SQT Stupid Questions Thread

>A rock is tossed straight up with a speed of 22 m/s When it returns, it falls into a hole 10 m deep.

how do i find the final velocity as it hits the bottom of the hole?

i know this is a retarded question, but the formula vf^2=Vi^2+2a(xf-xi) doesn't get me the right answer

>>8355088
You first have to find out how far up the rock goes, then add that length to your 10 meters and then do the calculation.

Use
s = s_0 + v_0 * t + a * t^2
to find out how far up the rock goes.
Then add the 2 lengths and use that same equation for finding out how long it takes the rock to fall down to the bottom og the hole.
Then use
v = v_0 + a * t
to find out the final velocity of the rock.

>>8355059
p series

>>8355176
but i don't have the time, so what do i do about t in that first equation?

>>8355192
You have initial velocity
You have the displacement
And you have your acceleration
Find time through quadratic equation

>>8355192
I can't spoonfeed you any more than that, this is grade 10 tier physics.
>>8355190
P-series or power series? Haven't taken power series yet

>>8355192
Use the other equation that doesn't need time
v^2 = vi^2 + 2g(x – x0)

>>8355212
p-series. given 1/x^p if p > 1, conv

>>8355239

[math]\sum_{n=30}^{\infty}(\frac{1}{lnn})^{lnn}[/math]

[math]n > 30[/math]

[math]lnn > ln30[/math]

[math]\frac{1}{lnn^{lnn}} < \frac{1}{(ln30)^{lnn}}[/math]

[math]\frac{1}{lnn^{lnn}} < \frac{1}{n^{ln30}}[/math]

[math]\sum_{n=30}^{\infty}\frac{1}{n^{ln30}}[/math] converges by p-series as [math]p=ln30 > 1[/math]
Is that what you meant?

Apparently there's a really fast way of integrating x^2 / (x^3+1)^2 which starts with the chain rule for the denominator, then does something weird and it's suddenly done.
The normal method would be to use both the chain rule and quotient rule making for one gigantic mess of a calculation.

I didn't quite understand it though and wasn't even sure if it was entirely valid, anyone know?

>>8355286

[math]\int\frac{x^2}{(x^3+1)^2}[/math]

Let [math]u = {x}^{3}+1[/math]

Then [math]u' = 3x^{2}[/math]

Hence [math]dx = \frac{du}{3x^2}[/math]

Substitute dx with du and you get

[math]\frac{1}{3}\int\frac{du}[u^2}[/math]

Was this it?

>>8355286
i dont see how you're possibly applying the chain rule but you just substitute u=x^3+1, du=3x^2dx and then its easy to integrate

>>8355303

[math]\int\frac{du}{3u^2}[/math]

>>8355305
I just remembered this was integration and not differentiation.
Running on 4 hours sleep is like being drunk yet appearing sober.

>>8355270

Not him, but yes, that's pretty much how that works. Don't forget that it's also an exponential function, which will further increase p and make it converge "faster".

>>8355218
that equation just gets me 24.7 which doesn't make any sense

maybe i should just an hero :(

>>8355335
You should. You should also be over the age of 18 to post here.

>>8355088

Just use the difference in energy.

>>8355335
How the fuck did you get a 24.7?

[math]v_{f]^{2} = v_{0}^{2} + 2g(x_{f} - x_{o})[/math]

[math]v_{f} = \sqrt{v_{0}^{2} + 2g(x_{f} - x_{o})}[/math]

[math]v_{f} = \sqrt{22^2 + 2(9.8)(10)}[/math]

[math]v_{f} = 26.1[/math]

>>8355059

No idea what you're asking in the first question.

For the second, I assume that you mean:

[math]\sum_{n=2}^{\infty}\left(\frac{1}{(e^n+1)}\right)[/math]

If you're happy that 1/(2^n) converges, then you can compare it with this and see that the denominator of each term will be smaller for your series.

[math]\sum_{n=2}^{\infty}\left(\frac{1}{(e^n+1)}\right) < \sum_{n=2}^{\infty}\left(\frac{1}{(e^n)}\right) < \sum_{n=2}^{\infty}\left(\frac{1}{(2^n)}\right)[/math]

Since the value of the series will be obviously non-zero, but less than a half (the value of the 2^n series), then it can't diverge i.e. it has some finite value in that region. Indeed, you could use the formula for a geometric series to find the value of the middle term and it must be smaller than that.

It doesn't help you with the value of the series (if it even exists in closed form).

Does anyone know some good books that introduce modern physics? I'm having difficulty understanding relativity fully.

>>8355530
What's your mathematical background?

>>8355558
Finished Calc 1-3, in Differential Equations right now.

how the fuck does cos(arctan x) simplify to 1 / sqrt(1 + x^2)

Why is:

If 1 + 1 = 3, then unicorns exist.

true? The two statements are completely unrelated.

>>8355583
just draw a right triangle bro

>>8355690
nice troll

>>8355684
if (x) then (y) means Not(x and Not y).
In other words, the only way that If (x) then (y) could fail to be true is if x=True and y=False.

Now if x=False, then (x and Not y)=False, no matter what y is.
Thus If (x) then (y)=Not(x and Not y)=Not(False)=True.

Is calculus as hard as it is made up to be?
Studying Fourier Analysis btw.

>>8355700
It's the verse-inverse Pythagorean divide.

arctan is literally the same thing as arcsin(x/sqrt(x^2+1)). When you cos an arccos, you get 1 because 1/1 = 1. When you cos an arctan, you treat it like an arcsin. cos is sin(phi/4 - theta), so you get the denominator of arctan, ergo, cos(arctan(x)) = 1/sqrt(x^2+1).

Also, whoever invented trigonometry is retarded, powers of variables are always in descending order.

How do I get a function in frequency domain from that functions magnitude and phase? I was thinking of convolution but IIRC that's only for two frequency domain signals which magnitude and phase aren't.

Why is /sci/ more pessimistic than optimistic? Or is everyone too cynical?

I've been grinding away at an ODE for the last 3 hours without any progress, any tips/tricks/hints/etc?
dy/dx + (y^3)sin(x) = (y)e^(x^2) + (y^2)/((x^2)+1)

I can't help think it's something simple that I'm missing since it's of the form dy/dx = ay^3 + by^2 +cy. Tried to set it up as an exact equation, in the form Mdx +Ndy = 0, but the dM/dy kept going to 0. It's not linear, not separable, I tried to use the whole Bernoulli integrating factor method and that didn't work. I'm starting to go a little bit crazy.

>>8355561
I've only read one which was for my intro Modern Physics class, but I liked it. Modern Physics by Harris, the relativity bit made sense to me.

>>8355739
No. Just do enough practice problems and you'll get most of the tricks that'll get thrown at you.

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>>8355059
What the flying fuck are conformal blocks? I've been reading about conformal field theory and particle statistics and I have been encountering this nomenclature everywhere in the paper.
I understand that it's basically the conformally invariant part of an n-point correlation function but why is it called a "block"?

Hope you don't mind if I cross-post this here:

>>>/wsr/192374

Why is dividing fractions so much more elegant than diving integers?

>>8355684
math equivalent

(2 > 5) --> (2+3 > 5+3)

>>8355088
Notice that at it's peak the rock will have 0 velocity, then use conservation of energy to find velocity.

>>8355684

Neither of those things exist, thus the statement is true.

If P is 1+1=3 and Q is "unicorns exist"

Then the statement fails only if Q fails, and P is true. Basically, P is the assumption, but the conclusion, Q, was wrong. If they're both wrong (false), then it's a "true" statement, because neither of those things exist.

how long till we get software that scans people and animates a 3d porno that looks like them and lookes 100% real

lol

Will diamond spontaneously decompose into graphite even without the very high temperature the reaction requires, just very slowly?

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>>8356103
because the rationals form a field while the integers dont

Is global warming just a meme? How do I know for sure?

>>8355768

Do you know if there's an explicit solution? If not, I would advise a numerical method. That e^(x^2) term in particular is very nasty.

>>8355768
could try a continued fraction method?
http://digitalcommons.uconn.edu/cgi/viewcontent.cgi?article=1079&context=chem_educ

Lads is there a way to calculate the limit of a matrix? This is a question coming from someone studying input output theorem

How do I find the charge on the surfaces of two concentrical spheres? For example, say I have a hollow sphere of a certain net charge, with a solid sphere of another net charge enclosed in the hollow sphere. I know the all of my necessary radii.

