SQT - Stupid questions thread

[Anonymous No.8483709]

I don't understand the concept of potential energy.

"When a test charge q_0 is placed in an electric field created by some source charge distribution, the electric force acting on the test charge is q_0E. The force q_0E is conservative because the force between charges described by Coulomb's law is conservative."

Okay this is all fine.

"When the test charge is moved in the field by some external agent, the work done by the field on the charge is equal to the negative of the work done by the external agent causing the displacement"

What does that mean?

If there is a charge q_0 in an electric field E and I move that charge along the direction of the electric field then the work I do on the charge is qEd correct? Then then the work done by the field on is -qEd?

Can someone give me a better explanation? Where does the negative sign come from?

Some clarification on work done by the external agent and work done by the field would be helpful too. Why does the field do work when I am the one that moves it?

[Anonymous No.8485383]

How did time dilate over time as the universe expanded ?

[Anonymous No.8485402]

>>8483709
>Where does the negative sign come from?
Total work is zero, or the kinetic energy would have to change.

[Anonymous No.8485404]

>>8483709
>Why does the field do work when I am the one that moves it?
Both you and the field are exerting forces on the charge. Anything that exerts a force on something that moves does work on it.

[Anonymous No.8485411]

>>8485402
>>8485404
Adding a bit:
Work is the energy you put into something by virtue of exerting a force on it. The energy you put into the charge through your force is taken away by the field through its force, and becomes part of the potential energy of the field.

[Anonymous No.8485521]

Energy has a gravitational field. So does that mean that a sufficiently strong EM field can create a gravitational field?

Also, for a short time after the big bang, there was no particles because it was too energetic. What form did this energy take? Does energy really mean anything if theres no matter to act on?

[Anonymous No.8485527]

Does the mechanism of epigenetics throw a wrench into the whole "random mutations" aspect of evolution?

[Anonymous No.8485584]

>tfw most likely going to fail calc 1
>going to kill myself after i do

;_;

[Anonymous No.8485731]

can someone explain the libet experiment and it's implications on free will to me?

if i'm interpreting the results correctly, it means that free will (as in the ability to make conscious decisions or choices) are biologically/physically impossible, as decisions are apparently made subconsciously before we are consciously aware of them. the human brain is not exempt from the laws of physics (unless you believe in a soul or something that is not bound by them), which we can't bend using our will.

i'm not arguing that we don't think that we are making choices consciously, because we clearly believe that. but isn't this just a trick our brains play on as, i.e. an illusion?

[Anonymous No.8485740]

>>8485584
this is a stupid questions thread

you're looking for the give me attention while i whine thread

[Anonymous No.8486182]

>>8485521
>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?

[Anonymous No.8486274]

Why does d(1/r)dΘ=-(dr/dΘ)/r^2 ??

[Anonymous No.8486326]

>>8483709
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.

[Anonymous No.8486494]

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.

[Anonymous No.8486569]

>>8486494
> why is a prime factorization of a number unique.
en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Proof

[Anonymous No.8486650]

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

[Anonymous No.8486674]

>>8486650
yep

[Anonymous No.8486793]

>>8485527
no

[Anonymous No.8486799]

>>8486650
No

[Anonymous No.8486802]

>>8486494
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.

[Anonymous No.8486814]

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.

[Anonymous No.8486984]

>>8486814
> 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<c

The most common such function is the "unit step" or "Heaviside step" function:
u(t) = 1 | if t>=0
u(t) = 0 | if t<0

Any other step function can then be defined in terms of the unit step:
f(t) = b+u(t-c)*(a-b)

[Anonymous No.8487005]

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.

[Anonymous No.8487092]

how did they simplify this guise?

[Anonymous No.8487103]

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.

[Anonymous No.8487126]

>>8487092
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}

[Anonymous No.8487133]

>>8487103
>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

[Anonymous No.8487137]

>>8487103
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.

[Anonymous No.8487153]

>>8486814

The definition of step function in >>8486984 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.

https://en.wikipedia.org/wiki/Step_function

[Anonymous No.8487222]

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

[Anonymous No.8487239]

>>8487222
how fucked up are you?

[Anonymous No.8487248]

>>8487239
Very spotty. I'm just ready to reteach myself all of algebra and then get started with calc independent study.

[Anonymous No.8487252]

>>8487092

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.

[Anonymous No.8487259]

>>8486494
Because [math]\mathbb Z[/math] is a principal ideal domain.

[Anonymous No.8487281]

>>8485584
dont kill yourself please anon

it gets better

[Anonymous No.8487311]

>>8486793
How does it not if certain genes are being expressed depending on the environment? Doesn't it make it a lot less random?

[Anonymous No.8487545]

How do you approach this one?

[Anonymous No.8487621]

literally can't slove this one

[Anonymous No.8487628]

>>8487621
protip 3^n/(4^(n/2)+1)=1/4 (3/2)^n

[Anonymous No.8487644]

>>8487628
how can you tell, pls

[Anonymous No.8487646]

>>8487628
or did you write out and found another sigma

[Anonymous No.8487653]

>>8487646
3^n/4^(n/2+1)
=(1/4)3^n/4^(n/2)
=(1/4) (3^n/2^n)
=(1/4)(3/2)^n

[Anonymous No.8487654]

>>8483709
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

[Anonymous No.8487657]

>>8487545
i'm curious about this one too now, not too sure how to prove

[Anonymous No.8487664]

>>8487653
oh, god, how simple
cheers

[Anonymous No.8487668]

>>8486650
Sqrt of 0 is a real number so yes

[Anonymous No.8487698]

>>8487545
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.

[Anonymous No.8487858]

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

[Anonymous No.8487861]

>>8487858
the ratio test should give you

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

[Anonymous No.8487863]

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

[Anonymous No.8487896]

>>8487863
Your body glows slightly

[Anonymous No.8488016]

WHAT THE FUCK.

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

[Anonymous No.8488036]

>>8487545
Let x=u+v+1, y=u-v+1.

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

[Anonymous No.8488111]

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

[Anonymous No.8488352]

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?

