New SQT. Trig retard edition.
I don't understand the latter part of this example.
"The angle theta that s obtained is the angle -pi/2<theta<pi/2 for which tan(theta)=-2"
Why is it expressed as 2pi-1.11?
What happens if you jerk off a hermaphrodite while eating the pussy and they both cum?
>>8069905
It wants the angle between 0 and 2pi. A negative angle just starts in the fourth quadrant as opposed to the first, so you can just subtract it from 2*pi. Not sure why that's confusing for you.
>>8069913
oh, so it's just because any negative solution wouldn't work then?
I guess I was looking at -1.11 as more of an absolute value
>>8069920
Yes -1.11 is not between 0 and 2pi
As is shown on their graph, it is equal to 2pi-1.11
>>8069922
it's always stupid shit like this that gets me when I'm stressed and cramming, thanks low resolution nig
Anyone know how to get this one? I'm finding what I believe is Y12 but it's not in that form
I'm getting simply (2*s+2)/(2*s+5)
>>8069922
it's always stupid shit like this that gets me when I'm stressed and cramming, thanks low resolution nig
>>8069945
You have two components storing energy.
Therefore the denominator must have a quadratic term.
>>8069980
Well Y12 refers to I1(s)/V2(s) given V1(s) = 0 (i.e. there's a short)
Therefore the current I1(s) should just be -V2(s)/(impedance of the branch containing the 1 ohm resistor and then the parallel resistor and capacitor), correct? divide by V2(s) and you just get the admittance of that one branch which is (2*s+2)/(2*s+5)
Where am I wrong?
>>8069993
Oh I think I see what I've done wrong. We assume it's a current source at the 2 port, not a voltage source like I was presuming. My mistake.
I was thinking of getting the 5:30pm physics class, but I found no information on the professor. I have something to do on July 11 from 8am to 5:30pm. Is it bad if I miss one day of a Physics course? What if there is a test on that day? What should I do?
>>8070025
If the class starts at 5:30PM, and you thing ends at 5:30PM, what keeps you from going to class?
>>8070031
A two hour drive from the location I need to be to where the class is.
>>8070025
>but I found no information on the professor
You mean like ratemyprofessor? That shit is pointless, anyways.
>>8070039
this, most of those reviews are written by brainlets who are looking to blame someone else for their own failure
>>8070044
Yep.
>professor is foreign
knock off a star
>I was incapable of reading the syllabus
knock off another
>wasn't given questions on exam ahead of time
dock another
>I got less than an 'A'
automatic 1 star rating
>>8070052
the newspaper at my uni (UCLA) runs their own teacher review site that is pretty nice because they get the grade distributions of classes from the Registrar, so if you see a class where the professor gives consistently like 5% As then you might want to steer clear
>>8070057
It feels great taking the class and being the five percent, though. I met my favorite professor in a class like that, twice as many drops as As, and we wound up working on research together all through my undergrad. Dude was legitimately brilliant.
>>8069980
Are you still here? Can you maybe give me something else to go on? I've tried finding that admittance parameter a few different ways now but I'm not getting anywhere.
If spacetime itself can expand and stretch itself apart, does it make sense to assume it is doing this inside of a bigger, "real" space? For example, when filling a baloon with air, the air inside of the baloon expanding would be like our spacetime, while the space in which the air moves around in the baloon would be the real space.
>>8069905
I've got one month exactly for a scholarship exam, I am golden on math and physics but I'm crying in chemistry, what should I do? Khan academy the last month in chemistry? It's around A-level chem I believe.
A few questions:
What sort of resolution should I be looking for on a DAC for audio use? 8-bit? 16-bit? Can I get them in through hole?
What do I need to implement digital filtering? Is there a particular IC? Do I need a microcontroller? FPGA?
And if I have an audio signal converted from analog to digital is it stored in the time domain? Like, if I want to do the filtering do I have to do FFT to convert it to the frequency domain or can digital filtering be done in the time domain?
All my experience is with analog signal processing and while I've had digital classes I haven't worked with it much.
>>8070598
Take this with a grain of salt, but for my DSP class that I took at community college we used one of those myDAQ things from NI and were able to record audio using it then use labview to implement the filters
>>8070657
I've used myDAQ and Labview in some courses before and have labview installed at home. I'm really looking for something that better lends itself to being installed on a PCB though. I recently built an analog audio spectrum analyzer and as proud as I am of it I would really like to make an entirely digital equivalent.
