SQT - Stupid questions thread

>Energy has a gravitational field. So does that mean that a sufficiently strong EM field can create a gravitational field?
Yes. Well, any EM field creates a gravitational field, it will just be far too weak to detect.

>Also, for a short time after the big bang, there was no particles because it was too energetic.
Where did you hear this?

Why does d(1/r)dΘ=-(dr/dΘ)/r^2 ??

The work done by the field and by the external agent is the force times the distance times the cosine of the angle between the force and displacement vectors (I think this is also the dot product of the two vectors, I don't remember).

When you move the object in the direction of the field, the angle is zero so the cosine of the angle is 1 and the work is just the force times the distance. When you move the object in the opposite direction of the field, the angle is 180 degrees or pi radians, so the cosine of the angle is -1 and the work is the opposite of the force times the distance.

Another way to think about it is to consider a uniform gravitational field. When an object falls down i.e. in the direction of the field, gravity causes the object to speed up and gain kinetic energy. When an object is moving up i.e. against the direction of the field, gravity causes the object to slow down and lose kinetic energy.

holy shit guys I feel retarded but why isnt it possible thst a*b = c*d =f where a and b are primes.
Basically why is a prime factorization of a number unique. Why couldnt there be other numbers that divide it other than a two primes you found.

> why is a prime factorization of a number unique.
en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Proof

how would i write the domain of this function?
h(x)=\sqrt(2x-4)
D: [2,\inf) ??

yep

no

No

It all comes down to the definition of a prime and the definition of a factor. A prime only has itself and 1 as factors. If you multiply a prime by another prime, you get a number whose only factors are those two primes, itself, and 1. If you could find other factors, that would mean that your original two primes weren't actually prime.

Suppose you have two numbers a and b. a*b = f. If f is divisible by some other number c, then either a or b must also be divisible by c and so it is not prime.

So like, the difference of two step functions is still a step function right? I mean, intuitively makes complete sense, but it isn't mentioned anywhere even though they mention the sum of two step functions is a step function. I guess this could be reduced to asking if the negative of a step function is step function, which again makes complete sense but I can't find an answer and don't want to make a derp.

> So like, the difference of two step functions is still a step function right?
Not in general.

> even though they mention the sum of two step functions is a step function.
That's only true if both step functions have the same offset (in which case, their difference is also a step function).

In general, the term "step function" could refer to anything having the form:
f(t) = a | if t>=c
f(t) = b | if t=0
u(t) = 0 | if t

Is there a nice expresion for the integral of [math]f(x)=\sqrt{\frac{-2}{3}x^3 - x^2+C} [/math] with [math]C[/math] being an arbitrary constant.

how did they simplify this guise?

Having trouble with this. I've tried squaring both sides, but I'm not sure how to actually prove it even though it is clearly true.

1000/[pi(500/pi)^{2/3}]
=2*500/[(500)^{2/3} (pi)^{1/3}]
=2*500^{1/3}/[(pi)^{1/3}]
=2*(500/pi)^{1/3}

>I'm not sure how to actually prove it even though it is clearly true.
you shouldn't think of things as 'clearly true' if you have no clue how to prove them

work these in reverse:

ab+ad+bc+cd>= ab + cd + 2sqrt(abcd)
ad+bc>= 2sqrt(abcd)
ad-2sqrt(abcd)+bc>=0
(sqrt(ad)-sqrt(bc))^2>=0

Square both sides so you have [math](a+c)(b+d)\geqslant ab + 2\sqrt{abcd} + cd[/math] expandin in the brackets and eliminating terms you get [math]ad + cb\geqslant 2\sqrt{abcd}[/math] Its clear then when you pass the sqrt term that its the square of a differece of sqt(ad) and sqt(bc) which is always positive. So run it backwards.

The definition of step function in is not standard.

The more common definition is that a step function is a linear combination of indicator functions, in which case the difference is still a step function.

en.wikipedia.org/wiki/Step_function

I'm taking calculus 1 next semester over again.
For a reason I won't take time to explain, I failed. The concepts were easy for me to grasp but I have major gaps in foundation.

Can you gents recommend any textbooks for calc/algebra so I can rebuild my foundation

how fucked up are you?

Very spotty. I'm just ready to reteach myself all of algebra and then get started with calc independent study.

by the expression " the quantity 500/π raised to the power of two-thirds" is to be understood some "number", at first we don't particularly care which, such that: you square the thing (that is, 500/π), then you take its cube root, and you end up with the number when you're done.

by way of comparison, 8^(2/3) = 4, and 27^(2/3) = 9, say. This illustrates how we begin to generalize exponentiation to rational exponents.