How do I go about determining what amount of charge is distributed on the outer surface of the inner sphere, the inner surface of the outer sphere, and the outer surface of the outer sphere?

I am in an intro course and my initial guess was something like q/(4pi*r^2) but I do not think I am on the right track.

Thanks for any pointers!

>>8356734
concentric*

I'm learning VERY basic topology concepts, in particular proving that something is a metric space. Beyond really simple examples, I keep getting hung up on the triangle inequality condition. Is there a general approach I'm not aware of?

Where's the best place to study maths?

hey guys please do not bully me for this question

if you got a number like 1/3 you are infinitely adding a number that is 1/10 of the previous number

but if you are infinitely adding a number that is greater than 0 why dont you end up with infinity ?

i was studying for a test and then there was this question
we have the polynomial p(x), which has 5 roots between -1 and 1 (pic related) and to find each root (besides 0) we need to use a different method

all methods worked fine but Newton-Raphson using x0 = -0.8, E = 10^-5;
when i use the computer it works just fine, but when i try to make it just using paper, pen and calculator its diverging, ie the x1 ~~ -1.1 which is outside [-1; 1]

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>>8357105
forgot the pic

>>8357085
>if you got a number like 1/3 you are infinitely adding a number that is 1/10 of the previous number
only in base 10 and only when you allow negative exponents in your positional notation (so don't do this)

All rationals have a finite representation. At the very least you can choose a base for your positional notation which shares all the prime factors of your denominator, and then even allowing negative exponents in your positional notation will result in a finite expression.

e.g. 1/3 in base 3 is 0.1

>>8357105
When using Newton's method, each root has a basin of attraction where starting from any value in this basin will eventually lead you to the root. But in general the shape of the basin is very complicated and there's not guarantee that your first few iterations won't wander a bit.

>>8357119
you're right, i just keep doing it and eventually it started to converge to the solution
thanks for the patience and sorry for the stupid question

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It struck me that this picture may be right, should we be mapping these lines of force? (Determined by gravitational inconsistencies) to discover if there is a grid rather than randomness?

Areas of differing potential provide a posdible means of future energy extraction.

>>8357135
I'm interested, what other methods did you use to find the other roots?

>>8357146
those are not lield lines, this is a representation of the curvature of spacetime

>>8357112

So an ideal number system would be an infinitr-ary number system?

>>8357153
i'm not sure how they're are called in english, but they were:
newton-raphson
secants method
bisection method
linear iterative method

>>8356791
In practice you hardly ever have to prove something is a metric space, let alone something difficult. You mainly want to be able to prove it for the standard p-norms.

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>>8356791
its (usually) the only condition that can be non-trivial to prove, sometimes symmetry but not so often.

if youre the same anon who asked about the R2 triangle inequality before, it might be helpful to study more analysis first, i first learned metris spaces from kolmogorov's book and i found the pacing more appropriate

the notes you were using seemed a bit difficult if you don't already have a solid foundation. you occasionally need things like holder's inequality and minkowski's inequality in the kind of topology you're looking at

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How to solve this? I'm taking linear algebra

>>8357228
do you know how to compute an inverse at least? try one or two examples and it should be obvious
1 0
0 2

1 0 0
0 2 0
0 0 3

>>8357231
Yes, we are learning that. Thanks for your response, that helps

>>8357085
> but if you are infinitely adding a number that is greater than 0 why dont you end up with infinity ?

Take any monotonic increasing function which converges to a limit (e.g. f(x)=x/(x+1), which converges to 1), then start with f(0) and add f(1)-f(0), then f(2)-f(1), f(3)-f(2), etc. At each step you're adding some number greater than zero, but you don't end up with infinity.

>>8357228
(I hope the LaTeX here supports matrices. If not, I'll write it out and screencap it.)

Don't overcomplicate! A is diagonal, so let's suppose that A^-1 is diagonal too (just humour me):

[math]A =
\begin{pmatrix}
1 & 0& \cdots & 0 \\
0 & 2 & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & n
\end{pmatrix}[/math]

[math]A^{-1} =
\begin{pmatrix}
a & 0& \cdots & 0 \\
0 & b & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & ?
\end{pmatrix}[/math]

[math]A \cdot A^{-1} =
\begin{pmatrix}
1\cdot a & 0& \cdots & 0 \\
0 & 2 \cdot b & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & n \cdot ? \end{pmatrix} = \begin{pmatrix}
1 & 0& \cdots & 0 \\
0 & 1 & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & 1
\end{pmatrix}[/math]

It's easy, by inspection, to write down the ith element of [math]A^{-1}[/math] - it must be [math]\frac{1}{a_{i,i}}[/math]. Now I saw the 'trick' to the problem immediately by assuming that the inverse was diagonal, but I hope that this has justified it.

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I might actually be a goddamn retarded mongoloid but can you just spell out he fucking consumption matrix for this? Why the fuck isn't it stochastic? If you can find a mistake I might not kill myself literally now.

>>8357291
dont stochastic matrices have rows and columns that add to 1?

isnt this matrix just
( in basis manufacturing, agriculture, services)
0.2 0.3 0.1
0.4 0.1 0
0 0.5 0.6

?

>>8357297

yea, it should add up to 1 cuz consumption matrix need to be stochastic right? Like for instance where the hell does the other 0.4 that manufacturing products go???

>>8357304
>it should add up to 1 cuz consumption matrix need to be stochastic right?
i dont think so, why are you assuming it has to be stochastic?

these are just #s of units required from each, there's no reason they have to add up to 1

you could scale them so that they do, but you'd be measuring relative requirements, not actual requirements

>>8357319

I am a bit calmer now so let me get this right:

column interpretation of the matrix is that each column says how much of an industry A taking from industry A, B and C.

row interpretation of the matrix says this is what a given industry A give out to other industries.

So for instance the first row, manufacturing is producing a unit of a product and gave out exactly 0.6 of it, and the rest of it disappear into the 4th dimension? Or is the only requirement is that the row-sum is less than 1?

>>8357186
Ideal for what purpose? For expressing rationals with negative-exponent positional notation?

The best base in my opinion is no base at all: polynomials.

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>>8357354
but polynomials require coefficients from some ring

What is the archive for /sci/? Or alternately, link to the last /sqt/ pls.

>>8357365

>>8344746

For future reference, click on catalog to get to the archive. I don't know about a meta archive that holds everything. Did you want something specific?

>>8357365
>>8357383
https://warosu.org/sci/ for your future reference, sometimes it goes down due to what i assume is a lack of funding

Let f : A → B be a function. Show that
f is bijective ⇐⇒ ∀G ∈ P(A), f(A\G) = B\f(G), where P(A) is the set of all subsets of A.

I cannot think of a proof and I've been looking at this for at least an hour. I feel like all my proofs are just stating facts and/or making assumptions that go nowhere.

>>8357448
Look at elements: you want to show that if x is not in G if and only if f(x) is not in f(G).

>>8357531
Would that mean that I'd have to work with the inverse function? Since iff implies that I have to show that it goes both ways.

>>8357547
A bijection can be defined as a function with an inverse, so yes you can do that.

>>8357361
all positional notation does

>>8357281
Thank you for your detailed response, this helps a lot.

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3 masses are joined by massless rigid rods like pic related

A force (F1,F2) is applied to mass 3 for a dt amount of time(impulse?). What is the angular velocity and velocity of the system?

How do you even solve this kind of problems? Also how would you calculate the velocity and angular velocity of the system if there was gravity and it fell to the ground?

>>8357854
>How do you even solve this kind of problems?
Numerically.
This is basically the double pendulum, it has no analytical solution.

>>8357854
>rigid rod

hehe i've got one of those in my pants, if u know what i mean...

>>8357860
l thought the double pendulum had a solution using lagrangian. Can you give me an idea on how you'd solve this numerically? l literally have no idea how to approach. lt's for a computer program

>>8357860
the rods are not supposed to rotate, the angles a and b are static

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1. Can air bubbles act as a thin film lens, as I think is happening in pic related? (Fish/air in package in water)

2. If light cannot escape the gravity of a black hole, then how does hawking radiation?

>>8357920
hawking radiation is based on imaginary particles

particles and anti particles pop into existence and cancel each other out

the theory is that if this happens on an event horizon then one of the particles could be sucked into the black hole while the other escapes

>>8357885
this isn't related to your problem, since >>8357916 seems to address how to make yours solvable.