>>8070688
hmm I've only ever done anything like that with TI chips but that was a pain the fucking ass and probably more than you're looking for
>>8070688
Since obviously I can't offer anything, you might want to ask at >>>/diy/ohm
it's a slower general but you'll probably find someone more knowledgeable about this
>>8070428
why do you need the existence of something outside of the baloon? A baloon would still inflate if it was put in a void chamber. In fact it would inflate faster and more.
The universe is everything, it does not need to expand into something else (since there is nothing else)
I am going crazy over something idiotic.
Entropy is a state function, this is a fact. Then, taking the process A --> B --> C --> A, I should be able to calculate ฮS between A and C by doing ฮS(A-B) + ฮS(B-C) = ฮS (C-A).
Now, let's say that A is a folded protein in solvent, B is the solvent without the protein, and C is the unfolded protein in solvent.
Is ฮS (C-A) the folding entropy? it should be.
>>8070723
how the hell do you go from A to B? The proteins just hide for a while?
>ฮS(A-B) + ฮS(B-C) = ฮS (C-A)
ฮS(A-B) + ฮS(B-C) = ฮS (A-C)
that's the only thing you can say.
>>8070751
>The proteins just hide for a while?
Kinda. Through gromacs I can "turn off" the protein and use the Bennet Acceptance Ratio to calculate free energies.
Are there mathematicians out there who still study non-differential geometry, are papers about non-differential geometry still being written? Is that field still alive?
CSfag here.
Is there any objective definition for something being "Naive"? How do you know if code you've written is naive or not if you can't see any way of optimizing it?
>>8071613
it's naive if it's the first thing you thought about.
How much megaton of TNT will a 80 Kg of radio active material gives?
>>8071479
Go to any math department's website, sort faculty by research interest, and look through the geometry/topology section.
>>8071848
E=MC^2
What are some blackbox processes in modern computer science?
>>8072025
cryptolization
>>8070025
If you will miss a lecture, that's probably fine if you know what it covered and learned it yourself. If you will miss a test, then you will have to see how that will affect your grade, whether or not you can do a makeup(which professors may end up being reluctant to do). Additionally, you might be able to email the professor about this. At the very worst, you will get no response, but the professor might know about the planned schedule.
>>8070050
>>8070052
>>8070057
My undergraduate research adviser had some of the best reviews I've ever see on ratemyprofs. He was also probably the best professor I've had. Meanwhile, another favorite prof of mine had terrible reviews because he was Japanese and had an accent, but all of my friends who were serious about learning agreed that he was a good professor. My recommendation on finding the quality of a professor is to search if your university makes student evaluations available. Mine allows anyone with a university email to see the evaluations, which is what I usually used to preliminarily evaluate professors.
How to sterilize surgical instruments?
If I don't have autoclave?
will putting in in oven for 5 min at 200 C enough?
>>8072077
what're ye cuttin into boy, depends how clean we need er
>>8072085
Enough to kill hepatitis virus if need to.
I have suturing kit at home.
How do I sterilize it after I use it?
Soaking it in iodine solution? putting it in oven?
It's stainless steel needle holder, hemostat, scissor, toothed forceps.
>Trigger warning, retard post ahead
Heyo, okay so a really retarded question, say we got two numbers, for ex. 18 and 7. And let's say there's a task saying 18 is couple of times bigger than 7, and it asks us to set up an equation to calculate it.
Firstly, I'd set it up as, 18=x7.
Secondly, I have no fucking idea what that means.
Funny, I can set up an equation and I know that's the way it goes, it's "logical", but then again, I can't quite wrap my head around what it means.
Like, what the fuck does it even mean that 18 is a couple of times bigger than 7? Does it mean that both had to start out as 7s, and one became x times bigger? Or that 18 contains more of a certain number than 7? What's the exact relation?
pls I know I'm a retard, just help me out this once.
If we take an exothermic reaction of 2 reagents and then repeat the same reaction with the same reagents but now using 1000 times the amount of reagents we used first, then the temperature increase of the mixture should be the same in both cases right?
