Adding these two equations gives

2sin(a)cos(b) = sin(a-b) + sin(a+b) (*)


Next, note the corresponding formulas for cosine:

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

Subtract the former from the latter to get

2sin(a)sin(b) = cos(a-b) - cos(a+b) (**)


Now divide (*) by (**) to get

cos(b)/sin(b) = [sin(a-b) + sin(a+b)]/[cos(a-b) - cos(a+b)]

Finally set a=5t/2 and b=t/2.

>>7544124
But why, if its net acceleration is still zero?

>>7544120

F_total = ma. In both cases a = 0.

Therefore F_total = +F_air - F_gravity = 0.

Since F_gravity is the same (assuming constant gravitation field, which is actually false) then F_air is the same.

>>7544162

Of course, if you wanna be a dick, you can say that there is frictional air drag on the moving helicopter or the earth is a sphere. These have opposite effects.

Would studying category theory before learning how to program make the latter easier in any way? I've had a bit of math, but am a total pleb when it comes to computers and tech.I have all of the prerequisite courses to take an introductory course in category theory. I would like to eventually learn both, but I only have time to study one at the moment. Also, what do you recommend as a first language for someone in my position? When/where will I get to start using some of the cool math I've learned (linear algebra, discrete, multivariable calculus, abstract algebra)?

I need advice:
I want to use retard ritalin every sunday while reviewing and working on subjects.
Does the tunnel vision permit more subjects per session?
Can I change from mathematics to chemistry?
I am a 80/20 guy, how disciplined do I have to be to not get addicted to it?
How long does it take to leave the body and rebalance the brain chemistry after a small dose of retard ritalin?

>>7541036

Is it even possible to take notes from a math book without writing almost the whole thing down?

I'm broke and read from ebooks but at this point it might be better to just buy the paper edition so I can quickly scroll through when revising.

>>7544079
1 and 3 are exactly the same compound.
2 is the more substituted (Zaitsev) product

>>7544079
Give the IUPAC name of the three compounds, you'll see then. And 2 is the major product.

>>7544203
Buy a duplex printer with refillable cartridges.
Then send the paper to a printing service,
They will bind them into a book.
Costs no more than 1/4 to 1/20 of the original book or bought pdf.

Best would be a duplex laserprinter though.

The printing service can print and bind it for you, too.

>>7544065
>>7544067
>>7544129
I'm genuinely surprised at the replies...
I meant if the reaction was normal, nor if it was normal for me. I'd assume it would be a normal thing here. Hell, I'm not even that hardworking. But it's like asking if you love your wife or God to a religious person. Math is too big... It's special. It's above all of us, it's an omnipresent, timeless, deep truth... Even more closer to the real world than physics...

>>7544180
Category theory is very dry, and you will not enjoy it if you're learning it to help program better, especially having not ever programmed. It will not make you a better programmer, either.

>>7544203
Make a skeleton of the chapter and leave almost all I the examples out. Include one hard example per formula.
Now you have awesome notes that is also an awesome study guide

>>7544576
>leaving out examples
Personally, I'd recommend against doing this. Keep a separate work book where you go through all the worked examples. They're a really good way to understand the topic, since they're typically harder examples

Why do CSUs accept c++, but do not accept java? You would think they would accept c++ and java.

Chances of getting into a california CSU with just Physics I? I mean, can't I just take Physics II in the CSU?

>>7545292
california csu's are piss easy to get into. you literally need a 3.0gpa; you can get in with a 2.0 provided your sat/act are high enough, with that said it all depends on your major


Also can someone explain this to me??

Alright here's a very stupid question:

Assume you have pic related. Tank on the left has infinite water supply so no worries about that, tank in the middle is still not filled up but the water level is high enough for it to spill into the tank on the right.

Now question is, for the purpose of height calculation (and from that, flow rate) between middle tank and right tank, is the height I should account for h, or h2? I mean the water in middle tank is still rising, but on the other hand it is directly connected to the left tank. I know pressure should be distributed equally inside a continuous liquid body but it feels off.

I feel fucking ashamed not to know the answer but I never really thought about this.

Could someone please help me with solving recurrences?

Here I have this recurrence:
T(1) = w
T(n) = y + T(n - 1)

I don't really know how to solve this, but I do know that this has to do with some kind of recursion or something. So let's pretend we have a bunch of calls on the stack and work our way up.

If T(1) = w
then T(2) = y + T(2 - 1) which we already solved as w, so T(2) = y + w
so then T(3) = y + T(3 - 2) which we already solved as y + w, so T(3) = y + y + w, so T(3) = 2y + w
so then T(4) = 3y + w
so then T(5) = 4y + w
so then T(6) = 5y + w
Now since we have a pattern here, we notice that our coefficient for y is always (n - 1). And w stays the same. So based on the pattern we noticed, is it true that for T(n) = y + T(n-1), that T(n) = O(n) since y is always going to have a linear relationship wrt. n?

Thank you so much in advance. Not asking anyone to solve this for me, but please just tell me if I'm on the right track or not.

>>7546303
Apply Bernoulli's equation for energy through a flow line between left and middle, then between right and middle. Notice anything?

The fuck am I doing wrong?

>>7547378
You've got some awful handwritting

How can one learn more about biology and transhumanism when it took them three years to pass high school geometry?

Anyone have those feels when you're so close to transferring, but realize you're so far?

Classes I'm taking:
Differential Equations
English - Critical Thinking (GE)
Java
Interpersonal Communication

Classes I still need if I pass above classes:
Physics I
Physics II
Area E (Lifelong learning and self-Development) class for CSU in California
C++(CSUs want this instead of Java)
History
Chemistry 101
Biology class

Spring Semester plan:
Physics I
History
Chemistry
Biology
C++/Area E

I don't even know if I should bother trying to apply at a school when I need so many. Should I bother?

>>7547424
even programs which are usually prereq heavy (e.g. engineering) don't give a fuck at CSU, just do your gen ed's and a few core classes and assuming you have above a 2.0 you'll get into most CSU's as a junior, above a 3.0 and basically every CSU

ffs

>>7547424
I feel your pain. I should have just went into CSU directly after high school. But I didn't know what I was going to do and didnt wanna waste money. I regret it. I got accepted into CSUF in high school.

>>7544018
Real Analysis is the study of functions over the reals

Modern Analysis is the study of functions over the moderns

I really don't see the confusion tbh

>>7547433

I currently have a 3.662 GPA. Who know after this semester.

how do I fix my brain so that I'm actually motivated to fix my life?

>>7547424
U wot m8? Are you a freshman placed in Diff?