[Anonymous No.8488357]

>>8485521
Nice fantano pic, is it OC?

[Anonymous No.8488359]

>>8488352
Post it bitch

[Anonymous No.8488389]

>>8488352
>>8488359
y^2 + ( xy - 1 ) y' = 0

[Anonymous No.8488398]

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

[Anonymous No.8488457]

>>8483709
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)

[Anonymous No.8488465]

>>8488389
Which integrating factor you used? Remember ypu must get either something that only depends on x or y.

[Anonymous No.8488471]

>>8488465
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...

[Anonymous No.8488475]

>>8488465
>>8488471
I just multiplied both M and N by u(x), but it ended up having both x and y in it

[Anonymous No.8488498]

>>8488389
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.

[Anonymous No.8488503]

>>8488498
Thank you. Is it solvable using integrating factors thought?

[Anonymous No.8488542]

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.

[Anonymous No.8488561]

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?

[Anonymous No.8488579]

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?

[Anonymous No.8488608]

>>8488542
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.

[Anonymous No.8488654]

>>8488398
> 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.

[Anonymous No.8488691]

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

Can anon help? I will post work too

[Anonymous No.8488694]

>>8488691
Here is work

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

[Anonymous No.8488695]

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

[Anonymous No.8488697]

>>8488471
Your integrating factor needs to only depend upon one variable. Try the other one.

[Anonymous No.8488706]

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.

[Anonymous No.8488728]

>>8488694
0.732m is the distance from the smaller mass. The question asks for the distance from the larger (3m) mass.

[Anonymous No.8488731]

>>8487252

continuing with this high-school problem, plugging in this "first phase" into the anon'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 anon's thing out of boredom. It's on you to understand the step if you haven't done that yet

[Anonymous No.8488735]

>>8488695
b[n]->1/5, so the sum isn't convergent.

[Anonymous No.8488748]

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?

[Anonymous No.8488756]

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

[Anonymous No.8488765]

>>8485731
>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.

[Anonymous No.8488872]

>>8488756
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.

[Anonymous No.8488875]

looking for help with a basic proof by induction question:

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

[Anonymous No.8488877]

>>8488875
that should be
[math] n \geq 1 [/math]

my bad.

[Anonymous No.8488903]

>>8487005
no

[Anonymous No.8488919]

>>8485527
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.

[Anonymous No.8488945]

>>8488579
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]

[Anonymous No.8488978]

>>8485731
>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.

[Anonymous No.8489006]

>>8488875
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)

[Anonymous No.8489015]

>>8485731
Check this out. I think it'll help you get to the bottom of things, about free-will and consciousness:

https://www.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.

[Anonymous No.8489020]

>>8488875
(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

[Anonymous No.8489030]

>>8487311
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.

[Anonymous No.8489040]

>>8487005
yeah any derivative of that shit you posted

[Anonymous No.8489053]

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

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

[Anonymous No.8489060]

>>8485383
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.

[Anonymous No.8489062]

>>8489053
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.

[Anonymous No.8489070]

>>8487222
Still awaiting an answer.

[Anonymous No.8489094]

>>8489006
>>8489020
thank you very much! i feel stupid now seeing how blatantly obvious it was.

[Anonymous No.8489099]

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?

[Anonymous No.8489142]

>>8489099
Yes you need all 9 derivates, it just means find the derivate of each of X,Y,Z by each of U,V,W

[Anonymous No.8489143]

>>8489099
>Do I really have to find nine partial derivatives?
yes.

[Anonymous No.8489148]

>>8488457
Finally at home, haven't gotten an answer and I realize that my wording was kind of strange, so this image should explain it better.
This is what I've been trying. It should work in theory, but it's not and I don't know why.

[Anonymous No.8489153]

Why don't cats get constipated? All they do is eat meat and lie around all day.

[Anonymous No.8489183]

>>8488731
Is this stupid answers thread?

[Anonymous No.8489185]

>>8489148
I mean.. The way I learned Riemann Sums was as follows:
SUM( f(i*∆x + [initial_point] ) * ∆x) [sum is from i =1 to i=n, as 1/∆x approaches 0 (n -> inf) ]

This way, you are evaluating areas ... I'm not entirely clear what the purpose of the f(∆x * x) * ∆x is, though

[Anonymous No.8489197]

>>8489148
Maybe show your working and we can help?

[Anonymous No.8489206]

>>8487621
[eqn]\frac{1}{4}\sum_{1}^{\infty}(\frac{3}{2})^{n}[/eqn]

Diverges by nth root test.

Get gud kiddo, this is child's play at my uni

[Anonymous No.8489213]

Is the hamitonian function of a hamitonian system necessarily of class C^2?

[Anonymous No.8489234]

>>8489185
Basically, the sum of f(∆x * x) is the sum of the heights of the rectangles, while ∆x is the width. Because every rectangle's area has a common factor of ∆x, I factored it out and multiplied it at the end. ∆x is (b-a)/n.
>>8489197
I suppose I could jot it down on a piece of paper and take a picture, but I feel like the issue is more in the formula rather than the execution. Anyone can put numbers into a calculator, after all.

[Anonymous No.8489247]

>>8489234
Nevermind, apparently I'm just retarded. It wasn't working earlier when I was at uni, but while working on a couple as example problems for it not working, it has suddenly started working again. I guess I was just too stupid to enter numbers into a calculator earlier.
Thanks for the help, though.

[Anonymous No.8489253]

>>8489234
Okay... The way you're explaining it makes sense, but I still have a question

the sum of f(∆x * x) from one to n isn't the sum of all values of a function over an integral starting at x = a... It's the sum of the values starting at x = 0. ∆x + x represents the x-value of one vertex in the rectangle you're taking the area of, but you don't always start at zero, you start at x_0... I'm sure you're doing this already, but it might be where you're going wrong...

What do you usually get wrong on these problems? Do you not get the simplification right? Or is it something else?