A Lagrangian formulation tells you the equations of motion governing a classical system. Whether or not those equations are solvable is something else entirely. In the case of a double pendulum, they're nonlinear coupled equations which are typically hopeless to find an analytical solution. Further, the equations make up a chaotic system where even if you use numerical methods, it's extremely sensitive to initial conditions and will essentially be in an unpredictable state beyond the first few seconds of simulation.

1) yes, these are typical problems in introductory optics involving soap bubbles/air bubbles. But you can get non-trivial structures from soap bubbles as well--something like optical caustics which are bright spots/fringes with patterns determined more by defects in the spherical shape of the bubble than thin film refraction.

2) hawking radiation doesn't come from within a blackhole and escape, it's the result of phenomena near the event horizon like >>8357940 states. The anti/particle pairs are referred to as *virtual* particles, not imaginary particles. They have very real effects on physical observables, such as an electron's magnetic moment.

i have one day to git gud for my first physics test
any tips?

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How do I do this problem? Been stuck on it for a while

>>8355059
How can this be true: [math] \displaystyle \sum_{k = 0}^{n} (-1)^{k} {{n}\choose{k}} = 0[/math]

If when [math] \displaystyle (-1)^{0} {{0}\choose{0}} = 1[/math]

I can't wrap my head around this proof...

>>8358355
Why does that second statement call the first into doubt?

The alternating minuses all cancel out

>>8356407
http://www.skepticalscience.com/

>>8357955
Soooo, how does a virtual particle falling IN
reduce the mass of the BH?

>>8358355
the binomial theorem says
(a+b)^n
= sum_{k=0}^n (n choose k)a^k*b^(n-k)

so if a=-1 and b=1 both sides are 0

why does solving on np-complete problem solve them all?

>>8358471
Because they are isomorphic. Specifically, every NP problem is polynomial-time reducible to an NP-complete one. So it takes some time to convert one into the other, but it's "negligible."

If time stands still for anything moving at the speed of light, does that mean that from a photon's perspective it experiences its entire timeline instantaneously?

>>8358121
Do you take physics 160...

>>8355088
Dont listen to the other retards

Calculate kinetic energy, add 10m potential energy, calculate speed

Really fucking simple

>>8358121
https://www.youtube.com/watch?v=-l0fLVh0Bas
What is that website btw? Is this the online textbook component which you're graded on?

Good book on probability theory? For statistical machine learning mostly. I dont know if I want to read Jaynes, 2000

>>8358474

Yes.

Help a complete retard with basic QM please

For spin 1/2 stern-gerlach

I have a state that is up in z-direction
Now I measure this state in x-direction.

Just apply Sx operator to |z;+> right?

[math] S_x| z;+ \rangle = \frac{\hbar}{2}\Big( | x;+ \rangle\langle x;-| + | x;- \rangle\langle x;+|\Big)| z;+ \rangle [/math]

What do i do now?

How do I calculate [math]\langle x;-|z;+\rangle , \langle x;+|z;+\rangle[/math]?

In order to get an object moving, you must push harder on it than it pushes back on you.


How the fuck is this false?

I'm trying to learn physics but my professor can't speak English and can't teach for shit. I am splitting a Chegg membership with my brother and it gives me all the answers, but I am not learning shit. Also:

An object is moving to the right, and experiencing a net force that is directed to the right. The magnitude of the force is decreasing with time. The speed of the object is increasing over time.


HOW? How is it going FASTER if the magnitude of the force pushing right is decreasing????? Like it seems so obvious what the answer is, but then the answer is the opposite of what makes sense?

>>8358794
Newton's first law.

An object with no forces acting upon it will remain at rest or continue to travel with constant velocity if it is moving.

As long as there is a net non-zero force acting upon the object, it will accelerate in the direction of this force.

I feel really stupid cause I am not seeing this, but here goes.

Let [math]p[/math] be a prime number. The amount of numbers in the discrete interval [math] [1, p^{n}] [/math] that are a multiple of [math]p[/math] equals [math]p^{n-1}[/math].

I can see that it is obviously true, but I cannot prove it.

Super noob math question:

sinx /< 1/2 for [0, 2pi]

I know this is true for b/w 5pi/6 and pi/6 on the circle but how do I represent it on interval notation.

is it just [0, pi/6] u [5pi/6, 2pi]?

>>8358799
But it says that the magnitude of the force is decreasing, how can the speed be increasing if the object is literally slowing down?

>>8358794
A force causes an object to accelerate, if there is a non zero force acting to the right then the object will accelerate to the right. So if its already moving right then it will get faster.

When there's no force acting on it then it will move at a constant speed and when a force is applied to the left it will accelerate to the left i.e. slow down its right movement.

>>8358834
Let's make a simple example.

You have an object at rest, that is v=0.

Apply a force that accelerates the object by 10m/s^2

After one second the object now has v=10m/s

Now after this second, decrease the force by half. This means that we accelerate the object with 5m/s^2

Waiting another second (t is now 2s) the object is moving at 15m/s.

Even though the force decreased, the object is moving even faster than before.

Now say we remove the force completely.

The object has velocity v=15m/s.

Since no force is acting upon it, it will maintain a velocity of v=15m/s until another force acts upon it.

>>8358841
This makes sense! Thanks. I am shitting myself in this class because I don't know anything.
By any chance:

Do you know any resources that would help me learn?

I am using the textbook, Chegg, and Khan Academy right now.

Beer's law Q:
Determination of the molar extinction coefficient for NADH

Trendline equation: y = 5.145x – 0.0288

molar extinction co-efficient: A = e * c * l, where l = 1cm

How would I PROVE the extinction coefficient which is e = 6.2 mM-1 cm-1?

Doubt anyone has an answer `

>>8358784
>>8358784
If you're measuring in the x direction you'll get up or down with some probability defined by the amplitudes of those eigenstates in the z state. You don't need to apply Sx, you just need to find the amplitudes.

You have the state [math]|\uparrow_z\rangle[/math] which is an eigenstate of the [math]S_z[/math] operator, you want to rewrite that in terms of [math]|\uparrow_x\rangle[/math] and [math]|\downarrow_x\rangle[/math] states which are eigenstates of the [math]S_x[/math] operator. This is easier to see with column vectors.

Writing in the [math]z[/math] basis:
[eqn]|\uparrow_z\rangle=\begin{pmatrix}1\\0\end{pmatrix},|\downarrow_z\rangle=\begin{pmatrix}0\\1\end{pmatrix},\space S_z=\frac{\hbar}{2}
\begin{pmatrix}
1 & 0\\
0 & -1
\end{pmatrix}, \space S_x = \frac{\hbar}{2}\begin{pmatrix}
0 & 1\\
1 & 0
\end{pmatrix}[/eqn]

It's easy to find the normalised eigenvectors of the [math]S_x[/math] so once you do that just do an inner product of each with [math]|\uparrow_z\rangle[/math] and the result will be the amplitudes.

What is the math for logic circuit called?

I saw a post once along the line of

c = ab + a + b where c E {0,1}

what is it called? I want to be able to prove stuffs like can we use SR-latch be used to implement other latches? If I have OR and AND, can I use them to do everything in a logic circuit?

is there an easy way to remember how to do matrix multiplication?

>>8358931
You just have to keep doing it and eventually it just sticks.

I guess one way to think of it is if you put the matrices on top of each other (so the top left corners are in the same place) then the shape of the intersection will be the shape of the result and the value at each entry will be the inner product of the row and column that intersect there. I don't know if that helps in doing it faster though.

>>8358931

remember up-side-down

you start "up" with the first what??

the first row ---> "side"

then you multiply it by what???

the first column ----> "down"

desu matrices are pretty dumb, like one time it's row x column the other it's column first then row.

>>8355059
If I have n different cosine functions which each have distinct phases, what is a basis for their span?
I'm assuming this problem already is considering the phase angles distinct mod 2pi.
What are some interesting ways to tackle this problem /sci/

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How does this look like?
I know its a circle but is there ahole in the middle? And is the whole think 4 big?

>>8359015
It will be a set of points on the 2D plane bound by two circles, one of radius 1 and one of radius 2.