When entering into a Master's program, is it normal to not get a research or teaching assistantship during your first year? (I'm assuming they're based moreso on a year-basis rather than semester.) I know a lot would depend on the program itself and the length and whatnot, many variables, but I figured it may be more realistic during the second year?
Look at the pic bros what are the steps involved in between, I understand the derivation up until that point, but the book says it's trivial after please help.
This is proving the convolution theorem, and tilda (~) represents the Fourier transforms
>>8069905
Hi /sci/!
How do I know if a language is regular OR context-free but not regular OR non-context-free?
My book is giving me fuckall on this distinction.
>>8073548
the top one is clearly the inverse fourier transform of
[math]\widetilde{f}(p) \widetilde{w}(p)[/math]
>>8073620
Oh...
I'm retarded lmao, cheers man
Is it possible to calculate distance of n-dimensions with n being greater than 3?
>>8073874
the distance of what?
>>8073904
You answered your own questions.
As a beginner the last thing you need is hard theory, just intuition and hands on experience, as this is the only thing you will need until you are like doing the circuitry of the LHC or some shit.
I remember when I was a teen the first thing I used my UNO for was making a simple circuit that got the input from two button-like switches, then I wrote in C (in the arduino IDE) a program that would send a specific character depending on which button was pressed, and then I wrote a program in C++ that would just loop endlessly while catching input from the C program and then depending on the character it received from the C program it would use windows,h to send to the operating system specific keyboard commands (the keys Z and X) and then I used my arduino controller to play 'OSU!', which is a rhythm game.
Good times.
>>8073922
Yeah that was a really lazy post on my part. I've found the resources I've need since then. Thanks anyway.
>>8069905
Someone please explain me what the fuck should I get from this. I know a capaitor sort of stores electricity for very little before releasing a lot, and resistor is meant to (slightly?) restrict the current or something, and that I can ignore the ground thing, but I don't really know to put this together to explain what is happening here.
How do you write a discussion for a report?
Nobody cares of you, do it yourself
>>8074088
you can't even english, shut the fuck up faggot
>>8073973
Closing the switch will charge the capacitor. The current charging the capacitor will also be going to ground through the resistor but this will not effect how fast the capacitor charges (you can assume that happens instantaneously). When the switch is opened the capacitor will discharge through the resistor following a decay function.
>>8073920
the distance between two objects in the >3 dimesion
>>8074402
yeah but there are different distances like euclidian, hamming, geodesic, etc
This is a simple question about rectilinear movement, I already know the answer but I don't understand a thing. Example:
>car traveling at 15.5555m/s
>there's a wall 34m in that direction
>hits the brakes instantly
>four seconds later in hits the wall
What was the average deceleration of the car? This is how I think it:
>15.5555m/s
>multiply it by 4 seconds, that's how far it should've gone without deceleration, 62.222m
>take 34m from the 62.222m, answer is 28.222m; this is the distance lost because of the braking
>divide 28.222m by 4 seconds, to know the average braking; answer is 7.0555m/s
I solved it with a software online and it turns out that the answer should be 3.5278m/s, which is the half of what I got. My question is, Why should I divide by two? What am I not considering?
>>8075007
Why are you measuring deceleration in m/s and not m/s^2?
>>8075013
I typed it wrong, but I know what you mean. I don't see the logic behind dividing by 2 though.
>>8075007
look up the derivation of this equation
>>8075022
It's not as simple as "typed it wrong". Your units are wrong, which is a huge red flag that your method is not correct.
You derived a velocity, not a deceleration.
You know distance, initial velocity, and time. That's enough to solve for deceleration.
>>8073973
when the switch is open, the input current starts charging the capacitor up. Because you have a resistor in parallel, the voltage is going to taper off, forming a sharkfin-like curve. When the voltage reaches a set threshold, the switch is going to deplete the charge from the capacitor instantly and the whole cycle is going to repeat itself.
You basically have a sort of oscillator. The frequency of oscillation is controlled by the threshold voltage of the pulse thingy on the right.
>>8074122
nope, gtfo
>>8075052
Please don't. I'm doing it this way because I don't want to even look at the formulas. Also I'm trying to avoid calculus as much as possible, since I should be able to solve this by imagining the situation instead, right?
>>8075054
I just wrote the units here so you could understand, when I do it IRL I don't use units or signs. I just add the units at the end based on what they should represent and add the signs (also at the end) based on the direction the stuff was going.