[Anonymous No.8489256]

Okay... Given the line integral
∫(sqrt(x^2 + y^2)) ds along r(t) = cos(t)i + sin(t)j + 3tk,

can I just say x = cos(t), y = sin(t), and z = 3(t), and solve from there? I'm still a bit confused how we convert a multiple-variable function into a function of t

[Anonymous No.8489257]

>>8489247
Oh shit... Didn't see this till after I posted... No problem!

[Anonymous No.8489261]

>>8489256
jesus christ just find [math]\frac{dr}{dt}[/math] and its magnitude and literally substitute the formula
you should also be given another curve or line

[Anonymous No.8489387]

>>8489256
if i corresponds to the x axis, j to the y axis, and k to the z axis, then sqrt(x^2 + y^2) = sqrt(cos^2(t) + sin^2(t)) = sqrt(1) = 1, so the integral is just integral 1 ds along r(t). By the definition of Riemann integration, the integral just becomes r(t) (more specifically, r(t_2) - r(t_1)).

[Anonymous No.8489394]

>>8489253
>>8489257
Sorry for the late response, I have a habit of leaving once my problem is solved.
The example problems I was working on were only coincidentally correct, but working on them made me realize that all it needed was a small tweak. It's f(a + ∆x * x) rather than just f(∆x * x)
Thanks for the help, anon!

[Anonymous No.8489396]

If I am on a train moving at relativistic speeds, and I turn on a white light in the middle of the traincar, will a person at the back of car see it as a blue light? Would a person at the front of the car see it as a red light?

[Anonymous No.8489403]

Anyone know if it's possible to convert from the unitary DFT to the DCT without doing an inverse transform on the DFT? If so, how?

[Anonymous No.8489407]

>>8489394
Glad I could help!

[Anonymous No.8489452]

>>8487545
Since (x-y)^2>=0, then xy+x+y<=(x^2+y^2)/2+x+y.

Using (x-1)^2+(y-1)^2>=0 you can show that the last expression is <= x^2+y^2+1.

[Anonymous No.8489495]

>>8489452
>Since (x-y)^2>=0, then xy+x+y<=(x^2+y^2)/2+x+y.
why?

[Anonymous No.8489500]

Why is Brownian motion only "almost certainly" 0 at t=0? Seems like it would be just surely.

[Anonymous No.8489519]

how the FUCK do i do b)

[Anonymous No.8489543]

>>8489519

once you've found T set up an equation T=RSD, where the general form of each of these operators is known, e.g. R∈SO(2,R), D=a*I, etcetera, then solve the equation. that could work....maybe. otherwise you might just have to figure it out by messing around and actually thinking.

[Anonymous No.8489617]

Anybody know what causes cayenne pepper's distinctive taste?

[Anonymous No.8489628]

All the atoms that make up the matter in the universe will decay eventually. Space will go on to expand forever whilst being completely empty? This, as of now, is the the most probable fate of the universe?

[Anonymous No.8489662]

>>8489500
It's the same concept as "almost everywhere".

[Anonymous No.8489664]

>>8486802
>If you multiply a prime by another prime, you get a number whose only factors are those two primes, itself, and 1.
You just stated the conclusion, brainlet.

[Anonymous No.8489760]

>>8489617
Probably like, chemicals or something

[Anonymous No.8489761]

>>8489396
No. The other passengers are moving the same relative to you, so their frame of reference is the same as yours. It's called relativity for a reason.

[Anonymous No.8489765]

>>8489153
They lick their buttholes for a reason anon

[Anonymous No.8489793]

Does intelligent life exist outside the Earth?

[Anonymous No.8489794]

>>8489153
Their digestive systems are built for it.

[Anonymous No.8489796]

>>8489793
Statistically I would think that it would be very unlikely that this is the only place it has happened. But because of the distances involved we will probably never encounter another intelligent life form, barring new tech that is improbable with current understandings of physics.

[Anonymous No.8489797]

Is it possible to directly experience the universe, rather than getting imperfect secondhand impressions through the senses of your body?

[Anonymous No.8489798]

>>8489797
Most scientists believe that this is what happens after you die, and your soul is finally able to escape the confines of your body.

[Anonymous No.8489811]

>>8483709
>"When the test charge is moved in the field by some external agent, the work done by the field on the charge is equal to the negative of the work done by the external agent causing the displacement"
>What does that mean?

Work is a type of energy. Energy of an isolated system is conserved. So W + (-W) = 0 corresponds to that fact that energy is conserved.

[Anonymous No.8489851]

Really stupid question. I'm using Pearson's MyMathLab and looking at transforming polar coordinates into rectangular coordinates and I came across this step in an example and Pearson doesn't explain it. I've plugged it into a calculator but maybe I'm doing it wrong...

tan(theta) = tan(5pi/4)
tan(theta) = 1

I can't get why it equals 1...

If it explains anything, I'm in community college Trig and pre-cal. It's weird. I like math quite a bit but small things stump me.

[Anonymous No.8489860]

Mathematical induction, i don't find the idea for the 8. Can someone see it ?

[Anonymous No.8489866]

>>8489860
you have to prove that the sum of the terms of the harmonic series from (2^n)+1 to 2^(n+1) is greater than 1/2

[Anonymous No.8489872]

>>8489851
Because tan(5pi/4)= tan((4pi+pi)/4)= tan(pi+pi/4)=tan( pi/4) = sin( pi/4)/cos(pi/4)=(√2/2)/(√2/2)= 1

[Anonymous No.8489876]

>>8489866
Yes, i'm arrived here. But it seems impossible to demonstrate or too complicated.
There must be something else.

[Anonymous No.8489880]

>>8489876
the sum from 2^(n-1) +1 to 2^n is greater than The sum of its minimum term repeated

[Anonymous No.8489898]

I am asked to find a topological space (X, T) and subsets A ⊂ B ⊂ X so that:
- A is closed in B with regards to the induced topology on B
- B is open in X
- A is open nor closed in X
I can give some trivial examples, but how would I find a non-trivial one?

[Anonymous No.8489901]

>>8489872
Thank you. I noticed it made one complete rotation also.

Am I the only idiot that found trig harder than pre-cal?