Leaving details aside, this particular type of exponentiation is amenable to a few simple observations: everything is manifestly positive: π, 500, even the terms of the fractional exponent 2 and 3. The quotient of 500 and π is thus manifestly a postitive real number, and to begin with, rather than fussing about other roots, it is sensible in the case of extracting a cube root (which is ultimately necessary in this part) of a positive number to /start/ with identifying that positive real number which, when cubed, gives the other positive real number. This can be done by simply manipulating the initial expression:

[eqn] \bigg( \frac{500}{ \pi} \bigg)^{ \frac{2}{3}} = \sqrt[3]{ \bigg( \frac{500}{ \pi} \bigg)^{2}} = \sqrt[3]{\frac{250000}{ \pi^{2}}} = \frac{ 25 \sqrt[3]{2^{4}}}{ \sqrt[3]{ \pi^{2 }}} \approx 30 [/eqn]

Using the same convention about cube roots implied above, we take some positive real number, get an idea of its cube root, and compose these items into the latter expression. It thus ends up that we have some positive real number which is "about thirty".

This is the thing which is to be plugged into the LHS of your thing. basically pi times thirty is "about" 900, and 1000 divided by 900 is "about" 1, on the north side of it. Or, etc.

I don't know just what your 2r is supposed to be in reference to (some circle), and so I do not comment on it apart from this.

Because [math]\mathbb Z[/math] is a principal ideal domain.

dont kill yourself please user

it gets better

How does it not if certain genes are being expressed depending on the environment? Doesn't it make it a lot less random?

How do you approach this one?

literally can't slove this one

protip 3^n/(4^(n/2)+1)=1/4 (3/2)^n

how can you tell, pls

or did you write out and found another sigma

3^n/4^(n/2+1)
=(1/4)3^n/4^(n/2)
=(1/4) (3^n/2^n)
=(1/4)(3/2)^n

The negative sign comes from the fact that the displacement is a vector.
The force you exert acts in one direction, while the force of the field acts in the other direction.
The magnitude of the displacement is the same for both forces, but because of the oposite directions one is negative while the other is positive

i'm curious about this one too now, not too sure how to prove

oh, god, how simple
cheers

Sqrt of 0 is a real number so yes

What kind of class is this? The way I'd do it is minimize the function x^2+y^2+1-xy-x-y directly and check that the minimum is non-negative.

how come pic related is true
if you do ratio test
then, the limit of (3n+3)/(n+1)^2 as n approaches inf = 0
meaning, it converge, unless it doesn't simplify to what I wrote

the ratio test should give you

(3n+3)(3n+2)(3n+1)/(n+1)^2 which diverges as n goes to infinity

How can you see in a dark room. Where and how are the photons coming from

Your body glows slightly

WHAT THE FUCK.

HOW DO I FIND THE LIMITS OF INTEGRATION FOR TRIPLE INTEGRALS OTHER? DO I HAVE TO DRAW THE SURFACE? WTF!!!!!!

Let x=u+v+1, y=u-v+1.

Then the difference LHS-RHS = u^2+3*v^2, which is always >= 0.

mathematica

>d*a + (b - d*b) === d*a + (1 - d)*b
>False

but that's fucking wrong isn't it?

this is true, isn't it:
d*(a - b) + b = d*a + (1 - d)*b

I have an example which seems to be an exercise in Integrating Factor method, but after performing it the equation is still not Exact. What does it mean? That it's unsolvable?

Nice fantano pic, is it OC?

Post it bitch

y^2 + ( xy - 1 ) y' = 0

If inductor and capacitor in parallel using DC, wouldn't the components require time to collect charge before they become open/short circuits? My profs don't account for this

Will someone explain Riemann sums to me? I understand how to integrate, but I'm consistently getting the wrong answer with Riemann sums, which tells me that my method is incorrect.
What I've been using is: the limit as n approaches infinity of (Δx * the sum of f(Δx * x) with n terms)

Which integrating factor you used? Remember ypu must get either something that only depends on x or y.

I ended up with u = xy-1, but it makes it so the new My = 3xy^2 - 2y, and new Nx = 2xy^2 - 2y, hence it still isn't exact...

I just multiplied both M and N by u(x), but it ended up having both x and y in it

Most of the time integrating factors are used just to help get the equation into the form I y + I' y = (I y)', by using the product rule.
So not bothering with the integrating factors
y^2 + (x y-1) y' = 0
y (y + x y') - y' = 0
y (x y)' - y' = 0
y -(x y)' e^(-x y) + y' e^(-x y) = 0
(y e^(-x y))' = 0
y e^(-x y) = C
-x y e^(-x y) = C x
-x y = W(C x)
y = -W(C x)/x

W(x) is Lambert Omega function.