>>8358794
> In order to get an object moving, you must push harder on it than it pushes back on you.
> How the fuck is this false?
1. You can't push harder on the object than it pushes back on you. By Newton's third law, the two are equal.
2. The object pushing back on you don't matter. In order to get an object moving, you only need to apply a net force to it.

> HOW? How is it going FASTER if the magnitude of the force pushing right is decreasing?????
Force determines acceleration, not velocity. If the force is non-zero and in the same direction as motion, speed will be increasing. If the force is decreasing, it just means that the acceleration (rate at which speed increases) is decreasing.

> Like it seems so obvious what the answer is, but then the answer is the opposite of what makes sense?
In many practical situations, there will be a force which opposes motion (e.g.drag), so to maintain a constant speed you need to maintain a constant motive force to oppose drag or other resistance. Constant velocity occurs when the two forces cancel resulting in zero net force.

>>8358916
> What is the math for logic circuit called?
Boolean algebra.

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Hi, been learning a bit of maths in my free time recently and i stumbled across this problem in one of my books that i just can't seem to figure out.
I've been thinking about it for a few hours now and i feel like i haven't made any progress, hoping someone could at the very least point me in the right direction!

(Translating the question to English, so some of it might not be 100% grammatically correct.)

"You have a map that shows a treasure buried in a lone island. The map says the follow: Start at point O. Walk towards point G and count the number of steps. Turn 90 degrees to the left and walk the same number of steps. Make a mark X_1
Then start from point G and walk towards point P while you count the number of steps. Turn 90 degrees to the left and walk as many steps. Then turn 90 degrees to the right and walk the same number of steps once again. Make a mark X_2.
The treasure (S) lies halfway between X_1 and X_2.

You find the island, and point O and P still stand, point G however is gone. Your knowledge of complex numbers gives you an idea on how to find the treasure regardless.

Put the map in the complex plane with origin point O and let point P be the complex number Z. Show that the treasure (S) is buried at [eqn] z+ \frac{1}{2} i z [/eqn]"


pic related is a diagram of the map

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>>8358931
1) write a program
2) never do it by hand again

>>8359030
ok thanks. And when I want to calculate the surface with integrals. What would be the borders of the integral? (top and bottom of the integral. I'm not a native english speaker)

>>8359063
Can't you just calculate the area of the 2-circle and subtract the area of the 1-circle?

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What is the area of the triangle?

tip: it's not 30

>>8359069
>tip: it's not 30
but it is

>>8359066
I can but they want us to calculate it with integrals.
How would I need to choce the integrals?

>>8359073
why should i trust your answer?

>>8359077
I guess you'd do a couple of polar integrals, one for the inner line and one for the outer line and then subtract but you'd get the same thing as I just said.

>>8359078
That triangle is half of a rectangle with area 6*10

>>8359014
k*sin(a+b)=k*sin(a)*cos(b)+k*cos(a)*sin(b)
= p*sin(a)+q*cos(a) where p=k*cos(b), q=k*sin(b)
Conversely:
p*sin(a)+p*cos(a) = k*sin(a+b)
where k=sqrt(u^2+v^2), b=atan2(q,p).

>>8359069
there isn't enough information since this describes all rectangles with a diagonal of 10, including squares, no matter how misleading your picture is

>>8359086
nah dude, the perpendicular distance from the diagonal to the opposite corner is 6, says right there.

>>8359088
oh, I thought it was a "b"

>>8359088
>>8359093
in this case the drawing is not a possible triangle

>>8359095
Well I guess this is the stupid question thread

>>8359047
Multiplication by i is a 90-degree counter-clockwise rotation. Multiplication by -i is a 90-degree clockwise rotation.

So:
X1-G = -i*(O-G) = -i*O+i*G
=> X1 = (1+i)*G - i*O

Q-P = i*(P-G) = i*P - i*G
=> Q = (1+i)*P - i*G
(Q is the unlabelled point between P and X2).

X2-Q = P-G
X2 = P-G+Q = P-G+(1+i)*P-i*G = (2+i)*P-(1+i)*G

S = (X1+X2)/2 = ((1+i)*G - i*O + (2+i)*P-(1+i)*G)/2
= ((2+i)*P - i*O)/2
= (2*P + i*P - i*O)/2
= (P + P + i*P - i*O)/2
= (P + (P + i*(P-O)))/2
= (P + (P - i*(O-P)))/2

IOW: find a point X3 such that P->X3 is a 90-degree clockwise rotation of P->O. S is half way between P and X3.

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>>8359098
>>8359095
that was actually a problem our linear alg. professor left us in my freshmen year. Told us the answer wasn't 30 and made us try to come up with a solution.
>spend two hours trying to solve it
>really into it
>even tried to consider the legs as lines connecting the foci of an ellipse to a point on the ellipse and drowned in calculations.
>mfw realize prof. just wanted to fuck with us

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>>8358800
>I can see that it is obviously true, but I cannot prove it.
then you cant see that its true

the numbers are p, 2p, 3p, 4p, ..., p^(n-1)p=p^n

Is 1/2sqrt(2) or 1/sqrt(6) more simplified? I always fuck this up, what are the actual rules of simplification?

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>>8359315
1/sqrt(8) I mean

>>8359317
[math]2^{-3/2}[/math]
is most simple ;)

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What is the evolutionary advantage of rape? A male who cannot get a female to consensually have sex with him obviously has a large number of unfit genes, so why is it beneficial to force the creation of offspring with these genes?

>>8359315
sqrt(2)/4 or (1/4)*sqrt(2). Roots go in the numerator. Numbers inside the sqrt() should be square-free.

>>8359327
Your genes don't care how it is passed on, as long as it is.

If you are too weak to manhandle a woman, then your genes don't deserve to be passed on.

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>>8359327
Bait, I know, but you're actually not baiting as hard as you think you are.

Long ago rape was used as a tool in war. Invaders would rape the women of who they were invading. This would cause those next generations who were a result of rape to side with those who invaded. This is due to combination of being the offspring of said invaders and being rejected by those who were invaded. Thus the invaders genes are spread and the "invadees" genes are greatly reduced.

>>8359327
Eliminating males who lack the physical fitness to procreate by force? Or those who have insufficient reproductive urge? Safety mechanism against over-selecting for (inevitably imperfect) desirability criteria and excessively reducing diversity?

Related: what's the evolutionary advantage of trolling?

>>8359346
If the invaders truly had superior genes, then the women would have consensual sex with them. Basically, rape is working against natural selection.

>>8359317
They are equal. If the denominator is 2rad2, then you square the coefficient and put it under the radical through multiplying. They are both 1/rad8

>>8359362
no it just shifts the 'selection' from the women to the men

>>8359371
If the men are raping as a "tool of war" for control, they aren't selecting women based on fitness. They're just fucking all the women to create offspring with their genes, which the women selected against.

>>8359346
> to side with those who invaded
I'm pretty sure this is nonsense.

A more straightforward explanation is that a gene for procreation by any means necessary has an inherent advantage over a gene for more limited procreation. Even if that weakened the population, the effect would have to be fairly drastic in order for it to be a net minus.

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>>8359362
>>8359374


>superior genes
Back then superior genes was physical strength, this is why people are becoming more attractive and intelligent. Those traits are more valuable now.

There's no fucking way Igor, the 300lb woodcutter is gonna let pic related fuck the woman he chose to be his wife. Keep in mind women were still treated like objects in terms of ownership.

In order to get their seed in their bitch pic related must be able to fight Igor/Igors village.

By default if they could not defend, they were not as strong. Thus the stronger(fitter) genes were selected.

Look at Mexico as a recent example. The Spanish wiped them out and fucked the women. Now we have mexicans who speak Spanish.

>>8359124

Thank's so much!

Thought about vectors earlier but i didnt think about multiplying by i to rotate the vectors!

>>8359381
>nonsense
Simplified? Yes, but not nonsense. Perhaps 'side' was a poor choice of words.

I'll elaborate a bit. Here's a hypothetical to explain what I mean.

Region A gets attacked by region B. B loses, A is now in control of this territory. The men of A are killed, or put to use in some way, and the women are raped.

These mothers have the bastard children, on one hand they are their children so they will still likely raise them and love them. However, to the mother(and the community for that matter) that child is a permanent reminder of losing her previous peaceful life, her husband, and being raped by some random foreigner in the dead of night. She will hold some resentment towards that child, and likely hatred towards B.