>>7547445
just condense it down so that you're only there for 2 years
get in contact with advisors at schools you wish to transfer to and ask which specific courses you should prioritize (assist.org doesn't tell you everything)
it's not like you're trying to get into stanford
anything more than 2 years of CC to get into a CSU is ridiculous (assuming full time student)

>>7547452

No, I started off in Elementary Algebra. I also started in a remedial course for English.

If I get accepted to UCI via TAG and I don't finish the requirements in time before I transfer will they rescind my admission? Also can I re-TAG and still have a higher chance of getting accepted if it gets rescinded?

>>7541036
IF I PULL THAT OFF, WILL YOU DIE?

>>7547522
No. You'll have to finish shit there instead.

>>7547544
Oh really thats a relief. I don't want to be stuck at CC for another year.

>>7547424
Im not sure for CSUs but some transfers at my UC went in with an incomplete IGETC. No biggy for them, especially since you still need to upper division courses regardless of complete IGETC.

What CSU are you planning for?

>>7547559
oh I'm glad you can go in without a complete IGETC.

What are some good ways to see if a function (multidimensional) is Lipschitz continuous? I need it, so that I can apply Picard-Lindelöf or Peano.

i just started my research position yesterday but i also just caught a cold/the flu.

would it be better for me to stay home and rest and reduce the risk of getting others sick, or should i go to the research lab today and tomorrow, even if im sick to show that im not a slacker?

>>7547559
Csu long beach, Sdsu, and Pomona since they are and hour and a half or less away from my house. Computer engineering major.

>>7547817
buy a mask and go to work and you'll achieve both.

I'm taking an intro class to algebraic structures and the book we're using isn't as precise as I would like.

Is this true in general? If a binary operation * on a set S is a function, *:SxS->S, then would *, as a set, be

* = { ( (x,y), z) ∈ (SxS)xS | ∀(x,y)∈ SxS ∃! z∈S, where ((x,y), z) ∈ (SxS)xS }

From the definition of a function this must be correct (right?). When would defining an operation like this be useful?

One more quick question for the ambitious anon, if we were to define an operation on a set as above, could the commutative property be defined as:

∀(x,y),(y,x)∈ SxS, ((x,y),z),((y,x),z)∈*

>>7548216
whoops, when defining * as a set, at the end it should say "where ((x,y), z) ∈ *}"

>>7548216
(x,y), z) ∈ (SxS)xS
Is that notation normal?

2nd question, weird punctuation but that's correct.

1st one. That looks really circular. If you're defining Set * from *, then use *, not that circularity. If you're defining what a binary operation is, then you're not talking about a single concrete *.

PS: I just started group theory, don't trust me, but whatever the case I certainly do not trust you.

>>7548216
>then would *, as a set, be
* is an operation, not a set. It doesn't have elements.

>>7548407
He said "AS A SET WOULD BE", it's a hypothetical. I understood that he meant the set *' equal to {((x,y),z) in (SxS)xS| x*y=z}.

>>7548438
so you agree with the definition of a set that uses itself ?
lel

>>7548466
I said the set *', not the set *.
Sorry I should have used something more visible than '.

>>7548407
Should be ((x,y), z) ∈ (SxS)xS (you forgot the very first parenthesis). I'm not sure if it's normal notation for operations, but I'm pretty sure it would be correct for a function say f:X->Y to say that
f = {(x,y)∈XxY | ∀x∈X ∃! y∈Y, where (x,y)∈f},
with XxY being the Cartesian Product of the two sets. So if * on a set S is a function from the Cartesian Product of S to S itself, couldn't * be defined as a set of 2-tuples analogous to f. The major difference being the first entry in the tuple is, itself, a tuple for *. I'm not sure about the parenthesis around the Cartesian Product of "The Cartesian Product of S with S", it just seemed a little more clear than SxSxS.

Perhaps defining f:X->Y would be better as

f= { (x,y) ∈XxY | ∀x∈X, (x,y),(x,z)∈f --> y=z}

how do i compute the indef integral of the square root of 8+8sinx? i realize it's a dumb question, but what wolfram wants to do seems strange and takes some big leaps

>>7548667

to clarify: it's sqrt(8+8sinx), not (sqrt8)+8sinx

What are some real life applications of numerical systems? I'm trying to understand where I could implement them, so far I can see binary, hex and octal are used heavily in computers and microprocessors, while others like Gray code are used in equipment to measure height. So basically what I'm asking is I know that they can be used to input data in several electronics, but what about other things? are there any other things they can be used for? (also thinking in their operations, sum, subtraction, division and multiplication)

>>7544031
Yeah, that's basically just finding the second term of the taylor expansion, but less general.

>>7546260
Write out the truth table and it should be easyish

My professor uploaded the lecture slides I was going to look at as PDF's instead of as a powerpoint, so they only have questions without explanations as the explanations were set up to stay hidden until cued to appear in powerpoint.

So I've got a conducting plate, a dielectric slab, a conductor, another slab, and another plate, all stacked up like a sandwich. How do get the capacitance from one side to the other? Is this just a "capacitance between two plates containing a dielectric" problem, but with a third plate? Still kinda lost.

>>7548788
Oh nice, I got dubs

I think I'm remembering how this works, like the total C = 1/C#1 + 1/C#2. I'm pretty sure I just need to add the reciprocal of each sandwich or something.

>>7542975

distance = rate × time. you integrate instantaneous velocity over the time interval. the distance traveled is the area under the velocity curve, thus...(a).

>>7548811

ill be honest, Im always tentative about responding to these because I dont know if there just too baby tier or well beyond my level and I am missing some crucial component

Assuming z is a function of vector X length N (X has N elements: x1 to xN).
So, to empirically calculate the derivative of z with respect to the entire vector X, we must calculate its derivative for each of the xi by modifying xi = xi + theta then calcualte (zi - z)/theta. We have to repeat that process N times for i = 1 to N. I understand this so far.
But, in this tutorial, section 2.1:
http://www.robots.ox.ac.uk/~vgg/practicals/cnn/index.html
They bypass the i = 1 to N loop by using a Normal pseudorandomly distributed vector called 'ex' sized N, mean zero. So now the empirical derivative of z is:
dz/dx = (z(x+theta*ex) - z(x)) / theta.
How the fuck does that even work?

Helpppp! I have been stuck here. I tried l'hopitals rule but I can't use it since we haven't covered it yet.

>>7548909

I believe for the first one all you need to do is multiply by (sqrt(x)+sqrt(8-x))

>>7548909
l'hopital's works on both

>>7548909
On the second, let a = 2^t and substitute

>>7547851
I got accepted into Pomona with a worse gpa and didn't finish general chemistry. Transfered EE.

Keep in mind, they're impacted there.

>>7548826
Please help me on this.

Rate the difficulty of a College Algebra Math 111 course. 1 being easy, 10 being hard.

>>7549023
2

>>7549024
The key words "College" and "Algebra" threw me off. As a calculus student, this should be cake.