Thank you. Is it solvable using integrating factors thought?

I can't figure out what's happening. The first sentence says: "Try replacing -1 with i^2, and the solution is (-4)^n.

I have trouble understanding the step, where we discard the imaginary part and use only the real one, especially why i^2k becomes i^k and the whole sum's upper index becomes 4n. Thanks for answers.

what actually happens to a material on a microscopic metal (if the material is a solid) during an indentation? Is there a very tiny displacement of material elsewhere in the material or does some of it just become more dense?

What did I do wrong?
Why can't you equate y^2 + x^2 =9 to y=sqrt(9-x^2) for above the x axis?

All imaginary parts are being squared, so it's all real. i^2 is real. They absorb the 2 into the k in the exponent. This means they have to change the index.

> wouldn't the components require time to collect charge
A step function (i.e. where the voltage changes from zero to non-zero) isn't DC. "DC" implies a steady-state voltage, i.e. where the voltage has remained constant since forever.

The step response of an R-C or R-L circuit is an exponential approach:

For R-C:
V(t) = Vin * (1-e^(-t/RC))

For R-L:
I(t) = (Vin/R) * (1-e^(-t/(L/R)))

where Vin and (Vin/R) are the eventual steady-state (DC) voltage and current.

Legitimately, am lost with what I am doing that is wrong!!!

Can user help? I will post work too

Here is work

What am i doing wrong? Am I just entering answer in wrong? Really need help anons

spent 50 minutes on

inf sigma n=0 bn
where bn = (n^1.5)/(1+5*n^1.5)
and I can't solve it
pls halp

Your integrating factor needs to only depend upon one variable. Try the other one.

Failed out of CompE, so I decided to take a community college course to fill a pre-requisite needed to change my major to Accounting. Anyone know how hard Statistics will be in a 8-week course? I went up to Differential Equations when trying to get my engineering degree.

0.732m is the distance from the smaller mass. The question asks for the distance from the larger (3m) mass.

continuing with this high-school problem, plugging in this "first phase" into the user's original problem gives

[eqn] \frac{1000}{ \pi \bigg( \frac{25 \sqrt[3]{16}}{ \sqrt[3]{ \pi^{2}}} \bigg) } = \frac{40}{ \sqrt[3]{16 \pi} } = \frac{ \sqrt[3]{64000}}{ \sqrt[3]{16 \pi}} = \frac{ \sqrt[3]{64} \sqrt[3]{2} \sqrt[3]{500}}{ \sqrt[3]{8} \sqrt[3]{2} \sqrt[3]{ \pi}} = 2 \sqrt[3]{ \frac{500}{ \pi}} \approx 10.+ [/eqn]

At which point I've effectively worked the LHS and middle part of the above user's thing out of boredom. It's on you to understand the step if you haven't done that yet

b[n]->1/5, so the sum isn't convergent.

Let's see you have 8 weeks left for the german equvialent for Calc II and Calc III. You're attending both courses at the same time.
Mind you, I have access to lecture videos and old exams.

Is it doable in your opinion? What's the best way to tackle it in your opinion to learn the math with a deep understanding?

What keeps a person from killing themselves? Why is there a natural fear of death?

>can someone explain the libet experiment and it's implications on free will to me?
The result experiment shows that when I want to press a button at some random time, the process of pressing the button that started in my brain happens before I am aware of the choice. Implying that you have no conscious free will when wanting to press a button at a random time.

Self preservation is an evolutionary advantage. Individuals with a fear of death are more likely to live longer and reproduce more than individuals without it.

looking for help with a basic proof by induction question:

[math] 80 | 9^{2n} - 1, \forall n \geq 4 [/math]

that should be
[math] n \geq 1 [/math]

my bad.

no

No. Epigenetics just refers to pre-programmed stretches of DNA that can be turned on or off in response to certain stimuli. It is not a fundamental rewrite of our understanding of how we evolved, it's basically a neat trick our cells can do that we weren't aware of.

Even if there are stretches of DNA that need to be activated to work, the mechanism that activates them and the dormant DNA itself are still subject to the normal method of evolution-- i.e. random mutation.

You can't just reverse the chain rule like that when you integrate. You have to use a u substitution. In this case [math] x = 3sinu [/math]

>isn't this just a trick our brains play
You have to ask what consciousness or free will even is. It's possible to be only peripherally aware of something, or for processes to happen partly consciously and partly unconsciously. It's possible to make a decision, but have no memory of the decision actually being made. In general, we're very bad at describing the internal workings of our mind in any kind of accurate detail, and there's a lot of "cheats," filling in the gaps that pop up along the way.