The child will feel that resentment, towards him as well as the hatred towards B. Since he wasn't actually there to experience the pillaging and that he is still a child he wont and can't fully understand why it seems like his mother does not love him as much as she should. He may feel like an outsider.

In addition, B is now established themselves as the rulers. They aren't raping and pillaging their own lands anymore. The bastard doesn't see them as evil, just authority. He has no reason to hate them, and he doesn't feel that same resentment from them as from his community.

>>8359098
What you can use to understand this is that the 10 leg is a diameter of a circle. No matter what third point you connect on the circle, you will get a right angle there by connecting chords to that point. (Thales' theorem.) Since the radius of the circle is 5, the greatest possible altitude is 5 precisely when the point you chose is on a diameter perpendicular to the given line of length 10. If your altitude is given as anything greater than 5 then this is inconsistent with the right angle given.

How do I find a power series expansion of

[math]\frac{1}{x^{2}-3x+1}^{n}[/math]

Nothing was really explained to me beyond the basic formula being

[math]f(x)=\frac{1}{1-x} = \sum_{0}^{\infty}{x}^{n}[/math]

I've been trying to do this for just a little over an hour, I know that we should fix the function's form to look like the original

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I know the answer to this question is no, but I'm just curious if anyone can come up with a better proof.

I tried to show that's impossible to even fill the most outer square of the board with the 3 by 3 pieces without leaving at least four open squares.

>>8359509
Never mind, after some serious thought I figured it out. So easy yet so hard at the same time.

>>8359519
If anyone knows how to do this problem, can they please explain it. I'm really struggling on this problem set and feel like I'm fucked...

Is it possible to see color with an electron microscope in the future

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>>8359519
If rotations aren't allowed, then it's trivial. 8 isn't a multiple of 3 so each row has 2 3x1 tiles and 2 tiles left over.

If rotations are allowed, then it's possible.

Show that the curve x=2t, y=t^2, z=1-t^2 lies on a plane and find the equation of this plane. Where does the tangent line at t=2 intersect the xy-plane?

>>8359573
Oh wow I was way wrong. Thanks

Find a spacecurve and obtain two different parametrizations of the same spacecurve.

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What about this one. I'm not sure what she means by the hint. I numbered a 6 by 10 board from 1 to 4, but i'm not sure how to use this.

>>8359573

mathematically what is the actual explanation for it? I am thinking of some sort of algebra.

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What is the difference in gravity between a full moon and a new moon?

I'm trying to self-learn how to do math proofs. Can anyone give me an idea of what "induction on the size of a set" means?

So this is going to be absolutely retarded but I really could use some perspective.

Doing Physics 1 Vector problem. Plane traveling due north at 220 m/s. Wind traveling at 12 m/s 40 degrees east of south. When i translate into polar coordinates and try to convert, or really do anything with the problem, I end up with an answer that doesn't make sense, graphically or analytically. I'm fucking stuck.

Can anyone help? It's simple vector addition but I cannot figure out what I'm doing wrong. It's been 2 hours and I can't find an answer in google that isn't pajeet-tier.

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What the fuck does this notation even mean?

>>8359887
derivative of y over x when x=-3 if y = what it says there

In human speak: get the derivative of y and then plug in -3

>>8359887
what is the value of the derivative at x=-3 if y=etc.

>>8359896
>>8359897
Thanks, anons. I used to think I was pretty good at mathematics, but I'm a CS major, so I guess the memes about CS are more true than I realized.

>>8359645
Not possible. That can be formulated as an exact cover problem and solved using Knuth's "algorithm X".

I'm assuming that the hint is referring to the four-colour theorem, but no idea how that helps.

I'm not quite sure I understand the notation for derivatives. Let's say we have this differential equation (my keys are broken so I can't use the exponent thing):

(4xxxyyy-2xy)dx + (3xxxxyy-xx)dy = 0

Is this the same as?

(4xxxyyy-2xy) + (3xxxxyy-xx)y' = 0

Because examples always use the second way, and I know that y' is dy/dx, then I'm confused about how to rewrite it. Maybe these things have nothing to do with each other and use different methods to be solved?

>>8359957
yes it is the same.

>>8359976

Is it because you divide everything by dx? So if there was something instead of a 0 it wouldn't work right?

>>8359875
>induction on the size of a set

What book are you reading? I am trying to learn math proofs by myself too and I've never encountered this. Are you studying real analysis? There's stuff in there quite similar to what you are asking.

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I don't understand how both electron count and current can be used for a hall effect calculation.

>>8360053
Current, electron density and dimensions allow you to calculate the speed of the electrons.

5 amperes = 5 coulombs per second = 3.12e19 electrons per second. Dividing by the electron density gives 3.67e-10 m^3/sec. Dividing by the cross-sectional area (1e-5 m^2) gives 3.67e-5 m/s.

Lorentz force:
F = q*(E+v×B) = 0
=> E=v*B
= 3.67e-5*1.5 = 5.5e-5 V/m
V = E*w = 5.5e-5*1e-2=0.55uV.

For the second case, the electron density is ~1e9 times lower, so the electrons will be moving much faster for a given current. I get 9.35mV.

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>what can you conclude
Fuck vague questions like this in general, but more importantly, what the fuck am I looking at? Specifically the one I have to do is #4. How are y1 and y2 both solutions of dy/dt = f(t, y) when they obviously don't have the same derivative?

>>8360131
Ah, that's clear!

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Similar problem for problems 5-8. The only thing I can think is that it says the solution exists and is unique (duh), but surely just that can't be the answer for all four problems, can it?

>>8360141
>>8360149
If your differential equation has a unique solution for every initial value then the solutions for two different initial values can't intersect. This means you can quickly give lower and upper bounds.

What would happen to feces if it was left to sit in a sanitary room for years at a time? (Think Bubble Boy levels of sanitation.) What about if a huge mound of feces was left to sit?

Not just asking this for the sake of shitposting. I legitimately need to know for a story I'm writing.

>>8360164
Thanks, that is helpful.

>>8360131
What's going on in the last line?
I don't know what w is.

>>8360174
Microorganisms would eat that shit and then shit it out again and the process repeats. After a while it will look the soil in forests which is also nothing but shit from microorganisms.

>>8360174
Depends on your sanitation method.
For a big mound in a room actively cleaned of anything but air, you'll likely have a dry, crusty exterior while gut flora decompose the interior until that dries out too.

>>8360181
Sanitary room tho

>>8360178
W is the width of the conductor, i.e. the distance between the -ve and +ve terminals (1cm in this case).

The electromagnetic force q*(v×B) cancels the electrostatic force q*E, which tells us the electric field strength E. The field strength is voltage divided by distance, so multiply field strength by the distance to get voltage.

Are exact differential equations always a sum of two partial derivatives, or can they also be a subtraction?

I've seen them like M(x,y)+N(x,y)=0, but could they be like M(x,y)-N(x,y)=0? I'm guessing that not, but I need to be sure.

>>8360236
Well, that definitely is a stupid question.

I'm just saying that if there's F(x,y) and there's some property saying that it's partial derivatives add to 0, then the subtraction would be a whole different thing not related to that property. That's why I think that exact DEs can't be M-N=0 and so far I've seen no example on the Internet or books that features a subtraction instead of sum.

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Not sure what the change in colors means in terms of this problem.

Part A if I'm correct is 8!

What about parts b and c?

>>8360334

I guess all rooks are considered the same, so even if you swap two of them it's still the same position. A would be two this way, or 16 by the way you did it.

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How come the (1-y) and (1-x) turn into (y-1) and (x-1)? I can see how they become denominators after writing it as (1-y)dx=(1-x)dy and then moving everything but the dy to the other side, but shouldn't it be 1/(1-x)=1/(1-y) * dy/dx? Why do the signs inside the ( ) change?

>>8359242
Well youre right, thanks!

>>8360396
They change on both sides, so it just doesn't matter. It's probably because Mathematica's CAS simplifies the equation after every step algebraically and the criterion that is applied to the equation trees prefers writing "x - 1" over "1 - x" for some reason in this case. It usually arranges it the other way around, so it is weird, but for other reasons than you think.

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This is probably a very basic question, but what method is used to solve this differential equation? I know the basic stuff, but as soon as trigonometric functions are involved I don't know what to do.

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got no idea...

>>8360559
>complex logs

REEEEEEEEEEEEEEEEEEEE, these made me fail a whole subject last year

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Made a thread but nobody replied, so I will try it over here.