[Anonymous No.8489903]

>>8489880
Ok, thanks. So the point is i need to demonstrate than the sequence sum from 2^n+1 to 2^(n+1) is increasing. That isn't seem easy, because the start of the sum move with the value of n.

[Anonymous No.8489934]

>>8489898
don't get it, is A open but not closed on X?

[Anonymous No.8489940]

>>8489898
(X,T) = standard topology on R
A = [1,2)
B = (0,2)

[Anonymous No.8489953]

Help with this? I get [math]\nabla(u) = \nabla(\frac{1}{u})[/math], but, even if that is correct, I'm not sure what to do next.

[Anonymous No.8489958]

>>8489903
> Ok, thanks. So the point is i need to demonstrate than the sequence sum from 2^n+1 to 2^(n+1) is increasing.
Um, no. The point you need to prove is that the mean value is at least 1/(2^(n+1)). There are 2^n terms in the range (2^n,2^(n+1)], if their mean is at least 1/(2^(n+1)) then their sum is at least 1/2.

If the sum to 2^n is at least 1+n/2 and the sum from 2^n to 2^(n+1) is at least 1/2, then the sum to 2^(n+1) is at least 1+n/2+1/2 = 1+(n+1)/2

Proving that the mean value is at least 1/(2^(n+1)) is trivial: the final value is equal to that and every previous value is greater because 1/x is monotonic decreasing.

[Anonymous No.8489959]

>>8489940
God damnit, it was so easy. I was thinking about all these fucked up topologies I overlooked the obvious choices.

>>8489934
Not open or closed. For instance in a metric space [a, b) is not open and not closed. In a topological space (X,T) the subset O is trivially both open (O in T) and closed (X\O = X in T).

Thanks for replying, both.

[Anonymous No.8490124]

Apologies for being a brainlet
If you have a probability mass function of a variable X and you want to find the probability mass function of a variable Y=X-n could you just replace each instance of x in the X PMF with x+n?

Specifically in the case of a negative binomial distribution

[Anonymous No.8490142]

>>8489953
Interesting! What is the Laplace operator applied to 1/u

[Anonymous No.8490149]

Okay, I'm autistic and I need to pass chemistry.

Last year of highschool, 18yo. Ca(OH)2 + Ca = 2CaOH?

[Anonymous No.8490153]

>>8490142
I get L(1/u)= -u^(-2) L(u) + 2u^(-3) || grad u ||^2. Thus grad u = 0 and the result follows.

[Anonymous No.8490186]

>>8490149
I don't remember enough high school chemistry to remember, but I don know the right hand side is incorrect. If it isn't an ion, CaOH needs to be Ca(OH)_2 so the charges cancel out...

If it is an ion, then the right hand side be 2CaOH+

[Anonymous No.8490191]

>>8490149
I don't remember enough of HS Chem to know if this is the right answer, but...

The right hand side isn't right. The RHS either contains a neutral charge (It'd be Ca(OH)_2 ) or it'd be an ion (Ca(OH) + )

[Anonymous No.8490222]

Haven't touched math/physics in ages and have an exercise to first calculate the total braking distance in meters, given the speed, traction and reaction time and then calculate the speed again, using said distance, traction and reaction time.

Basically given the speed of 100km/h, traction of 0,7 and reaction time of 1 it would be 83.9598760937531m and then given the distance of 83.9598760937531m, traction of 0,7 and reaction time of 1 I need to calculate the speed again, which would be 100km/h in this case.

I'm using v*r-t+v^2/(2tg) to get said distance in meters (converting km/h to m/s before, of course) but I'm having trouble coming up with a way to get the speed again.
I know that normally it would just be the square root of distance*2tg but how do I get the speed if I calculated it with that speed*reaction-time at the beginning?

[Anonymous No.8490428]

What is the fastest growing sequence you can write with 3 simbols? Eg. x^e^e ?

[Anonymous No.8490441]

>>8490149
nothing happens there without water
not sure what bs they teach in highschool these days tho

[Anonymous No.8490442]

>>8485527
Not even in the slightest

[Anonymous No.8490449]

>>8490428
wouldnt x^x^x grow faster than x^e^e?

[Anonymous No.8490453]

>>8490449
I just gave an example of what it should look like, anyway there is something that grows faster then x^x^x.

[Anonymous No.8490455]

Does a laptop get heavier the more files you download and store?

I mean like only in theory

[Anonymous No.8490462]

>>8490455
no, conservation of mass.

[Anonymous No.8490463]

>>8490453
there is x^(x^x)! as a ferinstance

[Anonymous No.8490470]

>>8490455
the answer is, it depends
if it has an SSD in it yes, if no, no.

[Anonymous No.8490478]

>>8490222
Is there any way to do this without quadratic equation?

[Anonymous No.8490480]

>>8490463
but that has 4 symbols

[Anonymous No.8490483]

>>8490480
I probably don't understand your stupid rule then
what do you call a symbol?

[Anonymous No.8490510]

>>8490478
Probably find the derivative or something.

[Anonymous No.8490548]

what to do for b?

[Anonymous No.8490555]

How "good" can I get in math from now till August?

I'm pretty shit at math but want to get good because of college application next August.

I'm currently around first year of high-school level, and need to be at least last year of high-school or a bit above.

[Anonymous No.8490598]

Steampressure for C02 is 0.204 atm at 22.75 º and 0.638 atm at 0ºC.
Calculate Delta Gvapº and boiling point at 1 atm?

[Anonymous No.8490608]

>>8489872
5pi/4 is 225 degrees, not 45.
Though you still get 1 anyways so meh

[Anonymous No.8490615]

>>8490548
Average value for a two-variable function is:
1/(AREA) * ∫∫f(v)*f(u)dudv... Have you tried this?

[Anonymous No.8490617]

>>8489183

no, it's the stupid questions thread. The answer as given and worked is correct.

[Anonymous No.8490620]

>>8490608
He didn't say it was 45', he said the tan was the same.

[Anonymous No.8490631]

When you calculate the standard deviation, you can do either for a population or a sample. The different is just that you end up diving by either n or n-1.

Why should n-1 be valid for a population?