>>7549023
e/2.

Honestly the reason it's so hard for certain people is obstinate learned helplessness

>>7541036
Just going to try this equation.

<span class="math">
\frac{\cos4a-4\cos2a+3}{\cos4a+4\cos2a+3} \Rightarrow \frac{-4\cos2a+3}{4cos2a+3} \Rightarrow \frac{-1}{1} \Rightarrow -1 \Rightarrow \sqrt[4]{\arctan (-1)} \Rightarrow \frac{\sqrt[4]{-\pi}}{{\sqrt(2)}}
[/spoiler]
>>7541394
>>>/biz/

>>7549072
\frac{\cos 4a-4\cos 2a+3}{\cos 4a+4\cos 2a+3} \Rightarrow \frac{-4\cos 2a+3}{4cos 2a+3} \Rightarrow \frac{-1}{1} \Rightarrow -1 \Rightarrow \sqrt[4]{\arctan (-1)} \Rightarrow \frac{\sqrt[4]{-\pi}}{{\sqrt(2)}}

If that still doesn't work, I got <span class="math">\frac{\sqrt[4]{-\pi}}{{\sqrt(2)}}[/spoiler]

How doable is thermodynamics as a freshman in the spring? That would be the third quarter, after having done precalc and calc 1 and concurrently doing calc 2. no experience with statics, dynamics or mechanics of materials. This is at a community college

<span class="math">
<\psi | Q \frac{d\psi}{dt} > = <\frac{dQ}{dt}>
[\math]
I think I'm just being retarded but wtf how[/spoiler]

<span class="math">
<\psi | Q \frac{\psi}{dt} > = <\frac{dQ}{dt}>
[/spoiler]
===

>>7549258
=== was supposed to be ???
How's this shit work? Can I just throw the d/dt around to the left of Q just like that?

>>7549258
use \langle and \rangle along with \left and \right brah.
<div class="math"> \left\langle \psi | Q \frac{d\psi}{dt}
\right\rangle = \left\langle \frac{dQ}{dt}
\right\rangle </div>
It looks more pimp, you see. Even better if \bigg works here
<div class="math"> \left\langle \psi \bigg| Q \frac{d\psi}{dt}
\right\rangle =
\left\langle \frac{dQ}{dt}
\right\rangle </div>

>>7549280
Ohh nice, will remember next time. Not written any inner product in latex till now

i have to take the integral of the square root of (8sintheta+8)dtheta

wolfram's first step is to u-sub with u=8sintheta+8, but it ends up with 1/root(16-u)du, and i'm very confused as to what kind of trig bullshit is happening there.

>>7549302
does arcsin ring a bell ? Do you know how to make a substitution ?

>>7549333
there's a reason i'm posting in the stupid questions thread; i can trig sub well enough, but i don't really understand where arcsin comes in. am i supposed to get theta on its own or something? i realize this is pretty basic algebra/trig.

>>7548826
Please help.
;_;

>>7548466
This Is how functions between sets are defined. I don't know what issue you're having.

How come in movies, especially older movies, when the camera moves, some lights will flash right before they move out of frame?

Is there a good research paper done on the health and mental benefits of studying/reading vs. watching TV/ playing video games for more than an hour? And I don't mean long term consequences like better job more money more knowledge better reaction time etc but what goes on in your mind and body during that time. Sorry for the vagueness, biology/psychology isn't something I am very knowledgeable about but I hope you understand what I want.

Is there a website that ranks universities by major in California?

Sorry to do this but I'm really not good at this.
I need help with the boxed question, I just need an equation and maybe a quick runthrough of what I'm supposed to do. I'm really terrible at maths, I'm sorry if this trivial.

Can someone check out this Materials problem and give me a hand? Using torque equation t*allow = TC/J I'm getting the equation 75 = (-3900)(0.040) / (pi/2)(0.040^4 - x^4)

X should be 33.3, but I'm not getting that with what I did above.

Not a question at all but I don't want to start a new thread for this but what do you think about this:
>>7157567

I need to prove Pythagoras theorem holds for any exponent integer >2

>>7543013
i just saw this in another thread - this was the answer given. I dont have a clue - but people seemed to agree.

>>7544018
Is this picture a master ruse? There are so many things wrong with this cheat sheet.

Okay guys I'm gonna be real here. I love science, I want to be an engineer, I couldn't imagine being apart of any other field. I'm a freshman in college and I'm seriously struggling with math. My high school was god awful at teaching math and the state was aware of it, however I don't want to put the blame on anything other than myself. I'm absolutely terrified that I may not be able to do the only thing in life that I feel is my calling. I am desperate here. Any help please.

>>7552060
lmgtfy.com/?q=online+math
If you're struggling you have to spend more time practicing. If you still can't make it then that's just the way it is, people have different aptitudes and there's no easy way around that. You could study at half pace.

Can air be compressed into a tank then the same air is used to make balloon? My friend is trying to convince me that they mix normal air with hydrogen to lower the cost of making balloon

>>7552223
can my dick be compressed into your mum

>>7552223
Google "hindenberg" then come back and tell us why that's a bad idea.

Chemistry question here.
I do not get anything about the Tanabe Sugano Diagram. Let's say, I have a d3 ion like Cr(III). I know that L=3 and S=4, each for high spin. So my ground term should be 4F and my following terms should be A1, T1 and T2. For low spin, that would mean L=5 and S=2, so 2H (which has to be wrong I guess).
What transitions should I see? For high spin, I am guessing A1=>T1 and A1=>T2. Is this right?

Where do you all go for textbooks besides Library Genesis?

I need a book that's not very academic but is certainly more /sci/-related than /lit/-related.

Any leads? Looking for IFSTA Essentials of Firefighting.

>>7542982
OP's picture is actually true for all x.

Anyone know what's up with this crazy daisy?

Found it years ago and was curious about it since I've never seen any daisy so fucked up in my life. Anyone know if it's a relatively common thing or something?

>>7553659
And yeah, unfortunately these pictures suck, but they're all I have.

Whats a formula representation of all functions that our their own inverses?

>>7554280
{f | f^2 = id}

Sorry for the noob question but what's going on in the red box? I understand the restrictions on the domains of both the function and its derivative, but why does the boolean conditional "or" show up? And what's with the simplification in the second line? Some variation of De Morgan's laws?

>>7553661
>>7553659
It's a simple mutation that isn't all that rare.

I've learned about it because people posted pictures of similar daisies they found in teh fukushima area trying to extrapolate some shit about how radioactive the area is from that.