I want to buy a book about electromagnetic radiation, specifically about the effects of electromagnetic radiation on materials and how the waves/energy behave.

My first choice atm is pic related.

Does someone know a better book on the topic?

Thanks.

>>8360559
Alright, i figured out the first part already. How do the heck do i find the laurent series?
>>8360593
lol this shit never appeared closely on the homework exercises...

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How can I do laplace transform without starting parameters? [spoiler]Someone help pls[/spoiler]

>>8360553
simplify and get it to dy/dx = y/x - tan(y/x) then sub y=vx, y' = v'x + v

How does a gas behave in microgravity?
Example:
Have a sphere filled with "normal" air, r=50km, pressure is around 1atm. Now bring this sphere around a stable orbit at 1000km height around earth.
Now pop the baloon and tell me what will happen.
What about a torus with 1atm and r~1km-10km around earth?

>>8360681

I can see how you make tan from sin/cos and I understand the substitution, but what happened to the yCos(y/x)?

I want to expand a sum of cross products into u1*v2+v1*w2 etc to get a better overview of what is going on "behind the scenes" and to see if I can simplify the expression.

Mathematica seems unwilling to deal with cross products in this way and the suggested ways to configure Mathematica seem very complicated, incomplete and prone to causing problems.

Any idea of what I can do besides doing it manually?

>>8360677
just use some arbitrary constants instead. If the initial conditions are not given it's not possible to "fully" solve it. Just use y'(0) and y(0) and treat those like constants, since constants can be pulled out of the inverse transform anyway it's not a problem.

>>8360686
Well traditionally gas is defined as filling the volume it's in. This remains true in microgravity. The only thing that would be different is the lack of a pressure differential due to height, and the lack of convection currents. So I presume the total effect is that the gas moves around a lot less, so the temperature would be lower.

I think liquid is a much more interesting material in microgravity. Usually we define liquid as filling the shape of the container while keeping a constant density. In microgravity, there is no container to fill, but the intermolecular forces create a surface tension, it basically becomes it's own spherical container.

The ISS should get a special room where they can do experiments with fire, oobleck and other stuff that's too dangerous or might make small particles which is bad to have in the rest of the ISS. Like bring some fucking mercury up there I need to see a sphere of mercury.

Is there a way to make a system of linear equations with 3 variables that ISN'T solvable with simple addition/subtraction of equations?

I remember solving those with all kinds of methods, but it was too long time ago, can't remember shit

I'd like to crate an "apple, pear, oranges equals X" puzzle for my kid that isn't easily solvable

>>8360749
thanks man

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Let [math] Q(x) [/math] be a unimodular positive definite quadratic form on a lattice [math] \Lambda [/math] of rank [math]2k [/math] and [math] B(x,y)[/math] the associated bilinear form with [math] Q(x)=\frac{1}{2} B(x,x)[/math]. Then for fixed [math]y\in \Lambda [/math] show the series [math] \theta_{Q,y}(\tau,z):=\sum_{x\in \Lambda} e^{2 \pi i (\tau Q(x)+zB(x,y))} [/math] satisfies the relation [math] \theta_{Q,y}(\frac{-1}{\tau},\frac{z}{\tau})=\tau^{k}e^{ \frac{2 \pi i Q(y)z^2}{\tau} }\theta_{Q,y}(\tau,z) [/math]

supposely this is 'immediate' by using poisson summation but i can't even figure out how to use it

any ideas?

>>8360779
If the system has a unique solution ten it can be simplified with Gauss method whether you like it or not.
If you want to make it harder then use some fractional coefficients or just put huge numbers.

>>8360779
I assume you want a system of three equations. If they represent a matrix that has a determinant of zero then they make an unsolvable system. e.g.
[eqn]\begin{pmatrix}
4 & 2 & 2\\
-1 & 1 & -1\\
2 & 1 & 1
\end{pmatrix}\begin{pmatrix}
x\\
y\\
z
\end{pmatrix}=\begin{pmatrix}
1\\
2\\
3
\end{pmatrix}[/eqn]

>>8360868
>>8360872

Yeah, i guess it can't be both challenging and with natural numbers. I wouldn't want the kid to do fractions and shit, at least not yet

i will have to think of some other puzzle

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How does the top of this DE become the thing on the bottom? I guess it's some identity + integration but I don't know how.

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>>8360924
Mathematica finds it easily enough.

>>8360930

>Mathematica finds it easily enough.

Can't tell if sarcasm or not. I just figured that since theres a c on the right the steps probably involve

dy/dx = some trig identity

And then integration of both sides. But I don't know the steps and I don't know any identity like that either.

>>8360924
Separation of variables.

x*sin(u) + x^2*cos(u)*du/dx = 0
> Multiply by dx:
x*sin(u)*dx + x^2*cos(u)*du = 0
> Divide by sin(u):
x*dx + x^2*cos(u)/sin(u)*du = 0
> Divide by x^2:
(1/x)*dx + cos(u)/sin(u)*du = 0
> Replace sin/cos with tan:
(1/x)*dx + (1/tan(u))*du = 0
> Subtract terms involving x:
(1/tan(u))*du = -(1/x)*dx
> Integrate both sides:
log(sin(u)) = -log(x) + c
> solve for u:
e^log(sin(u)) = e^(-log(x) + c)
sin(u) = (e^c)/x
u = arcsin((e^c)/x)

Treating du and dx as algebraic terms is wrong but it works and can avoid a lot of pointless formalism.

>>8361070
Clearly they're not the same number.

As an angle, 15π/2 is equivalent to 3π/2. A complete circle is 2π, not π.

I.e. sin(15π/2)=sin(3π/2), likewise for other trig functions. But you can't just simplify 15π/2 => 3π/2 because you'll get the wrong answer for sin(x/2) etc.

>>8361099

Did you just bully that nigga into deleting his post? Savage.

where can i find reading material, worksheets, etc., regarding boolean functions?
i am given questions such as: how many linear boolean functions satisfy the following:
f(0,0,1,1) = 1
f(0,0,0,1) = 1

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Help

P is the middle-point on the line. Z is a complex number. O is the point of origin in a catrtesian coordinate system. Prove that the position of P is z+1/2*z*i

When you burn alcohol what does it become?

>>8361230
Carbon dioxide and water

Is it true that these are solved with Laplace transform?

>>>/wsr/193451

I don't think that's it, because I haven't even learned that.

>>8361245
The first can be solved directly with Laplace transform. For the second differential equation you have to do a substitution first to make it linear and then apply the Laplace transform.

But you can obviously solve them without the Transform too.

>>8361237
THANKS! Sometimes stupid question appear in my head for no reason and I can't figure the proper search terms to google.

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Im going to buy a hard drive enclosure, and im worried about heat.

Should I buy a plastic one, or an aluminum one?

Left is plastic, has a small amount of venting. Right is aluminum, has no venting.

Will the aluminum dissipate heat better than the plastic, or will the aluminum insulate and keep the heat more than the plastic?

I plan on cutting vents into the top of whichever one I buy

>construct a sequence of rational numbers with the property that, for any real number alpha, or for alpha= +infinity or alpha = -infinity, there is a subsequence approaching alpha
H-how is this possible?

>>8361108
I deleted it before I got a response because I found out how retarded I am.

Is it possible to solve complex numbers in polar form in your head?

Or at least solve them if you have a calculator which can't into i.

>>8361328
Do you mean "turn them into" polar form? If so, yes

>>8361305
cutting vents in plastic will be easier

>>8361371
No, basically turn them back from polar form. If yes, then how?

>>8361305

Don't worry about that, just keep it in a cool place.

>>8361400
if you have z=re^{i theta} then z=r(cos(theta)+isin(theta))

>>8361308
do you know this is possible/is it from a textbook? it seems unlikely at first glance

i feel like you would need an enumeration of all of the rationals which is obviously doable, but how to order them in a way that you could get any real number as a limit of a subsequence is unclear

>>8361500
i mean i guess you could take any increasingly accurate subsequence of decimal approximations for that real number?

>>8361497
And how do you go from re^{i theta} to a + ib without losing your sanity when your calculator can't solve it?

I'm asking because the calculators we're allowed on the exam can't do fancy graphs or calculate imaginary numbers, so if you get an assignment of finding the roots for z^6 or something, it would be very useful to be able to get an answer and not flunk out.