[Anonymous No.8490642]

>>8490631
oops I menant "why should n-1 be valid for a SAMPLE"

[Anonymous No.8490676]

>>8490222
>>8490510
Solved using quadratic equation...

[Anonymous No.8490733]

Why do Operational Amplifiers have frequency dependence?

[Anonymous No.8490744]

Serious question: How do you internalize concepts for a long time and can work with them on transfer problems?

Is the 'Feynman technique' for example just a meme?

[Anonymous No.8490835]

Polar coordinates question:
How would I solve this on wolfram or any other calculation system?
(-4,3pi), r>0, -2pi<=theta<0

[Anonymous No.8490900]

>>8490642
Because it's an unbiased estimator for the standard deviation of the population.

The population standard deviation (square root of variance) of a sample is more likely to underestimate the standard deviation of the population as a whole than to overestimate it.

Roughly, a sample will have tend to have fewer extreme outliers due to quantisation. E.g. if the expected number of people over 7' tall in a sample is 0.1, the actual number will probably be zero.

Scaling the variance by n/(n-1) prior to the square root (Bessel's correction) compensates for this.

[Anonymous No.8490913]

>>8490733
Because they're physical devices which, unlike mathematical models, are constrained by reality.

Apart from the fact that the gain of a transistor will drop at high frequencies, every connection starts to look like an RLC low-pass filter at high frequencies.

[Anonymous No.8490914]

>>8490428
something with graham's number and/or up-arrow notation

[Anonymous No.8490928]

>>8490744
idk what the feynman technique is off the top of my head, but if you use something to solve a problem you actually care about or apply it to figure something out for yourself, you'll most certainly remember that concept much better.

If you just read something in a book that makes sense, you might not give it a second thought. When a concept becomes vital to your research or application to something, you'll probably internalize it to a greater degree. I've found that this is true especially when you mess something up initially and this concept/method is the correct way to approach your original problem.

[Anonymous No.8491005]

>>8490835
no one?

[Anonymous No.8491027]

>>8490835
What are you trying to do?

[Anonymous No.8491032]

>>8491027
plot the point (-4,3pi) given in polar coordinates and find other polar coordinates (r,theta) of this same point for which the following are true: various intervals

[Anonymous No.8491036]

>>8491032
you have no idea what you're talking about do you?

[Anonymous No.8491042]

what biology related fields are going to be in high demand in the next 5 or so years?

[Anonymous No.8491051]

>>8491042
Probably biotech.

[Anonymous No.8491082]

How come the scientific community is so slow to cure diseases?

I keep reading articles where researchers prove that they can reverse hairloss and despite it being anywhere from 20 to 10 years later the treatment still isn't available.

Plus can CRISPR be used to edit the DNA of thousands of cells at once, or does the cas9 protein just attach itself to one cell, do the edit and then die off?

[Anonymous No.8491257]

>>8491042
Biomedical engineering

[Anonymous No.8491290]

Are there real world examples of undamped harmonic oscillators?

[Anonymous No.8491319]

>>8491290
A LC circuit with a function generator to offset the resistance?

[Anonymous No.8491363]

How can I develop a solid work ethic, /sci/? I have the intelligence, but my will to succeed just evaporates when I start actually doing work. I usually end up wasting a lot of time on the Internet instead of accomplishing what I set out to do.

[Anonymous No.8491371]

>>8491290
Ideal undamped? No. But you can aprozimate anything you want to a harmonic oscillator. That's half of whst physicitswdo.

[Anonymous No.8491377]

>>8491082
1- It's slow for many reasons. Trial and error takes a long time, most experiments don't work as planned, and the ones that do need to be rigorously tested in animals, and then in humans before approved for public use. So it can take 10+ years for a disease treatment to even reach the market.

2- Articles≠truth

3- Cas9 just cleaves the DNA sequence it attaches to (although there are other forms of CRISPR tech that can do more complicated things). Once it is cleaved it is released, so it can do this to thousands of sequences within a cell if required. They'll work until they are degraded, for any one of multiple reasons.

>>8491363
I had the same problem. I found waiting a few years helped me a lot, I became more patient over time.

[Anonymous No.8491384]

What are the prerequisites for learning differential geometry?

[Mandingo No.8491430]

kok

[Anonymous No.8491488]

>>8491363
no other way than to just sack it up. Important to note that you won't just become amazing at controlling your will right away, but if you make it a habit to push yourself everyday, you'll start to see improvement.

[Anonymous No.8491520]

>>8491384
one course in geometry and two classes in differential

[Anonymous No.8491534]

>>8488748
yes it's certainly doable for me. don't know about you.

[Anonymous No.8491540]

I don't get this third law. Two forces are applying equal and opposite forces, but they do not cancel out? Am I over thinking this?

[Anonymous No.8491558]

>>8491540
they're moving (accelerating)

[Anonymous No.8491560]

>>8491384
linear algebra, analysis, topology

[Anonymous No.8491676]

>>8491377
So in that case if you wanted to CRISPR the thousands of cells that made up an organ you'd need just as many cas9 proteins, or you'd need a different CRISPR system.

And thank you!

[Anonymous No.8491682]

>>8490124
Yes, but don't forget to do it for all the times where P(X = x) = 0 as well (i.e., for all integers x, including the nonpositive ones).

[Anonymous No.8491685]

>>8491540
That diagram has nothing to do with Newton's third law.

[Anonymous No.8491707]

if i have (a + b)^1/n >= a^1/n + b^1/n, a,b > 0
am i allowed to raise everything to the power of n, i.e turn it into
(a + b)^n >= a^n + b^n

[Anonymous No.8491761]

>>8491707
>>am i allowed to raise everything to the power of n
>Yes, but
[eqn]\left( a^{1/n} + b^{1/n}\right)^n \neq a^n + b^n[/eqn]

[Anonymous No.8491772]

>>8491560

The first two much more than the last one. I'd also say "advanced calculus" rather than analysis.

[Anonymous No.8491785]

Help me anon!

How do I calculate the time it will take for the ball to hit the ground?

What was the speed given to the ball?