One take is that the human mind is made up of one or more "executive" parts, (which may or may not be where your sense of self comes from), and a lot of subordinates that it can delegate instructions to.

In Libet's experiment, the executive had primed another part of the brain to just wait for a random time -- it didn't care when -- to trigger whatever action we're talking about, and then the subordinate part went about carrying it out. The process of making the momentary decision happened peripherally to the subject's consciousness. When the external senses reported back that the button was pushed, it agreed with the executive's expectations... "yep, it was 'me' that just pushed that button!"

It's shocking to pull the curtain back and think about how your mind actually works, but I think it's absolutely necessary if you want to have more conscious control over yourself-- more free will. Very often, people will be easily influenced by things that they think came from the inside, but which were actually planted there by a savvy advertiser or a skilled persuader. Other times, you'll have emotional reactions from inside to things that, on closer examination, don't really matter that much to you.

9^2n = (9^2)^n = 81^n

f(n)=81^n-1
f(n+1)=81^(n+1)-1
= 81*(81^n)-1
= (80+1)*(81^n)-1
= 80*(81^n)+81^n-1
= 80*(81^n)+f(n)

Clearly, 80 | f(n) => 80 | f(n+1)

f(1)=81^1-1=81-1=80 => 80 | f(1)

Check this out. I think it'll help you get to the bottom of things, about free-will and consciousness:

youtube.com/watch?v=aCv4K5aStdU

The speaking left-brain appears to be the side that most often rationalizes things, tells expedient lies, just to keep the rest of the brain ticking over like it should. This is completely unsupported, but just from my own intuition/introspection, I hypothesize that the right-brain is more likely to just report the truth-- if only because it doesn't have the ability to quickly rearrange things into a pleasing lie. OFC it could also be the case only because the right brain can't speak.

Since I started reading about this stuff, I notice in my daily routine, myself justifying things that are actually wrong, rationalizing things that make no sense, or making dumb decisions, at least once a minute. I'm not stupider or more impulsive than other people, so I assume it's the same for everyone.

With better "software," though, I think you can work with it, be aware of its limitations and blind spots. Become more human.

At the end of the day, your brain is *you* and it's doing the best it can. It doesn't intentionally lie to you-- it's just telling the best story it can with the information available to it.

It's weird, scary and depressing at first, thinking of yourself as not really this monolithic indivisible thing, a "soul" that you can easily single out. After you get used to it though, it becomes somehow liberating. You are a amalgamation of smaller things, fibers woven into a thread in the fabric of the infinite.

It also helps to have religion. More than half your brain is dedicated to processing emotion so don't neglect it.

(9^(2 n) -1) - ( 9^(2 (n-1) ) - 1) = 80 * 81^(n-1)

so if 80 divides ( 9^(2 (n-1) ) - 1) it also divides
9^(2 n) -1

That is not an actual mutation, though. It's a built-in failsafe. Every species has a range of environments and situations it can survive in-- those dormant stretches of DNA also evolved.

Just from understanding the, there's not (likely) going to be a stretch of DNA that has never had relevance to an organism's survival before that gets turned on in a targeted way by an epigenetic processes in response to a stimulus.

You know about locust swarms right? The swarming locusts look extremely different from the normal members of the same exact same species, and the transformation is in response to environmental overcrowding. The swarming behavior helps the species spread out over a large geographical area.

This can be considered an epigenetic process, but the swarming behavior still evolved. An organism that can adapt to that extent has an extreme fitness for its environment.

yeah any derivative of that shit you posted

How is it that protons just "don't decay" ? Surely they must

A very small perpetual motion machine is nonetheless a perpetual motion machine

At every point, time moves normally with respect to that point.

So, even if there's a sphere of distant galaxies around us receding fast enough that time has almost completely stopped for them, it can still be true that time is, in their own local frame of reference, moving completely normally, and we are the ones suspended in the past.

There is no single measure of time that applies everywhere in the universe, and things that are far away aren't just separated by distance, but by the time you'd have to travel to get there.

We don't know that they don't decay, and if there's no friction, no emission, nothing that siphons off energy, they don't need to stop.

Also if you subscribe to the Copenhagen interpretation, they aren't actually moving at all, they're just a cloud of probabilities until interacted with.

Still awaiting an answer.

thank you very much! i feel stupid now seeing how blatantly obvious it was.

Doing Multivariable Calc. right now. Currently on Jacobians and changing coordinate systems.

For a 3-D coordinate system, Do I really have to find nine partial derivatives? The textbook I have says I can use:
Partial of (X,Y,Z) with respect to (U, V, W) (pic related), but what does that mean?

Yes you need all 9 derivates, it just means find the derivate of each of X,Y,Z by each of U,V,W