So far I've discovered that my method always yields twice the amount of the answer, and my guess is that since I broke the 62.222m in two intervals and then accounted for the braking of only the 28.222m one (but not the 34m one), I somehow have to compensate for that by halving the result. I don't know why it makes sense mathematically but it gives me the same result the software does. Do you know if that's the reason of the 1/2?
>>8075007
if the car hits the wall, it clearly hasn't decelerated enough to give you any sort of useful information
the velocity on impact could have been 0.0001m/s, 5m/s or 15m/s
flawed question
>>8075066
the reason for the 1/2 is innately related to calculus and the fact that acceleration is the integral of velocity
>>8075071
>acceleration is the integral of velocity
Derivative, sorry i've been up very long XD
>>8075066
> I'm trying to avoid calculus
> avoiding the mathematical study of change
> on a problem about change
> what am I missing here?
I think I found the problem bub.
>>8075066
>quadratic equation
>calculus
does it hurt to be this fucking stupid?
>>8075066
why are you trying to avoid calculus? it's not a very hard thing to do, especially with regards to what you are trying to understand, and without at least an intuition for calculus you won't get the intuition for this problem.
>>8075078
the kinematic equations are derived using calculus, which is what I think he meant
>>8075076
People solved these problems hundreds of years before calculus even existed though. I should be able to solve it by imagining the car moving.
>>8075078
>>8075079
I am very good at calculus, but right now I have a medical condition that makes it extremely hard for me to think about abstract stuff. If I can't see in my mind the situation the numbers represent I won't be able to understand it. That's why I'm avoiding formulas and other stuff I can't imagine.
>>8075087
>I am very good at calculus, but right now I have a medical condition that makes it extremely hard for me to think about abstract stuff. If I can't see in my mind the situation the numbers represent I won't be able to understand it. That's why I'm avoiding formulas and other stuff I can't imagine.
lmao what the fuck
>>8075079
using the derived equations still doesn't require any sort of integration or differentiation, just some equation flipping
>>8075087
Ok here's a way to understand it assuming linear deceleration
The area under the velocity curve is the distance traveled (since the area is simply velocity * time at each point). We can express this area as a trapezoid
A = .5(B1+B2)*h
The two bases are simply the first and final velocity, while height is the time it takes (4 seconds in your problem), which is t. So,
d = 1/2 * (v0+vf)*t
We know that vf is simply v0+at. So,
d = 1/2(v0+v0+at)*t
d = v0 + 1/2*a*t^2
>>8075087
Pretty sure deceleration is a calculus term.
>>8075096
I guess this uses calculus since it uses \sort of Riemann sum but I don't know how else to explain it
>>8075096
>>8075104
I really appreciate the fact that you went the extra mile to draw that image (albeit shitty), it's more than what most people would do. Thanks. I can't totally understand it from what you typed, but I know what you meant because I remember that concept. For now I will keep dividing my stuff by 1/2 and that should be enough to make my homework.
>>8075112
trying to salve my soul for gorilla posting
I have this formula/ theorem/ whatever saved on my computer and don't remember what is is. What is it?
>>8075151
https://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign
>>8075066
Bruh. The calculus required for uniform acceleration is grade school level. Literally all you need to know is what the area of a rectangle, and what the area of a triangle is to derive that formula
>>8075173
Fill up your report with cancerous memes
professors love cancer
>>8070025
hm it appears you go to mesa
Let [math]z = x^2y^3[/math]
Then is the following correct?
[eqn]\frac{dz}{dx} = 2xy^3 + 3x^2y^2 \frac{dy}{dx} \\
\frac{dz}{dy} = 3x^2y^2 + 2xy^3 \frac{dx}{dy} \\
\frac{โz}{โx} = 2xy^3 \\
\frac{โz}{โy} = 3x^2y^2[/eqn]
>>8075327
The partial derivatives are correct. But the first two derivatives I have no clue what the fuck you even tried doing.
>>8075331
Implicit differentiation. Like if [math]x^2y^3 = 1[/math] and I have to find the derivative at a certain point.
>>8075334
Okay, bad example.
Try [math]x^2y^3 + x^3y+2 = 1[/math].
>>8075336
Oops
[math]x^2y^3 + x^3y^2 = 1[/math]
>>8075331
First two are the total derivative
>>8075007
>>this is the distance lost because of the braking
No it's the distance lost because you hit a fucking wall in addition to the braking.