-------------------------------------------------------------------

1) t=sqrt((2*height)/g) = sqrt(10/10) = 1s ?

2) v=sqrt(2*g*height) = sqrt(100) = 10m/s?

Does not feel right to me. Can anyone, please, clarify about this horizontal projectile motion?

[Anonymous No.8491789]

>>8489015
>>8488978
>>8488765
thanks guys!

[Anonymous No.8491795]

Is the progression of time a real thing within the universe, or just something the human brain imposes on us?

[Anonymous No.8491798]

>>8491761
Not only that, but he said to the power of n, not n^2.

[Anonymous No.8491799]

>>8491785
also, the ball was kicked by a man.

[Anonymous No.8491802]

>>8491785
The first part is correct. The second isn't (horizontal velocity is unaffected by gravity).

[Anonymous No.8491864]

Question about BSTs, in pic related, if I delete 56, how do I decide whether it gets replaced with 49 or 59? What decides which subtree is traversed to find a replacement node?

[Anonymous No.8491956]

>>8491864
You can choose either one.

If you can easily tell which choice will result in the most balanced tree, use that.

[Anonymous No.8491982]

Time dilation related question.

Spaceship is going to Tau Ceti (11.9 light years away)
From the crew's perspective, it only takes 6.8 years to arrive due to time dilation.
How long did it actually take and what was the ships average velocity?
Would the time dilation effects have been any different if the ship was going at a constant speed the whole way there versus accelerating constantly until the halfway point and then decelerating the last half?
How can I figure this shit out on my own?

[Anonymous No.8491985]

Network theoretic question

I'm trying to calculate the neighborhood overlap in an undirected graph. I am given #nodes connected to A and B. How can I now calculate the #nodes connected to A or B.

[math] \textrm{overlap} = \frac{\textrm{#neighbors of A and B}}{\textrm{#neighbors of A or B}}

[Anonymous No.8491988]

>>8491985
Why the fuck doesn't the [math] tag work?!

[Anonymous No.8492155]

>>8491988
you need to close the tag after opening it brainlet

[Anonymous No.8492156]

>>8491988

you didnt close it

[Anonymous No.8492159]

>>8492155
>>8492156
Didn't have to close it [math]\frac{\textrm{In the good}}{\textrm{old days nigga}}[/math]

[Anonymous No.8492168]

>>8491772
Yeah, I guess more multivariable calculus than analysis (but if you want to prove Stokes' theorem or Sard's theorem you will need some measure theory). And I was really thinking about a minimal amount of topology, enough to understand what a manifold is (but once you talk about group actions on manifolds and orbit spaces, you actually need to do some topology).
I guess it depends how far the course is going

[Anonymous No.8492169]

>>8491985
I'll rephrase the equation then

[math] \textrm{overlap} = \frac{\textrm{#neighbors of A and B}}{\textrm{#neighbors of A or B}} [/math]

[Anonymous No.8492171]

[Anonymous No.8492180]

>>8492171
Surely it would be easy if you just expand both expressions?

[Anonymous No.8492189]

>>8492169

I have no idea what other information is available to you, but:

(# neighbors of A or B)
= (# neighbors of B) + (# neighbors of A but not B)
= (# neighbors of B) + (# neighbors of A) - (# neighbors of A and B)

Draw a Venn diagram if you're not convinced.

[Anonymous No.8492200]

How do you show that something is invariant under some transformation? I've got to show that some the light cone [math] \eta _{ \mu \nu } dx^{ \mu } dx^{ \nu } =0 [/math] is invariant under the transformation [math] x^{ \mu } \rightarrow x^{ \mu } / x^2 [/math]. I've sort of been winging it, my thinking was that if the light cone is invariant then acting on it with a couple of Jacobians [math] \eta _{ \mu \nu } \Lambda ^{ \mu } _{ \rho } \Lambda ^{ \nu } _{ \sigma } [/math] Should equal [math] \eta _{ \rho \sigma } [/math], after going through all the steps. The only problem is I end up with [math] \eta _{ \rho \sigma } / x^4 [/math]

Is my approach right, and more importantly is it general?

[Anonymous No.8492224]

Guys what's the derivative of this
[eqn]
\frac{1}{2}||f(x)||^2
[/eqn]

is it just

[eqn]
\frac{d||f(x)||}{dx}
[/eqn]
so always positive?

[Anonymous No.8492234]

>>8492224
You're lacking a ||f(x|| in front of the derivative. Also just because the norm is positive doesn't mean it's derivative is positive

[Anonymous No.8492236]

>>8492224
[eqn] g(x) = \frac { 1 } { 2 } \left | f ( x ) \right | ^2 \\ \text { Let } ~ u = f(x) \implies u' = f'(x) \\ g'(x) = \frac { d g } { d u } \frac { d u } { d x } = | f ( x ) | f'(x) [/eqn] If [math] | f ( x ) | [/math] is just the modulus then you can differentiate that again using the chain rule.

[Anonymous No.8492242]

>>8492180
Doh you are right. I didn't realize I could show that the difference between the two was positive, so thus the inequality held true.

[Anonymous No.8492243]

If I have a system of differential equation like:

dx/dt = 2x-y
dy/dt = x

I derivate the first one and do the elimination thing to get rid of Dy and -DY, then I have:

DDx-2Dx+x=0

I solve this for a general solution and get:

C1*e^t + C2*t*e^t

I know that in order to solve the equation I need to do this process for both variables, and the do other stuff. Questions:

This one I did, is it y=C1*e^t + C2*t*e^t or x=C1*e^t + C2*t*e^t? I think it's x but also I'm not sure if it even matters.

Are y=stuff and x=stuff always the same? Because I have seen examples and they always are. So can I just assume it or will I have to do it from the beginning for the other variable?

Assuming that I have to do it for the other variable, I guess that I would have to find a way to eliminate the x's in the original equation, but could I also just take DDx-2Dx+x=0 and replace it for DDy-2Dy+y=0? Please help.

[Anonymous No.8492248]

>>8492236
>>8492234
Thanks guys I get it now!!