>>8361198
See:
>>8359124
>>8359047

Z=R+X
A=R+iR
B=R+X+iX+X = R+2X+iX
P=(A+B)/2 = (R+iR+R+2X+iX)/2
= (2R+2X+iR+iX)/2
= (R+X)+i(R+X)/2
= Z+iZ/2

But to be honest, if you can't figure out something this basic for yourself, it's time to drop anything involving math and switch to sociology or gender studies instead.

>>8361520
hopefully the re^{itheta} you start with has a nice r and a nice theta (preferably an easy fraction of pi) that gives some symmetry

for example sqrt(2)e^{i pi/4} is 1+i, since when you picture it you have something of length sqrt(2) whose angle is at a 45 degree angle with the x-axis. because of the 45 degree niceness you know that if you write it as a+bi that a=b

>>8361500
Yeah it's from a textbook.

>>8361527
>hopefully
Change sqrt(2) to 2. Now what?

>>8361532
you can probably make a case with this idea >>8361515

>>8361537
then 2=|z|=sqrt (a^2+b^2) (in a nice symmetric case with a= b or a=-b) gives 2=sqrt(2a^2)=sqrt(2)|a| so for example

2e^{i pi/4} = 2*sqrt(2)+2*sqrt(2)i

>>8361545
woops
since |a| would be sqrt(2) in that case to give you 2=sqrt(2)|a| you would have
2e^(i pi/4)= sqrt(2)+sqrt(2)i

>>8361520
> And how do you go from re^{i theta} to a + ib without losing your sanity when your calculator can't solve it?
The only functionality you need from your calculator is +,-,*,/, sin,cos,sqrt,arctan.

r*e^(i*theta) = r*cos(theta) + i*r*sin(theta).
<=>
a+b*i = sqrt(a^2+b^2)*e^(i*arctan(b/a))

[You may have to figure out the correct quadrant manually.]

>>8361545
>>8361550
Wolframalpha shows 2(cos(pi/4) * i sin(pi/4)) as (1+i) sqrt(2).

>>8361553
Will my calculator give me the right answer even if it doesn't have i?

>>8361560
thats the same as what i wrote, just with a sqrt(2) factored out

>>8361566
sqrt(2) * sqrt(2)i is shown as (2+2 i) sqrt(2) on Wolframalpha.

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>>8361525
I know anon, just wanted one last round to fully convince myself

>>8361566
>multiplication instead of addition
Damn, it's getting late.

Thanks for the help though, it's appreciated.

>>8361589
Even replying wrong now >>8361569

>>8361308
It's easy. First take a sequence [math](a_n) [/math] that includes all rational numbers. Such a sequence must exist since the set of rational numbers is countable. Now you can look at the sequence
[eqn](b_n) = (a_1, a_2 ,a_1 , a_3 , a_2 , a_1 , a_4 , a_3 , a_2 , a_1 , a_5 , \ldots ) [/eqn]

This sequence includes each rational number an infinite amount of times so it will have every possible sequence of rational numbers as a subsequence.


The rational numbers are a dense subset of the set of real numbers so for every real number [math] \alpha [/math] there is a sequence of rational numbers that converges against [math] \alpha [/math].

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so what is the best thing to study in university already?

>>8361308
Order the rationals by |numerator|+denominator. Values with equal keys can be in any order.

Consider the 2D plane with y>0. Any real corresponds to a straight line through the origin. Any rational is a point x/y where both coordinates are integers. If the rationals are enumerated in order of increasing "distance" from the origin, then you'll always be able to find one closer to any given real than any previous rational.

If x/y-z = eps, x,y integer, z,eps real, all >0, i.e. x/y>z
=> (k*x-1)/k*y-z = k*x/k*y-z-1/k*y
= x/y-z-1/k*y
= eps-1/k*y
<eps

Choose k > 1/y*eps
=> k*y*eps>1
=> k*y*eps-1>0
=> eps-1/k*y>0

ergo
0<(k*x-1)/k*y-z<eps
z<(k*x-1)/k*y<eps+z
z<(k*x-1)/k*y<x/y

i.e. (k*x-1)/k*y is closer to z than x/y

>>8361560
> Will my calculator give me the right answer even if it doesn't have i?
Look at the calculation. a,b,r and theta are all real. The calculations which obtain a,b from r,theta or vice versa only involve reals.

>why?

>>8361622
True, but I've noticed that I'll have to be aware of the i myself. 2(cos(pi/4)+sin(pi/4)) gives 2sqrt(2) on the calculator because that's what sqrt(2) + sqrt(2) is, however with the i it's clear that that's wrong.

>>8361668
Don't add the real and imaginary parts together. You can't reduce a complex number to a single real number.

2*e^(i*pi/4) = 2*(cos(pi/4)+i*sin(pi/4))
= 2*(1/sqrt(2) + i/sqrt(2))
= sqrt(2) + i*sqrt(2)

That's the final answer: 0.707+0.707i.

A calculation which yields a complex number turns into two calculations each yielding a real number: one for the real part and one for the imaginary part (or one for the magnitude and one for the angle, if you want it in polar form).

how to find a value k for the equation x^2-kx such that the line 4x-9 is tangent to it?

>>8361525
With those definitions P would be

(-A+B)/2, not (A+B)/2

when a cell differentiates, does that mean that it creates a new cell with the new features? Or that it itself becomes a new kind of cell?

>>8359124
So the "-" when you write O-P is to symbolize "vector from point O to P"?
What about when you wrote X1+X2 for S? Why isn't it still "-" ?

>>8361725
Nope. A and B are the endpoints of the line of which P is the midpoint, i.e. P=(A+B)/2.

R is the vector away from O, i.e. with both real and imaginary parts negative. X is to the left.

So Z=R+X, A=R+iR, B=R+X+iX+X

>>8361793
> So the "-" when you write O-P is to symbolize "vector from point O to P"?
No. It's a subtraction. O-P is P subtracted from O (as a vector, it's from P to O).

> What about when you wrote X1+X2 for S? Why isn't it still "-" ?
Because it's an addition. (X1+X2)/2 is the midpoint (mean) of X1 and X2.

This isn't some kind of invented notation, it's arithmetic.

>>8361794
So is A a vector or a point?

>>8361717
The difference between the parabola and the line is:
(x^2-kx) - (4x-9)
= x^2-(k+4)x+9
= (x-(k/2+2))^2 - k^2/4 - 2k + 5
That has a repeated root at x=k/2+2 when
k^2/4 + 2k - 5 = 0
=> k^2 + 8k - 20 = 0
=> (k-2)*(k+10)=0
=> k=2 or k=-10

>>8361828
Wait, no distinction, right?

>>8361828
O,Z,A,B,R,X are complex numbers. iR and iX are R and X rotated 90 degrees CCW.

If you want to think of them as vectors, R and X are translations, O is the origin, A, B and Z all correspond to specific points.

>>8361847
Not really, no (regardless of whether you consider them as complex numbers or vectors). A point is defined by its vector relative to the origin.

In homogeneous coordinates, a distinction is sometimes made between "directions" with w=0 and "positions" with w!=0. But that's not relevant here.

>>8361860
Ah, ok! So you didn't calculate P using vectors, but rather with A and B being regular numbers. Thus you averaged A and B. But you still defined A and B using vectors. Didn't know you could jump between vector and non-vector calulation like that

How hard is it to go from an applied math undergrad to an engineering Master's¿

Assume I will have 1 year work experience with the title engineer and working with engineers.

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Why would the amide have a lower IR spectroscopy carbonyl stretch?

>>8361804
>>8361794
So the clue all along was to find a way to define the endpoints of the line of which P was part of? Noice! Thanks guys, sorry for annoying brainletism-faggotry

>>8361890
Complex numbers are effectively 2D vectors, except that any operation on real numbers can be extended to the complex numbers.

>>8361918
Well, the only thing we're told about P is that it's the midpoint of the line. In order for that to tell us anything useful, we need to know the endpoints of the line (and most of that diagram is telling us that, in a roundabout way).