What's the difference between equilibrium points and attractors in dynamical systems?
Sorry if this isn't the right place for this, first time on this board.
If I have a 1350 gph pump which is pushing water through a coil of about 80 feet of half inch pipe, is the full 1350 gallons going to be making it through or will there be resistance?
How can I calculate how much water is actually going to make it through?
Okay, so I have a few doubts.
I'm starting ME next year, hopefully on a scholarship abroad, if I get chosen. I plan on doing my 4 years of career and then try to go for a Master's.
Is it worth to go the Masters with an ME degree?, how much further will it take me in my career? (I want to make good money and I like to learn)
What are my other options?
Also, advice for what to do during my 4 years of education to ensure my success?
Given [math] y=ax^2 + \frac{b}{x}[/math]
An open water tank is in the form of a circular cylinder having its base horizontal & axis vertical.
The costs are: In terms of
a for each unit area of base
b for each unit area of curved surface
c for total cost
Given radius is x cm, express volume of tank in terms of x, a, b and c. If x varies, find the cost of base when volume is maximum.
How am I supposed to solve this problem?
Mind helping me? Please.
>>8077107
a and b are constants
differentiate to find the maximum
>>8077096
By the time you graduate, a master's might be a requirement or highly preferred for getting your PE in the U.S.
If you have any idea what you want to do with your degree, contact the relevant engineering society. For whatever kind of work you want to go into, there's an organisation that would love to buy you a beer and show you the ropes.
>>8077096
Don't get a PhD if you don't want to do research.
Sign up for internships (srsly)
If you can't find a normal job, get someone to pay for you masters.
t. perpetual ME grad student
I graduate with my BS in EE in December. Ive talked to a professor at another university about graduate research and she agreed to offer me funding after I apply, etc. Basically all I have to do is get accepted to the university and I will have funding for a master's degree.
I told her I'd take the gre in June. I have a magoosh account already. What else should I do to do well on the gre?
If [math]G \cong G'[/math], and for some [math]H \leqslant G, H' \leqslant G' [/math] we have that [math]H \cong H' [/math], is [math] G/H \cong G'/H' [/math] ?
>>8069905
So I'm currently just fucking around and had the idea that I want to find all points shared by two circles.
My circles are:
I 1.4 = sqrt(x^2 + y^2)
II 1.4 = sqrt((x+2)^2 + (y-2)^2)
when I set them equal I got the equation
I = II: 0 = x - y +2
That's a simple function, but not all shared points. What do I do with this?
>>8078391
Wolfram alpha btw tells me that I did not fuck up the algebra
>>8078382
Is that Bjรถrk?
>>8078391
Use 2 functions rather than one equation
>>8078403
I'm retarded and sadly do not understand what you encourage me to do. Can you pretty please explain to me what I do need to do?
>>8078402
yeeees
>>8078391
Those are circunferences, not circles. The circles are
[math] D_1 = \{ (x,y) \in \mathbb{R}^2: \ 1.4 \geq \sqrt{x^2 + y^2} \} [/math]
[math] D_2 = \{ (x,y) \in \mathbb{R}^2: \ 1.4 \geq \sqrt{(x+2)^2 + (y-2)^2} \} [/math]
And you are looking for [math] D_1 \cap D_2[/math]
>>8078450
That makes sense! Sorry for being that stupid and thank you! Now I just need to figure out how the hell I will calculate that.
>>8078450
.. can you give me a point in the right direction please? I know that I need to somehow calculate the intersection of both sets, but I'm totally stuck on how I would go about calculating that.
>>8078627
>In general, the intersection doesn't have a simple expression, you can try operating with the inequalities that define the sets but probably there isn't much to do.
Can you please tell me more about that? My algebra sucks sadly in regads to inequalities.
>>8071479
Algebraic, enumerative, arithmetic, etc... geometries are all widely studied and none of them are inherently differential but there are correspondences still of course. Complex differential geometry has strong ties to algebraic geometry for example.