[Anonymous No.8492277]

>>8483709
Is it even remotely possible to naturally clone yourself over the span of 70 years through incest?

[Anonymous No.8492334]

Let's say Person A pushed Person B on an office rolling chair with five wheels across a concrete, flat surface. Person B managed to get 10.0m in 8.0s before coming to a stop.
Where do I even start to find the amount of force Person A used to push Person B?

[Anonymous No.8492349]

>>8492243
The second equation is just x=dy/dt, so substituting that into the first gives you
d^2y/dt^2 - 2dy/dt + y = 0
Which is a second-order linear ODE in one variable.
Solving gives you y as a sum of exponential terms with time constants of sqrt(2).-1 and -(sqrt(2)+1).

Then you can just differentiate y to get x.

[Anonymous No.8492360]

Is there a math function for this:

...
2 compared to 5 gives 2.
4 compared to 5 gives 4.
6 compared to 5 gives 5.
10 compared to 5 gives 5.
...

I'm looking for a clean shortcut instead of writing if n > 5 then 5 else n.

[Anonymous No.8492361]

>>8492334
You can't find the force, only the impulse (force-time integral).

10m in 8s is 1.25 m/s average. Assuming constant deceleration, that means that the initial speed was 2.5 m/s. Multiply by the mass of person B and the chair to get the initial momentum, which is is equal to the impulse.

[Anonymous No.8492362]

>>8492360
min(n,5)

[Anonymous No.8492363]

>>8492362
I'm the most retarded man on earth.
Thanks.

[Anonymous No.8492395]

I can see that it works for some examples, but how do I prove this?

[Anonymous No.8492411]

>>8492395
[eqn] a+b+c = 0 \implies a = -b-c = -(b+c) \\ ab+bc+ac = -(b+c)b +bc -(b+c)c = -b^2-cb+bc-cb-c^2 = - \left ( b^2 + cb + c^2 \right ) \leq 0 [/eqn]

[Anonymous No.8492417]

Does anyone have the graphic where social science majors were polled on how well they understood statistics, and none of them even knew what a p value is? Or was it actual social scientists?

[Anonymous No.8492427]

>>8492417
Paper:
https://www.researchgate.net/profile/Heiko_Haller/publication/27262211_Misinterpretation_of_significance_A_problem_students_share_with_their_teachers/links/0deec53198736a7dae000000.pdf

[Anonymous No.8492432]

How fucked am I this semester that is coming up?

[Anonymous No.8492436]

>>8492432
>only 3 classes
>at an easy school like Pomona
whats the problem exactly?

[Anonymous No.8492438]

>>8492427
Excellent, thank you.

[Anonymous No.8492443]

>>8492436

I'm afraid of the 4-week courses and I'm not smart.

[Anonymous No.8492444]

>>8492443
get a headstart? you have over a month

[Anonymous No.8492447]

>>8492411
Oh that makes sense. Good idea to solve for one of the variables.

Last question.

I tried multiplying to get a common denominator of abc for the left side, but not sure what to do with this.

[Anonymous No.8492454]

>>8492277
Yes

[Anonymous No.8492458]

>>8492432
4.0 + unlimited free time unless you're an absolute brainlet.

[Anonymous No.8492464]

>>8492432
>>8492443
>crying about business classes

If you can't do these courses this semester without at least getting a C in them, it's time to quit college and go into a trade.

[Anonymous No.8492468]

>>8492447
take a look at
(ab-ac)^2+(ab-bc)^2+(ac-bc)^2 >= 0

[Anonymous No.8492484]

>>8492395
c=-(a+b)

ab+bc+ca = ab-b(a+b)-a(a+b)
= ab-(ab+b^2)-(a^2+ab)
= -(a^2 + ab + b^2)
= -(4a^2 + 4ab + 4b^2)/4
= -(3a^2 + 6ab + 3b^2 + a^2 - 2ab + b^2)/4
= -(3(a^2 + 2ab + b^2) + (a^2 - 2ab + b^2))/4
= -(3(a+b)^2 + (a-b)^2)
<= 0

[Anonymous No.8492501]

>>8492432
Looks pretty cake anon. Mine is too
>tfw last semester and only taking an upper level statistics course, graphics theory and computer programming 2

Should I take intro to experimental design or probability models? I need one of the two for my statistics minor

[Anonymous No.8492502]

>>8492501
Kek, graph theory not graphics

[Anonymous No.8492525]

>>8492468
>(ab-ac)^2+(ab-bc)^2+(ac-bc)^2
Gotcha thanks, multiplied both sides by two and was able to factor it haha.


I thought I had this one, but got stuck.

[Anonymous No.8492566]

>>8492525
nvm figured it out. Had to multiply both sides by two twice after I squared both sides.

[Anonymous No.8492599]

If you randomly take balls from a box that contain eight red balls and five blue balls, how many do you have to take be certain to get two of the same colour? The answer given is three but how does that make sense? If you take up three why wouldn't there be a chance of them being different colours since there are five pairs of odd colour balls? Shouldn't the answer be 11 ?

[Anonymous No.8492607]

>>8492599
Son, are you retarded? There are two colors, of course there will be a repeat if you pick three balls.

[Anonymous No.8492646]

What are the terms for these two?
Double X and Y gets tripled
Increment X by one and Y gets tripled

[Anonymous No.8492660]

>>8492607
yes i am retarded i just realized and it's way past bedtime. I was the question asked for pairs for some reason

[Anonymous No.8492683]

>>8492660
If you take six pairs, at least one pair will have both balls having the same colour. You can't have six red+blue pairs with only five blue balls.

[Anonymous No.8492690]

>>8492646
> Double X and Y gets tripled
y=3^(log(x)/log(2))
> Increment X by one and Y gets tripled
y=3^x

[Anonymous No.8492716]

im a bit confused about something very simple. I have an equation k = P/v where k = 50kN/m and v = 30 mm. I assumed that P would be 50 000*0.03 but when i plug that value into further equations it gives values that are way off what they should be. Should it just be 50*0.03? should i ignore the 10^3 because it's the unit of the outcome?