Did I do it?
[math]5z^3+11z^2+11z+5=(z+1)(z+\frac{3}{5}+\frac{4i}{5})(z+\frac{3}{5}-\frac{4i}{5})[/math]

>>8361947
you can easily check this on wolfram bud

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I'm currently attending my first year at a local state school, partly for financial reasons, and partly because I made no substantial effort during my formative years to succeed in school. Throughout which I had condemned with a learning disability in 2nd grade, and moved down to lower level mathematics in middle school because I was too ambivalent to even care. I eventually shed the extra help I had been getting and rose to the normal levels of mathematics, but cannot shake a significant feeling of inadequacy. I feel that I have so much more undeveloped potential. During elementary school I took an IQ test and received a 143, but there was a gap between my potential and what I was presenting. Is there some way I can bounce back from these earlier years? I don't want to be tortured by false ideas of what could have been. Or, maybe I'm just a fag who blog posts on 4chan for attention, or better yet, advice.

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Is there no way for hair to grow back when the root's been removed?

>>8361978
Even when the root is removed, hair grows back. It takes a little longer though.

It's almost impossible to permanently remove hair.

Calc 3 fag here, having a more than likely retarded issue. I'm trying to prove that n/(n+1) converges at 1. However, the way I just learned to prove it is
|a_n - L|< ε => |n/(n+1) - 1|< ε
The way I'm looking at it I have to get the -1 on the ε side and I have to get rid of the absolute value. I'm don't think I can move the -1 until I get rid of the absolute value, but
|n/(n+1) - 1| is not the same as n/(n+1) - 1. Any tips on how to approach?

>>8362018
>baby's first limits
>calc 3
???

Let epsilon > 0. You need to show there exists natural number N such that |n/(n+1)-1|<epsilon for all n>N.

we have
|n/(n+1)-1|
= |[n-(n+1)]/(n+1)|
=|1/(n+1)|
= 1/(n+1)

to get 1/(n+1)<epsilon this is the same as n+1>1/epsilon or n>1/epsilon-1. so you can take N=1/epsilon, then for n>N you have n>1/epsilon -1

>>8362008
lasers do the job

>>8361960
It just says a lot of stuff. When I change a little on one side of the equation (which should make it wrong), it still says stuff.

Can't it just tell me whether it's true or false?

>>8362066
http://www.wolframalpha.com/input/?i=roots+of+5z%5E3%2B11z%5E2%2B11z%2B5

you did it right

>>8362072
Awesome.

>>8362044
Yeah calc 1 was ass for me, didn't have to deal with limits too much in calc 2, now it's kicking my ass that I never really understood limits. Thanks for this, It's been slowly coming back as I work through the problems but this one I couldn't get around.

>>8362062
Still requires a couple sessions though. "Almost" was the key word.

>>8361947
> Did I do it?
Not quite. The LHS is 5x the RHS. I.e. both sides have the same roots but they're off by a scale factor.

Calc 3 finding critical points

[math] fx = 1 - 2xy +y^2 [/math]
[math] fy = -x^2 -1 + 2xy [/math]
When I add these functions together it comes out to [math] y^2 = x^2 [/math]
I just need some clarification. By finding [math] y^2 = x^2 [/math] I'm able to find which x and y's to put into the equation. But those x and y's only guarantees that the [math] fx [/math] and [math] fy [/math] are equal?

It makes sense when I type it out I just need someone to confirm. I've been doing homework all day and trying to remember everything from earlier calc classes.

>>8362115
I get it now
disregard

>>8359605
You can do this without calculus if you just put in some values for t. Get three points and calculate the equation of the plane. Plug in the formulas for x y and z to prove all points lie in the plane.

>>8362112
I did get this at one point:
[math]\frac{-6\pm8i}{10}[/math]
But that's not it, is it?

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Is this a trick question?
Or am I thinking too algebraically?

>>8362153
Why would it be a trick question?

>>8362174
It sure looks like a trick question, I can't see how to negate if each term occurs only once.

For the set [math]\cap{S}[/math] to exist, does [math]S[/math] needs to be non-empty?

>>8362241
It has to have at least one element in common with the set it intersects with.

>>8362182
¬?

>>8362182
Isn't that just proof by contradiction? Why does it tell you to simplify though? Weird.

>>8362261
It is not an intersection of sets, it´s the set intersection

Why is the limit not 0, /sci/?
[math]$\lim_{(x,y)-> (0,0)}{x*(x^2-y^2)/(x^2-y^2)}$[/math]

>>8362438
You need to look at the 4 limits, half of them don´t exist and thus that one doesn´t exist either

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How do I convert these to fractions?

"Assume that every positive integer can be written in one of the forms 3k, 3k+1, 3k+2 for some integer k. Show that if the square of a positive integer is divisible by 3, then so is the integer."

Also, how to prove this corollary "Let a be a positive integer. If a^2 is even, then a is even. If a^2 is odd, then a is odd"?

Thanks so much for your help.

Given any set A, there can not exist a surjection f:A->P(A). So I'll assume there's some A and surjection f:A->P(A), and reach a contradiction.
For any x in A you have f(x) which is a subset of A. Any particular x might or might not be a member of the set f(x). Define a set S of the x that are not. Formally,
S = { x in A: not (x in f(x)) }
Then since f is a surjection, there must be some s in A with f(s) = S. Then to reach a contradiction you show that you can neither have s in f(s), nor have not (s in f(s)).
If s in f(s) and f(s) = S then s in S, and by construction of S you know not (s in f(s)), contradicting s in f(s).
If not (s in f(s)), then by the construction of S you know s in S. f(s) = S, so that means s in f(s), contradicting not (s in f(s)).


Someone explain this to me I've been looking t this for hours. This is an explanation for Cantor Cardinality theorem or sumthin.

>>8363148

why don't you just do it mate? Every integer can be written in those 3 forms, and he said if the square is divisible then so is the original integer. Look at the three integer forms given, only 1 is divisible by 3. So if you take (3k)^2 you have a square that is still divisible.

Other way you can do it is by cases, simply square the three and see that it if the square is divisible by 3, then so is the original (only 1 of them will work, but this doesnt disprove it).

The fact that only 1 will work shows that it has to start at some number (notice how he forms are made if you take k = 0, it's 0, 1 ,2).

For the second one ,use induction using the forms you have.

>>8363189

I meant to say ony integer will only fit into one of those, not any.

Let's say you had a robot that had an exact copy of your brain created and wired into it. Then you replaced one cell of your brain with the corresponding one in the robot's, once a day, until billions of years later your original brain has been fully transferred into the robot, and the copy brain has been fully transferred into your body. Where does your original consciousness now reside? In the original body with the duplicate brain, or in the robot body with the original brain?

If I have a function P(n) = 3n+1 how do I prove there is no n ∈ Z for which P(n)/3 ∈ Z?

>>8363319

Induction

>>8363329
well I can just say

P(n) = 3y
P(n+1) = 3(y+1)

and then the contradiction would be that there is no y ∈ Z for which that works but how do I prove that?

>>8363346

What is Z, Z is the set {1,2,3,4,5,6,7...}, or {0,1,2,3,4,5,6...}

Begin induction; if f(n) has the property then f(n + 1) must also have the property, something like that.

So P(n) = 3(n) + 1. Now is this divisible by 3? Let's assume it's not.

Then take P(n + 1); P(n + 1) = 3(n + 1) + 1 = 3n + 4, now is this divisible by 3? Let's see:

P(n + 1) = (3n + 1) + 3

This is not divisible by 3 because (3n + 1) is not because we assumed (3n + 1) is not divisible by 3.

So we just showed that if P(n) is not divisible, then P(n + 1) must also satisfy this property. Now take n = 1, both are not divisible, then P(1 + 1) must also not be divisible! We just showed P(2) as not divisible too. But wait a minute, what if we take P(2 + 1)?? Now ask yourself, can n = 2?? Sure it can, n E Z, 2 is also an element of Z. This is done infinitely many times such that we showed all n in Z satisfy the property.

I am supposed to meet my prof but im so unsociable fkkk

>>8363388
thank you

>>8363319
P(n)/3=n+1/3
Clearly if n is in Z, n+1/3 isn't.

>>8363470
It's (n + 1)/3 by the way so no it's not trivial.

>>8363481
If P(n)=(n+1)/3, clearly the statement is false. E.g. P(8)/3 is in Z.

How many hairs does a dog have?

how do I simplify this expression

[math]\pi\epsilon\nu\iota\sigma[/math]

so, i'm trying to learn the Gauss-Seidel method for solving linear equations and its quite easy
the problem is how do i know if it will converge or not? i really can't understand the sassenfeld criteria

can you guys help me out?