>>8078629
I'll elaborate a bit. You know the circles satisfy the inequalities
[math] x^2 + y^2 \leq r^2 \quad (1) [/math]
and
[math] (x-a)^2 + (y-b)^2 \leq r^2 \quad (2) [/math]
but you probably can't get an expression as simple as (1) or (2) for the intersection. A reasonable try might be considering the circunferences
[math] x^2 + y^2 = r^2 [/math]
and
[math] (x-a)^2 + (y-b)^2 = r^2 [/math]
and calculating their cut points (2, 1 or none). If there are none, the intersection is the empty set. If it's one, the intersection is that point. If they are two, then you can define a function by parts (call it f) and the intersection of the circles may be the points that satisfy [math] f(x,y) \leq 0 [/math] if f is properly defined. But again, the expression of f might be intractable.
>>8078450
>Those are circunferences, not circles
You literally just gave him the equation for a disk not a circle.
[math] S^1 = \{ (x,y) \in \mathbb{R} ^2 | x^2 + y^2 =1 \} [/math]
>>8078649
So I would solve the equation:
[math]x^{2} + y^{2} = (x-a)^{2} + (x-b)^{2}[/math]
if I understand you right. In my example I got the term
[math]x - y + 2 = 0[/math]
which has infinite solutions. Does this mean that this would have no cut points and hence that both circles do not touch? Would this be a sufficient prove for this?
>>8078665
That means you are forgetting to impose [math] x^2 + y^2 = r^2 [/math] (you should have cleared y or x, not r).
>>8078671
Sorry, but I do not understand what you're trying to tell me.
In my case [math]x^{2} + y^{2} = r^{2}[/math] is [math]x^{2} + y^{2} = 1.4^{2} [/math] because [math]\sqrt{x^{2} + y^{2}} = 1.4^{2}[/math] was my original circumference. (See >>8078391
). What am I missing here? This should be the same case for the second circumference and then both are equal to [math]r^{2} = 1.4^{2}[/math], hence why I should be able to set them equal and solve them for the cut points.
Am I retarded or what am I missing here?
>>8078687
The second term should be [math]\sqrt{x^{2} + x^{2}} = 1.4[/math]
>>8078687
The equation [math] x^2 + y^2 = (x-a)^2 + (y-b)^2 [/math] is entirely correct, it just doesn't have all the information. You have to solve
[math] x^2 + y^2 = (x-a)^2 + (y-b)^2 = r^2 [/math]
which are two equations. You partially solved them in your particular case with the
[math] x-y+2=0 [/math]
but you have to intersect that line with one of the circumferences.
>>8078689
So I'm trying to solve:
[math]\begin{cases} x^{2} + y^{2} = 1.4^{2}\\
(x+2)^{2} + (y-2)^{2} = 1.4^{2} \end{cases}
[/math]?
If I set [math]x - y + 2 = \sqrt{x^{2}+y^{2}}[/math] into the plot I only get this strange curve, but I think I should get an true statement as there are not cut points between both circles.
I'll guess I'll repost this from the old /sqt/ thread.
What separates a formal system from a deduction system in that formal system?
Why is decidability an important property in systems like first-order logic which is semidecidable but in every case where it is not decidable the reason it is not is because the process is infinite. Is this something that is only important for computers?
>>8078700
[math] x-y+2 = \sqrt{x^2 + y^2} [/math] means 0=1.4, it's obviously a nonsense. Solve either the system you posted or
[math]x-y+2 = 0, \quad x^2 + y^2 = r^2[/math]
For r=1.4 there aren't going to be any real solutions obviously.
Can humans manipulate spacetime in a way that allows us to travel between 2 point without actually having to traverse the distance between them?
>>8078708
I got an idea and solved [math]0 = x - y +2[/math] for x and [math]1.4^{2} = x^2 + y^2[/math] for x so that I could set them equal which resulted in a false statement. Is this know sufficient do prove that there are not cut points?
>>8078718
Absolutely.
>>8078721
Thank you very much!
How can I prove that a equation has no real solutions?
>>8078734
step 1
>be Abel
then profit
>>8078713
Nope
>>8078734
If your equation is a polynomial then you just have to show that it is irreducible over the real numbers.
If the roots are easy enough to find, you could just find all the roots and if none of them are real numbers you're done.
Question about rings.