I'm not a flower expert so I can't tell you whether this mutation has a name but here is a related article:

http://news.nationalgeographic.com/2015/07/150723-fukushima-mutated-daisies-flowers-radiation-science/

I've got a table of values and I'm supposed find the phase shift.

t mA
0.0 21.651
1.047 0.0
4.189 0.0
7.330 0.0

any way guessed correctly that the function was 25cos(1000t + 30(degrees)) mA
I just don't get how I was to derive the phase shift from the table.

>>7554609
>7554609
Thank you, that's good to finally know.

I only come to this board once in a blue moon (or a blood moon in tonight's case) so I'm not sure. is it just me or is /sci/ much faster than it was a year or so ago? I swear last time I came here half the threads were a month old or older and now looking at the board the oldest thread outside of the sticky is 15 days old. If I'm not imagining things was there any specific event that caused this?

Hello,
I'm a complete beginner at electronics, so please don't laugh at me for asking this question:
What exactly happens when electrical energy gets converted into other types of energy? I understand that the voltage is divided up between the different kinds of things that receive the energy such as LEDs, but what exactly does this mean? What happens to the electrons? Do they lose energy on their way which results in less voltage (because voltage is potential)? Does the current remain the same because the electrons are still flowing as before, just with less energy?

>>7543013
I managed to do it. Pic attached incase anyone tried it and would like to know the derivation

>>7544135
Thanks, I got it from your method as well

Can anyone explain the gist of Newtonian dynamics and everything I need to solve Newtonian dynamic problems? Every time I solve for something I miss a vector component or something

>>7557343
<span class="math">F(t,x(t),\dot x(t)) = m \ddot x (t)[/spoiler]

if you know <span class="math">x(t_0)[/spoiler] and <span class="math">\dot x(t_0)[/spoiler] then you can solve the DE to get <span class="math">x(t)[/spoiler] for all <span class="math">t \geq t_0[/spoiler].

>>7554360
There's an "or" because the binomial P(x)*Q(x) will be positive if and only if P(x) and Q(x) have the same sign, that is, P(x) > 0 and Q(x) >0 or P(x)<0 and Q(x) <0.

In the second line you have x>3 and x>-2 = x>3, because being higher than 3 means you're already higher than -2. The simplification for < follows the same rule, but you use the smallest of the two numbers to get the lower bound.

How does someone identify this as a quadratic equation? What form does it take? I am confused

>>7558098
send help

>>7558098
well try to solve for lambda_i and see for yourself.

>>7558218
I have, I ended up factoring out the lamdba_i on the right and then multiplying the left by (1+(2*lambda_c)/lambda_i) divided by itself to make 1. I go on from there, and get a nice simplification, but I see no quadratic expression and the answer I get from mine is wrong

>>7558232
wait I got it. thanks for the moral support >>7558218

>>7541036
Am I right in thinking the maths describes the rules of existence in physics and this is how it is used in hypotheses? Do physicists only think in terms of mathematical equations or is there a more "physical " visualisation process that occurs?

Let (X,d) be a metric space. Then show:
|d(x,y) - d(u,v)| <= d(x,u) + d(y,v),
for x,y,u,v in X.

>>7542975
you're girlfriend thinks the answer is Chad's d

Could someone please tell me what the lowercase 'e' in this equasion stands for? The website I'd normally look at isnt working. Sorry that this is low-level.

>>7558319
euler's constant

>>7558319
It's a constant.

>>7558324
>>7558320
Thank you for the fast response

>own a motorcycle
>live three to four hours riding away from a complete dark zone
What are the best ways to take photos of space, and to do some amateur astronomy with only a backpack's worth of space?
I imagine I don't need a very large telescope, or an expensive one, to get some good pictures that far out.
Keep in mind this would only be a passive hobby for me, and something to do while riding.

And can I actually send in observations and science to astronomers and be useful? That would be pretty cool.

The moon looks very yellow right now. Does anyone have any idea when this will last until?

For x,y in R, show for y>=x that:
x/(1+x) <= y/(1+y).

>>7558367
Try taking the derivative of f(n)=n/(1+n). What do you notice?

>>7558367
Also, to add to >>7558381, your statement only works in one of the following cases
> when both x>-1 and y>-1
OR
> when both x<-1 and y<-1

>>7558381
It's even easier than that I found out.

>>7558408
Derivatives are already pretty easy, so I'm interested in hearing what your solution is. I like elegant solutions.

>>7558422
Note x/(1+x) = 1 - 1/(x+1). Then bingo, easy proof. No need to use calculus.

The compass in a plane indicates that the plane is pointed due east; its air speed indicator reads 212 km/hr. There is a steady wind blowing from the north with a speed of 60.0 km/hr. What is the speed of the plane with respect to the ground?

>>7558437
I don't see how that proves it. Can you elaborate?

>>7558456
Replacing x with y yield the inequality easy with little more justification needed because of the form it is in. 1/(k+1) gets smaller as k increases. Hence 1-1/(k+1) grows larger.

>>7552016
Give examples then

>>7558460
Ok, that makes sense.

>>7558451
You are given th velocity vectors of both the plane and the wind, both of which are with respect to the ground. Think now, how do you find the velocity vector of the wind with respect to the plane?

I know this is full retard but how do I solve a DE of the form:

<span class="math">t^{2}u" + 5tu' + 5u = 2t^{2} [/spoiler]

>>7547378
Asif?

>>7558575
Substitute u=e^(ax). Find the two solutions that fall from a simple quadratic equation.
It's a 2nd degree equation, so the space of solutions has dimension 2, ie: You just need the 2 functions above and their linear combinations give you all the solutions.
prolly

>>7558606
Yeah, I tried that but got <span class="math"> a = \frac{1}{t} \frac{5 \pm \sqrt{5}}{2} [/spoiler]

which cant be right because when you sub it back into u, the variable t cancels out

is it safe to power a bunch of ccfl's extracted from old tv's with a 15 million volt (allegedly) shitty $10 taser? pic related

So the visualization behind double integrals comes quite naturally, but am I right to think that triple integrals need a fourth dimension for the integrand? Multiple integration can be done over any arbitrary number of dimensions, yes?

>>7558939
A triple integral is the "4-space under a volume" in the way that a double integral is the "volume under a surface", yes

I need the numbers involved. Probably the dumbest thing here.

Where did the -2 go missing?

well this seems a nice place to ask, hello /sci/ im new to this board and im wondering if this place is the place to talk about electrical motors, im studying electromecanical engineering and im wondering what could you tell me about variable field brushless motors? how will you implement them? what are your toughts and opinions about it, i trying try to implement one in an electrical motor, but the initial inertia break is something im looking forward to resolve right now, and i would be very pleased to hear your say about this (sorry for my bad english im foreign and sory for the wall of bad text too)

>>7559321
Byte=8bits
Megabyte=8*10^6bits
2 Megabytes=1.6*10^7 bits

And yes, Megabytes is in base 10, so your teacher is probably confusing them for Mebibyte, which is in base 2.

>>7547452
>tfw this will be me next year ;_;

Given this question in a lab:
It is possible to model any function in propositional logic with Bayesian Networks. What does this fact say about the complexity of exact inference in Bayesian Networks? What alternatives are there to exact inference?

What the fuck why would the modeling property of a network say anything about the complexity of exact inference?
I fucking hate AI mang, fuzzy-logic everywhere.
Anyone have any idea on how to answer this bull?

>>7559342
<span class="math">e^0 = 1[/spoiler] so you get the sum 3 in your R.H.S. subtract -3 from both sides and voilá.

>>7558309
You can use the triangle inequality for this.
<span class="math">|x+y| \leq |x|+|y| \iff ||x|-|y|| \leq |x-y|[/spoiler]

>>7558575
Might have no nice solution.
http://www.wolframalpha.com/input/?i=solve++t^2*u%22%2B5tu%2B5u%3D2t^2

Is the opposite vector of AB really -BA rather than BA?

Before you call me retarded, I got it wrong on a test for writing BA as the answer and almost got suspension for arguing with my retarded Calculus teacher.

>>7560579
It's BA or -AB, your teacher is wrong.

> almost got suspension for arguing with my retarded Calculus teacher
- learn to get your point across properly
- learn what calculus is

>>7558575
It's a cauchy-euler equation. Assume the solution is of the form
<span class="math"> u = t^{r} [\math][/spoiler]

>>7560787
<span class="math">u = t^{r}[/spoiler]

>>7559342
Your mistake came when you said:
<span class="math">ln(y-2)=frac{x^2}{2}+c[/spoiler]
means
<span class="math">(y-2)=exp(frac{x^2}{2})+C[/spoiler]

It should be
<span class="math">ln(y-2)=C exp(frac{x^2}{2})[/spoiler]

>>7559342
>>7560792
bleh

<span class="math">ln(y-2)=\frac{x^2}{2}+c[/spoiler]
means
<span class="math">(y-2)=exp(\frac{x^2}{2})+C[/spoiler]

It should be
<span class="math">(y-2)=C exp(\frac{x^2}{2})[/spoiler]

What are the practical uses of matrices and determinants?

>>7559629
>>7560794
Thank you very much

>>7561565
One example is numerical simulation. There are approximately billions of other practical uses.

>>7561565
Matrices, they simplify every fucking thing there is that uses Linear Operators, ie such that: f(v+u)=f(v)+f(u) and f(a*v)=a*f(v).
Linear operators are everywhere.
Even if they're not linear it's still useful because all well behaved functions f(x) are linear, when x only changes a little. A lot is known about matrices so you can apply that knowledge to anything that relates to Linear Operators.

As for determinants. Some Matrices are invertible, some are not. eg: If you're given the matrix A and the result of A*B. If A is invertible you can find B, otherwise you can't.
Determinant dumb down the process of finding out whether a matrix is invertible or not. If detA is 0 it's invertible, otherwise it isn't.
They're also useful for other things, eg: The area/volume/nth-hypervolume of a the shape spanned by n vectors with n coordinates is very simply the determinant of the matrix with those vectors as columns.

what's the difference between standard error ofthe mean and standard deviation?

>>7547383
at leat biology can be learnt without maths
read the campbell

>>7547448
stop taking drugs, join a self-help group

>>7547817
call them and tell them that you are sick and it it'S ok to start one week later
but attend one day of that week or so if you are strong enough

>>7562096
I'm not on any drugs, and self help wouldn't help me

>>7562107
join a soccer or hockey team

>>7562150
If I could afford to go to college I probably wouldn't be in this situation.

>>7562154
aren't there any sports teams in your place outside of college? do you even have a job?

>>7562155
If I had a job I don't think I'd be asking how to fix my brain/life so I'm not constantly depressed

If there were teams it would probably require some pay in type deal, and I'd be going for like tennis anyways if anything.

I mostly play competitive games and am fairly good at those, but naturally can't commit the time to getting on a team and going pro since I don't have any real income atm

>>7562107
How is it self-help is other people are involved?

>>7562163
you have to join a larger team no matter what. your problem is that you are alone.

>>7562167
I enjoy being alone

>>7562169
then why do you say your brain needs repair when you are actually happy?

>>7562174
I haven't been happy in years, I'm just more comfortable being alone working with machines. Eventually you get used to never feeling joy.

>>7560756
>- learn to get your point across properly
I do know how to get my point across properly. I politely asked but the old hag kept saying I was wrong and got pissed as fuck when I showed the textbook which stated that the opposite vector of AB is BA.

She just fucking hates me because I'm maintaining 95 average despite skipping 25 or so classes (public school, really loose attendance policy)

I'm good with math and sciences. I can do calculus with my eyes closed. For the record I have 148 IQ (did it at a somewhat certified institute) and got 99 in Gr.12 Physics.

>- learn what calculus is
Up here in Canada, we do a course called "Calculus and Vectors" which is basically Calculus for the first half of semester and matrices for the second half.

>>7547424
>C++(CSUs want this instead of Java)
thank em, a lot
we(embedded sw company) get a lot of fresh baked bachelors who only learned java and think C++ is java with pointers, explaining the dunning kruger matrix to them is fun....

>>7562348
I didn't ask about your IQ, grades and proficiency in babby maths. It sounds like you're pretty cocksure which is probably what irritated your teacher.

>>7562752
Not really, irl I'm as INTJ as they come. As I said, I asked politely.

My point was I know what I'm doing with this "babby tier" maths and it's fucking ridiculous how the only thing holding me back is this self centered bitch and her arrogance.

Nowadays most teachers at the public school boards are narcissistic power hungry social misfits. I was glad I'm out of this shit hole soon but if this sort of shit isn't supposed to piss people off I don't know what kind of sociopaths will be waiting at the uni. I guess I'll really have to try harder to be a normie and learn to take it up the ass then.

I know this is a weird question to ask on /sci/ but what's the best UofT college? What are the stereotypes for each college?

Should I learn real analysis or topology first?

>>7563200
Austin. Austin. Austin.
pic unrelated, just finished this series and it broke my heart

>>7563322
Real analysis. Topology is much more abstract if you don't have any understanding of the basics of the other fields. By the time you can see field theory at work in the reals, you're ready for more.

that moment when I haven't done any of the physics and I'm hoping that finishing DE and the core four classes will be good enough to get into Cal-Poly Pomona, CSU Long Beach, or SDSU. 65+ credits and a 3.6 GPA.

Page ranking help. Why does page 0 outrank page 2?

>>7563385
Pomona is impacted so you better have most of your shit done. They want you in and out.