I have this ring, R: [math]\mathbb{Z}[\sqrt{-2}]={a+b\sqrt{2}i/a,b\epsilon \mathbb{Z}}[/math]
I have the norm, N, [math]N(a+b\sqrt{2}i)=(a+b\sqrt{2}i)*(a-b\sqrt{2}i)=a^2+2b^2[/math]
If N(x)=p, with p being a prime number, how can I determine if x is irreducible? I think I need to prove R is an UFD, but don't know why.
How do i do this question?
Express x^2 + 4kx + (3 + 11k) = 0
In the form (x + p)^2 + q
Had this question in a test today and couldnt get anywhere with it.
>>8078917
intro to number theory?
N(ab) = N(a)N(b) so if x = ab then what can N(a) and N(b) be?
>>8078922
why not try to expand (x+p)^2 +q and then fit with x^2 + 4kx + (3+11k) ??
p will be uniquely determined by the factor in fron of x^1.
q will be determined from p and the constant.
>>8078930
Oh, so since N(x)=N(a)N(b) and N(x) is prime, N(a) and N(b) have to be 1 and N(x), is that it?
What is the best way to learn? People around me keep telling me that I should forgot about sleep if I want to study in a university, but a have seen many articles which says that sleep is very important for retaining newly acquired information. So how much do I really need to rest/work?
I have tried mind palace technique to memorize, but I have quickly ran out of places in my mind where to put information, and buildings which I create with my imagination quickly fade away... Any tips on this?
>>8078936
So (x+p)^2 + q = x^2 + 2xp + p^2 + q
=
(x+p)^2 + 4kx + (3 + 11k)
4k = p and 3 + 11k = q
Im not getting how to make the connection between the real term values for k, p and q from the variables.
>>8078945
Yes, you get a contradiction otherwise
>>8078917
>I think I need to prove R is an UFD
I'm not so sure
11=(3+2sqrt(2)i)(3-2sqrt(2)i)
11=11*1
5=(1+sqrt(2)i)(1-sqrt(2)i)
5=1*5
or am I misunderstanding something
>>8078959
Great, thanks for the help.
>>8078734
Study the variations of the function. It is probably differentiable so you need only prove that it does not vanish.
The problem is thus reduced to studying the extrema of the function, ie. where the derivative vanishes
>>8078960
11 and 5 aren't prime in [math]\displaystyle \mathbb Z[\sqrt {-2}][/math]. Also, I think you typed those incorrectly because those equations don't work out.
>>8078882
The only irreducible polynomials over [math]\mathbb R[/math] have degree 1 or 2, and proving irreducibility is in general much harder than proving something has no roots. This is a garbage post.
Is there a shortcut to this sum? I mean doing it by hand takes a long time and there is a very short test time.
[math] \sum_{k=0}^{10} \binom {10} {k} [/math]
>>8079269
What does [math]\displaystyle \binom {10} {k}[/math] count?
>>8079278
the exercise just goes
[math] \sum_{k=0}^{10} \binom {10} {k} [/math]
where [math] \binom {10} {k} = \frac{n!}{(n-k)!k!}[/math]
I mean I know how to get to the answer but I take a fuck ton of time, is there a better way?
>>8079290
Yes, there's a very short way that I am trying to hint towards. Ignore the formula for it -- what does a binomial coefficient actually count?
>>8079290
Think about what the binomial coefficient is saying. How many ways to choose 1 out of 10 plus how many ways to choose 2 out of 10, etc.
>>8079293
>>8079291
Oh shit, I think I got it.
Because [math] \sum_{k=0}^{10} \binom {10} {k} [/math] is like expanding by the binomial theorem but where both terms, a and b HAVE to be 1. Or else it wouldn't be [math] \binom {10} {k} [/math]
So it boils down to [math] (1+1)^n[/math] , n is 10 so 2^10=1024. fuck why couldn't I think of that before, I'm a retard.
Thanks for the help guys, would you mind formalizing my train of thought? I mean telling me exactly why it's like this. If it's not a bother of course.
>>8079344
You have 10 objects. You want to have a collection with these 10 objects. With each object, you can choose to include it or not include it in your collection. To count all of the possible ways, you allow all possibilities of including and not including your 10 objects. Thus, the answer is [math]2^10[/math] because it is (include or not include) 10 times.
>>8079402
Woah, this makes so much sense. Thank you for explaining it to me this way, how do I develop this kind of intuition for it? I feel like I've been learning math too mechanically....