Are STEM Fraternities worth joining? Will have a pickle shoved up my ass really help me out with job seeking?

>>7563497
Only has one outgoing link.

>>7563385
CSULB here. Going into any major under the college of engineering, you should have just gone straight here.

I'm certain other universities do this as well, but we've got a bunch of classes that double-count for our majors and our GEs. If you transfer here, your classes will transfer, but you may still be forced to take the previously mentioned classes.

CS department is OK.
CompE department is OK.
Both are poor in extracurriculars. Mostly caused by lazy fuck students.
That isn't to say that the tenured faculty aren't lazy fucks. We're actually in the process of a total generational change and tons of faculty are retiring and getting hired.

MechE/Aerospace department is breddy gud
Physics department is shit
Math department is breddy gud, but only at teaching.
Biology department has motivated professors, but they have a strong and obvious weed-out vibe going on.
Nursing is heavily impacted.

That's all I know.

This circuit meets all but the highlighted outputs. How can I improve it?

>>7563591
https://en.wikipedia.org/wiki/Karnaugh_map

>>7563591
More convenient pic.

>>7563594
Here's one of each. Now what? Note: I am 12 and what is this?

A black hole is basically just a perfect circle in space time right?

>>7563595
All combinatorial logic functions can be completed in 3 gates. Not, And, Or. Look up sum of products.

>>7561729
>>7562084
Thank you m80s.

>>7563647
That's just the boundary of the black hole, and it's a sphere, not a circle. But yes, orbits are actually straight paths in a gravitationally warped region of space-time. Black holes warp space-time into a singularity such that within the black hole, no physical path exists that leads back out. Space-time basically rips apart and we can't really model the inside because the parts of the equation that are supposed to model it are a division by zero.

>>7544139
>But why, if its net acceleration is still zero?

A stationary helicopter exerts mg Newton on the air.

A steadily rising helicopter exerts mg + X -X Newton on the air, where +X is the air resistance against the top of the helicopter and -X is the force of the wings upon the air below it.

Sure, +X-X = 0, but since air isn't a solid body, your experience standing under the helicopter is that it is pushing the air against you with more force than before.

>>7555937
>any way guessed correctly that the function was 25cos(1000t + 30(degrees)) mA
>I just don't get how I was to derive the phase shift from the table.

1: The signal is a sine, not a cosine.
2: The signal is supposed to be 0 at t=0, if it isn't zero, it is phase shifted.

>>7559321
>I need the numbers involved. Probably the dumbest thing here.

Whose megabytes?

The actual strictly true "hey teach here's a primary source" is

2*(mega)*(byte)
2*(10^6)*(8)
16000000 bits

because:

>Faced with this reality, in January 1997 the IEEE Standards Board has decided that IEEE standards will use the conventional, internationally adopted, definitions of the SI prefixes. Mega will mean 1 000 000, except that the base‐two definition may be used (if such usage is explicitly pointed out on a case‐by‐case basis) until such time that prefixes for binary multiples are adopted by an appropriate standards body.

But if you're any kind of actual computer person, Mega means 1024^2

vaguely /sci/ related science it's a note from Darwin, but could any of you guys translate in modern english this note:

"I think case must be that one generation should have as many living as now. To do this and to have as many species in same genus (as is) requires extinction . Thus between A + B the immense gap of relation. C + B the finest gradation. B+D rather greater distinction. Thus genera would be formed. Bearing relation" (next page begins) "to ancient types with several extinct forms"

It comes from pic related, and I'm having some trouble with it, not being a native speaker...

>>7542975
Could be any of them. x, v and t have not been defined.

>>7544576
>leave almost all I the examples out
>Include one hard example per formula.

Jesus christ how many examples do your textbooks have in them?

>>7548826
a hundred posts later and still no one could help me on this ;_;?

What do you guys think about that professor who uses homework questions as test questions? Is that good or bad?

Why is the boundary layer so important for lift ?

How does vortex lift works ?

Just applied to a college and I was wondering what will happen if I filled the "What city were you born in?" wrong? I don't know what city I was born in.

I applied for a college where they require you to select an alternate non-impacted major. If I don't get accepted to the intended program, but I do get selected for the alternate, can I still say no thanks?

What does it mean if I get accepted to a top 100+ to 130 ranked school in California.

The computer is telling me I'm wrong but I don't know where I made a mistake.

The question wants to know what the y coordinate for point B (on a tangent line) with an x coordinate of -1.8.

the question tells me that f'(-1.5) is -3.75 and that f(-1.5) is 2.875
I figure -3.75 is the slope so I set it up like this.

-3.75 * -1.5 + b = 2.875
b=0.51111111

so -3.75 * -1.8 + 0.51111111 = 7.26
Where did I fuck up?

>>7565324
I really am fucking retarded aren't I.
God dammit.

I just applied to 4 CSUs in California. Am I suppose to apply for financial aid right now or after I get accepted?

Is this a valid series of reactions for this synthesis?

I was supposed to do this in a maximum of 5 steps but couldn't think of any other way

>>7550306
yummy, delicious p-chem II

>>7541036
Can anyone help me out with this (it's babby physics)?

This is the diagram that we're given (horizontal pulley with different masses). We assume that there's no friction and the string is massless.

Here's the exact wording of the question:
>Look at the drawing of the apparatus in the Basic Concepts section. You now tilt the track (lifting the end with the pulley) so it makes an angle θ with the horizontal until the cart and hanging mass are in equilibrium. Using the given masses: find θ.

The mass of the cart is 0.677 kg and the hanging weight is 0.403 kg.

How the hell do I even begin?

I haven't had any calculus. Can someone teach me how to integrate? Is there some universal foolproof way to do it like the quadratic formula?

>>7567162
No it depends on the function.

Does the surface tension of water decrease when it's raining? Wouldn't the surface molecules attractive force weaken as the rain water came into contact with it?

And if so, then could someone jump into water from a higher height safely when it's raining as opposed to when it is not?

>>7566939
Read the problem until you really understand what it's asking. At this step in the course, your instincts should be to write down newton's 2nd law equations for each relevant direction and with convenient axes given the problem/

>>7567162
No, not really. Integration is kind of different from all previous types of math in that you have to use you brain a little bit instead of plugging numbers into a formula.

>>7567162
There's no fool proof way that solves all integrals of any function. There are techniques you can learn that make computing the integrals easier, but really the best thing you can do is do lots of practice problems. Reading through the examples in the text book helps a bit too, since they sometimes show you tricks to compute the integral faster.

Just grab a calc textbook and start doing problems (use /sci/'s recommended list of textbooks).

>>7567162
it's essentially the opposite. there's few general principles, and you've got to be creative for non-trivial integrals

>>7567162
The simplest sort of integration is in the Riemann sense. Basically it splits an interval [a,b] into several pieces [t_i, t_(i+1)] which dont overlap and together make up [a,b], then multiplies the width of each interval by the value of the function at some point in each [t_i, t_(i+1)] to get lower and upper bounds.

If L<c<U for all lower and upper bounds respectively, and if bounds exist such that U-L<d for all real numbers d, then the integral exists and equals c.

This is probably quite esoteric for someone without calculus. The good news is that integrating from the definition is largely unnecessary. By the fundamental theorem of calculus you can integrate a continuous function f(x) over [a,b] by just solving F(b)-F(a), where f is the derivative of F. If you want the "general" integral (without bounds explicitly stated), you just need to find some F which has f as its derivative.

>>7547378
I haven't done pde's in awhile, so this could be incorrect.

>>7567301
Your handwriting is sloppy as balls.

>>7558098
Multiply the first equation by $\lambda_i$ and $\lambda_i+2\lambda_c$.

Alternative: if those are the roots of a quadratic equation, that means you can write it as $(\lambda_i+lambda_1)(lambda_i+lambda_2)=0$. Work out the product, rearrange the terms and you should be able to get the original equation.

>>7562084
This guy meant
If detA=0, => the inverse doesn't exist

>>7567309
It's MS paint, I did what I could.

>>7567301
That's just an ODE, my man. Also, hacking the x on only works with constant coefficients.

>>7541036
Im thinking about majoring in Computer Science or a like wise field, how hard is the math? by friends say its more logic focused than mathematical, but what do you think?

>>7563595
Looks doable in 3 nand gates and 2 xor gates.

XOR1 takes inputs I2, I3.
XOR2 takes inputs XOR1, I1.

NAND1 takes inputs I2,I3.
NAND2 takes inputs XOR1, I1.
NAND3 takes inputs NAND1, NAND2.

O1 takes input NAND3.
O2 takes input XOR2.

If you definitely want a lesser gate depth, instead use a feed O1 with a tripple.-input NAND. That, in turn, will take the inputs (I1 nand I2), (I1 nand I3), and (I2 nand I3). I'm not going to bother with labeling those.

Best thing is, looking at the timestamp (as I finish writing this) I realise you probably won't read this.

>>7567273
I just have a hard time picturing this. How would it look like once the track is tilted?

>>7566939
The dynamics track excerts a force perpendicular to itself, upon the cart. This counters the downward force of the cart. These forces combine to make the force parallell to the track towareds the lower left corner.

These forces can be seen as constructing a right-sided triangle. Hypothenuse, which is vertical, is the mc*g, that is, the gravitational pull on the cart. The side paralell to the track should match the downward force of the hanging mass* (which you also know). Given that it's a right angled triangle with two known lengths, you only need to apply trigonometry to find the angles.

*because that's when the two are in equilibrium.

In circuits with two voltage sources, why can the electrons magically flow through one voltage source? E.g. from +1 to +2 to -2 to -1?

Are there any accurate IQ tests that can be taken online that happen to be free? Thanks in advance.

>>7568387
For example, do you mean 2 batteries in series? Why do you think electrons magically flow?

Since we can define the Transitive Property of a relation R on a set A as the implication

For all x,y,y in A, if xRy and yRz then xRz,

what exactly would the contrapositive be?

I know it would be something like

if x is not related to z then x is not related to y or y is not related to z

I'm just not sure what to do about the beginning; I know the negation of a universal quantifier is the existential, butit just doesn't look right for some reason

>>7569214
oops, should be "For all a,y,z in A"

>>7568861
I never found one but my IQ was such a burning question that I paid psychologists at a local clinic to administer the test for me. I paid about $500. It gave me a lot of reassurance, I'm glad I did it.
They told me I have a range from 114 to 124, and that if I had a faster thinking process I'd easily be 120 to 124.

I was concerned that I was deficient in some way, I had such a low self esteem that all I wanted to ensure was that I wasn't stupid. It was worth every penny. Maybe after college I'll do it again and see if my IQ improved just to see.

>>7569219
>>7569214

The quantifiers are outside the scope of the implication, so they remain so.

<span class="math"> \forall x,y,z \in A \ \Big( R(x,y) \land R(y,z) \implies R(x,z) \Big) [/spoiler]

has contrapositive

<span class="math"> \forall x,y,z \in A \ \Big( \lnot R(x,z) \implies \lnot R(x,y) \lor \lnot R(y,z) \Big) [/spoiler]

so I think it would be

"For all x,y,z in A, if xRz is false then xRy is false or yRz is false."

>>7569448

I never know what latex /sci/ supports. one more try

<span class="math"> \forall x,y,z \in A \ \Big( (R(x,y) \land R(y,z)) \rightarrow R(x,z) \Big) [/spoiler]

has contrapositive

<span class="math"> \forall x,y,z \in A \ \Big( \lnot R(x,z) \rightarrow (\lnot R(x,y) \lor \lnot R(y,z)) \Big) [/spoiler]

>>7543013
LONDON

>>7569234
The real test was to see if they could toy with your self esteem enough to make you pay for it, man.

How does one go about proving that the trigonometric functions are analytic?

>>7566939
>>7567273
>>7568031

the marked force component and force from the hanging mass need to balance.

Would anyone have a resource that would help figure out how N has been derived here?

>Objects with normal distributed weight
>Mean = 500
>Standard deviation = 100

What's the probability that 3 out of 14 randomly selected objects weigh at most 584?

I got 0.66 but heard it's wrong.

>>7564254
>x1, x2 points in the distance line
>v1, v2 points in the velocity line
it’s at least implied what x and v are
>>7542975
you are right. when integrating, units do magically change. you still need m to have distance. a) is m*s, b) is m*m/s, c)is also m*s. what you needed was s*m/s

>>7569836
First find the percent area under the curve<584. The Z-score is (584-500)/100=.84 When you look this up in the table you get .7995 or 79.95% is under 584. This means the probability of 1 randomly selected object is .7995. So two randomly selected objects would be (.7995)^2. Three would be (.7995)^3. And then the other 11 not being selected would be (1-.7995)^11. You're final answer should be (.7995)^3*(.2005)^11.

>>7569612
cos x = (e^(ix)+e^(-ix))/2
sin x = (e^(ix)-e^(-ix))/2
Then it follows from the analicity of e^x.
To prove e^x is complex-differentiable make like a calc one student and take the limit of the difference quotient.

>>7569872
But (.7995)^3*(.2005)^11 = 1.075755...
Which is higher than 1, which a probability can't be?
It isn't amongst the answer alternatives either. I'm so confused.

>>7569897
no, it's 1.075755...*10^-8 or .0000000108 which makes sense because 80% of the objects are under 584 so the probability that only 3 out of 14 are in that 80% zone would actually be pretty small.