I'm using mit-scheme, and I have code that is absolute breaking when I run
(append (list '+ num)vars)
where vars is defined in a let clause by
(vars (filter-not number? (cons a1 an)))
It gives me the error: " ;Unbound variable: |รข|
;To continue, call RESTART with an option number:" If I get rid of the let clause and write out the full phrase for vars everywhere, it works fine. However, this is not ideal because it shows up in another place. What the hell is going on? I can post more code if need be.
Since gravity is a theory, is it because gravitons have not been observed yet? Or is there more to it than that?
Trying to do a simple deconvolution.
I have an image I in MATLAB. I convolve it with a filter using conv2(I, h).
Let's say this gives me a resulting 258x258 filtered image named If given h = 3x3 and I = 256x256. Given the 258x258 filtered image and h, I want to recover I.
I've tried doing fft2(If) and fft2(h3, 258, 258), changing a 0 in fft2 of h3 to eps + eps*i, and then doing ifft2((the division), 256, 256), but I get a weird answer. If I don't truncate (i.e. leave it at 258x258), I get something close to the original but it's darker and obviously not the same size.
I can't see what the issue is, any advice?
>>8078382
Think Z and 2Z, 3Z for instance. The quotients are different
>>8075066
Lets say the average deceleration is a. Then your average speed is
(16+(16+4a)/2=16+2a
It is also 34/4=17/2
so we get that
16+2a=17/2
4a=17-32=15
a=15/4=3,75m/s^2
I rounded your velocity before to 16.
>>8069905
I've got a really dumb one. Years of advanced mathematics have killed my arithmetic skills.
What does subtraction actually give?
Like say I do 9-3=6. This is one plus the number of numbers between 9 and 3, is there a better way of looking at it? My intuition fucks with me if I try to do something like figure out the number of years between 2004 and 2009, my instinct is 2009-2004=5 which is, in fact wrong.
>>8080603
remove 2003 and "count".
2004-2003 -> 1
2005-2003 -> 2
...
2009-2003->6
1,2,3,4,5,6 -> 6 years
Hey Anons, 2nd Semester math student here, I just found myself completely confused, I don't know is it the lack of sleep of what. If I have a matrix [math] \begin{bmatrix}
1&1\\
0&1\\
\end{bmatrix} [/math] why is this not the same as a matrix with only 1 and 1 on the diagonal? If I can reduce the rows below why can't I do it above? What changes when I reduce the rows? I know the characteristic polynomial woudn't always be the same, but my geometric multiplicity also gets screwed when I row reduce it?
>>8080666
do linear maps ring a bell?
if your matrix is associated to a linear map A using a basis (b1,b2), then
A(b1) = b1
A(b2) = b1+b2
this is different from the identity for which:
I(b1)=b1
I(b2)=b2
>>8069905
Can anyone explain me this slide? I think I know what an N-dimensional polynomial is. For example for n=2 [math]P_2(x,y) = \sum_{k=0}^{n} a_k x^{i} y^{j}[/math] where [math]i+j<=k[/math]. But I don't see what the slides is saying
>>8080655
What about when it's too big of a cap to count?
>>8080754
Holy shit dude.
2009 - 2005 takes the numbers 1 through 2009, and removes everything up to and including 2005, so you're left with 2006, 2007, 2008, 2009. So you're always overcounting by exactly 1.
>>8080666
You can reduce rows down, it's just that row reduction changes one matrix into another.
>>8069909
bout tree fiddy
>>8078705
Pls help
>>8080713
looks to me they are treating the coordinates separately , so P_x =\sum c_k x^k and P_y = \sum d_k y^k
nobody says "N-dimensional polynomial" I think they just mean degree.
>>8079956
maybe you need to pad before using fft to deconvolve? I always get these things wrong at first... takes a lot of playing around to get it right.
>>8079956
also, maybe matlab has a deconv function?
>>8069905
Are General Genetics classes really as hard as premed students make them sound?
I didn't think it'd be too much different from your average bio class, but I've heard a lot of pre-med guys complain, and now I'm starting to doubt my schedule for next year.
[math] 2cosx- 3 < 0[/math] for [math]0<x<2\pi [/math]
find [math] ( )\pi <x <( )\pi[/math]
Does this question make sense? Or is there a mistake here, I mean
2cosx-3<0 implies that cosx<3/2, but that isn't possible, is it?