>>7569916
The answer alternatives are:
>0.70
>0.72
>0.68
>0.66
>0.74

So you must be way off, I'm sorry!

>>7569938
Well I have no idea then. Try reading the textbook or listening to your professor next class

>>7541036
Where can I get lecturers for upper level undergrad /basic grad math courses? Even MIT OCW just usually has the calc courses,diff eq,lin alg level. Most of advance courses just includes what books they use and samples of old test. Maybe some lecture notes but I want to get some decent recorded lectures

Can three vectors with two entries be linearly independent?

More general: Can N vectors with N-1 entries be linearly independent?

Elaborate it please.

>>7570109
Two components*.

>>7570109
no, that's the whole point of bases. A vector space of dimension N-1 has a base of length N-1. If you add an n-th vector, it has to be a linear combination of the base vectors (definition of a base)

>>7569731
You don't need a fancy resource anon, besides How To Take A 2nd Derivative by Isaac Newton.

In the horizontal direction,

<span class="math"> m \ddot{x}_{pendulum} = m a_{pendulum} = \sum F_{pendulum , x} = +N [/spoiler]

Assuming <span class="math">l[/spoiler] is the distance from the pivot to the center of mass of the pendulum, its x-coord is

<span class="math"> x_{pendulum} = x_{cart} + l \cdot sin \theta [/spoiler]

Take the 2nd derivative of that

<span class="math"> \dot{x}_{pendulum} = \dot{x}_{cart} + l \dot{\theta} cos \theta [/spoiler]

<span class="math"> \ddot{x}_{pendulum} = \ddot{x}_{cart} + l \ddot{\theta} cos \theta - l \dot{\theta}^2 sin \theta [/spoiler]

So

<span class="math"> N = m \ddot{x}_{pendulum} = m \ddot{x}_{cart} + m l \ddot{\theta} cos \theta - m l \dot{\theta}^2 sin \theta [/spoiler]

>>7570112
So if we have a set of N vectors with N-1 components, do we really know that there has to be at least one vector in the set that is linear combination of the others?

I would like to find a demonstration for this. Obviously, I searched in Google before asking it here, and found nothing.

Help me out here, /sci/.
How do I determine the direction of the components in a circuit? I need this to use Kirchhoffs laws properly.
Do I just pick a point and then go clockwise or counter-clockwise? If so, why does one voltage source point in the opposite direction? Do all voltage sources have to point in the same direction (+ -> - or - -> +) and because the first voltage source was defined to point from + to -, the second one has to do that as well?

>>7570130
The voltage sources can work against each other. That circuit is equivalent to a single battery worth 5V where the 9V one is. If you only have passive components, the direction of your loop won't matter in Kirchhoffs laws, just make sure you take account of all the signs properly.

>>7570154
Yeah, I get that clockwise and counter clockwise is the same after all, I was just confused because of the voltage sources.
How do I figure the signs of the components out, then? This is very confusing to me right now. If I define a flow from + to - to be positive, I can determine the signs of the voltage sources easily. But how does this decision affect the signs of the resistors?

>>7570115
oh, that's simpler than I expected. Thanks anon!

What influence does the diameter of a water wheel have on its efficency?

Like, I get a taller wheel rotates more slower, but what does a taller wheel add in regards to wattage? Greater inertia?

>>7570218
You're thinking too hard, mate.
A bigger wheel can catch more water.

>>7570228
WOuldn't that be a wide wheel, not a taller wheel....oh you mean more buckets.

...on a related note, why weren't water wheels wider?

>>7570209
>>7570130

OK. Kirchoff's loop law is like this. Say you are at home, that's ground zero in voltage (i mean elevation). Then you go to school. You drive up and down hills, you take elevators up, you walk the stairs down, but eventually you end up back home. Now since you're final location is the same as the initial, if you summed all of the changes in height over your whole loop, you'd have to end up with 0 at the end. It doesn't matter if you used coordinates were "up" is the negative or positive direction. It doesn't matter if you reversed your path.

Now look at your circuit, let's start from the point marked "A". First let's go in the clockwise direction, as marked. This means our current i will be considered positive in that direction.

As you start down the wire to the right of "A" you pretty much stay at the same potential/voltage until you hit the 6Ω resistor. This takes you "down" in potential by (6Ω)*I. Then you hit the 4V battery. This takes you "down" again by 4V because you are going from + to - (higher to lower potential). Then you hit the 4Ω resistor. This takes you "down" even more, by (4Ω)*I. Finally you hit the 9V battery, which goes from - to + (lower to higher potential). So you "gain" 9V in potential "up".

Kirchoff: 0 = -(6Ω)*I - 4V - (4Ω)*I +9V

So I = (5V)/(10Ω) = +0.5 A.

Next let's go in the anti-clockwise direction. Anti-clockwise current is now positive.

You hit the 9V battery and go "down" (+ to -) in potential. Then you hit the 4Ω resistor and drop "down" by (4Ω)*I. Then you hit the 4V battery and go "up" (- to +) 4V. Finally you reach the 6Ω battery, and drop "down" by (6Ω)*I.

Kirchoff: 0 = -9V - (4Ω)*I + 4V - (6Ω)*I

So I = (-5V)/(10Ω) = -0.5 A.

Why is I negative now? Because it's really going the other way (clockwise) relative to your anti-clockwise "coordinates".

>>7570301
Godlike explanation, Anon. I really got it now.
The dropping/rising potential concept is what I was lacking.
Thanks a lot, I feel a lot more confident with circuits now.

>>7564520
bump

>>7570218
My thoughts:

The power injected into the system by the water is going to be <span class="math">P=g h \frac{dm}{dt}[/spoiler] where h is the height the water falls through and dm/dt is the water mass flow rate. This is the maximum power transferable to the wheel -i.e. the power is set by the water flow, not the shape of the wheel.

However, the conversion is not 100% efficient and different designs will have different efficiencies.

The use of these wheels was probably in outputting high torque which will scale linearly with the diameter of the wheel.

>>7541036
Can someone explain the process of retrieving this simplified form?

>>7570748

<span class="math"> \Big[ x \ln(20x) - x \Big]_{1}^{\mathrm{e}} [/spoiler]

<span class="math"> = \Big[ e\ \ln(20 e) - e \Big] - \Big[ 1\ \ln(20 \cdot 1) - 1 \Big] [/spoiler]

<span class="math"> = e\ (\ln(20) + \ln(e)) - e - \ln(20) + 1 [/spoiler]

<span class="math"> = e\ (\ln(20) + 1) - e - \ln(20) + 1 [/spoiler]

<span class="math"> = e\ \ln(20) + e - e - \ln(20) + 1 [/spoiler]

<span class="math"> = (e - 1)\ \ln(20) + 1 [/spoiler]