[Anonymous No.8492736]

>>8492716
P=kv=50kN/m 30 mm = 50kN/m 0.03 m = 1.5 N

[Anonymous No.8492755]

>>8492736
1.5 kN *

[Anonymous No.8492809]

>>8492736
>>8492755
is it kN or N? cos N is giving me some values that i would expect when i put it into further equations and kN is not, but i cannot see why it would be N

[Anonymous No.8492815]

>>8492809
the only unit that cancels is the 'm', so you're left with 1.5 kN = 1500 N

[Anonymous No.8492816]

ses om [math]\pie[/math] dagar

[Anonymous No.8492818]

ses om [math]\pi[/math] dagar

[Anonymous No.8492913]

>>8490428
bump, looking for the fastest growing Formula you can write with 3 letters and it isn't x^x^x

[Anonymous No.8493075]

>>8492913
You need more constraints or it's impossible

[Anonymous No.8493087]

>>8492913
if I understand correctly, there is no such formula, since if you have any formula f(x,y,z), then f(x,y,z)^2 grows faster

[Anonymous No.8493106]

>>8493087
no, he looks for a formula f(x) which you can define with only 3 signs, e.g. f(x)= x + x or
x2! etc.
Also your statement isn't right in general.
Consider e.g. f(x)=1-(1/x), than we have
f(x)^2<f(x) for x>1.

[Anonymous No.8493111]

>>8493087
n^.5 vs n^.25?
For any fast growing function, you actually take the composition not the square.
and the limit of 3 letters changes the composition existence.
>>8492913
probably chained arrow notation or something.

[Anonymous No.8493124]

>>8493106
>with only 3 signs

then it strikes me as a not well-defined question unless we know what kinds of signs are allowed

and thanks for the correction; since we were talking about fast-growing functions, I implicitly assumed the function would be >1 for sufficiently large arguments

[Anonymous No.8493175]

Any math minors here? Is it worth it to minor in math or is it just a waste of time? I'm an electrical engineering major and want to minor in either math or physics. I am leaning towards math but I have heard it's not worth it by a few people simply because you hardly scratch the surface in a minor. Plus, although I haven't exactly planned my entire schedule for the rest of college, I might not be able to take all of the classes I would want to.

[Anonymous No.8493192]

>>8492361
Well, shit.
Thank you very much for the help, anon!

[Anonymous No.8493270]

Why does a wrong statemt imply anything?
are f ->w and f->f true? Is it just definition or does it make any kind of sense?

[Anonymous No.8493278]

Climate change is a thing right?

Too my understanding we're definietly contributing to the atmosphere's carbon dioxide levels, but it's not end of the world type shit; especially considering within the next 100 years or so we should have a way cleaner source of energy if technology keeps advancing.

Or am I missing something and climate change is actually way worse than what I think it is? Surely something as big as the atmosphere can deal with the amount of shit we're pumping into it? I guess 7 billion people is a lot to deal with though

[Anonymous No.8493295]

>>8488706
Elementary stats is baby tier, and I only had calc I when I took it. It would have been easy with only algebra, though. You'll be fine.

[Anonymous No.8493296]

why does my bicycle stays upright tho

[Anonymous No.8493302]

>>8493175

Math major here. I also minored in history and philosophy, and would you like fries with that.

Now some realtalk. You have to ask yourself what you want out of life, and what skill set you reasonably expect to have, and what employment you would like to find.

Your major is the important thing. As long as you actually like your major, as I did mine, and are satisfied with that being the core of your deep tertiary training, as I am mine, then the important stuff is taken care of.

>you hardly scratch the surface in a minor

This is true of all undergraduate minors. Furthermore, employers really don't give a shit about minors, it's just a puff piece during interviews to maybe get a sense of your personal interests. So, then, what is the minor /for/, really?

The minor is for /you/, mostly. I say that if you actually enjoy taking babby to babby+ classes in a particular area, /and/ it helps you to see your own major from a different point of view (as my minors did me), then I say do it. It's not your main employablility selling point, so there's no reason not to.

[Anonymous No.8493373]

>>8493270
The statement p -> q is true when p is false because implications dont make any promises for when p, the hypothesis, isn't true. so it's technically not lying and thus isn't false, so it must me true. I think an example will make this more clear. let p = you mow the lawn, and q = I give you $20. p -> q = if you mow the lawn, then I'll give you $20.

Let's examine all four possibilities:

If both are true then of course I am a man of my word and the implication is true

If you don't mow the lawn and I don't give you $20 I still haven't gone back on my word so the implication is true

If you do mow the lawn and I don't give you $20 then I of course lied to you and the implication is false.

Now, suppose you don't mow the law, but I give you $20 anyway. You can't call me a liar because I never said what I would do if you didn't mow the lawn. Thus the statement isn't false, so it must be true.

[Anonymous No.8493377]

>>8493373
thanks

[Anonymous No.8493405]

>>8483709
What did the Primordial soup taste like?

did it have duck noodles?

[Anonymous No.8493407]

>>8493405
Salty coins and milk + shinjis semen

[Anonymous No.8493423]

If someone knows a short way to show this is true i'd appreciate it.

[Anonymous No.8493426]

>>8493407
so like your mom's vagina?

[Anonymous No.8493435]

Why is the circumference of the circle the derivative of the area of the circle? Why is the surface area of a sphere the derivative of the volume? Just what the hey is going on here?

[Anonymous No.8493441]

>>8493435
Something something Stokes' theorem?

[Anonymous No.8493470]

Sounds like some voodoo magicks. Elaborate.

[Anonymous No.8493477]

>>8493407
Who is shinji?

[Anonymous No.8493546]

What is a good telescope that can take pictures? Any suggestions?

[Anonymous No.8493555]

>>8493477
The guy from this anime

[Anonymous No.8493578]

>>8493423
How about this?
[eqn]
\left( \sum_{i=1}^n i \right)^2 \\
= \sum_{i=1}^n \sum_{j=1}^n ij
[/eqn]Split this into [math]j \leq i[/math] and [math]i < j[/math] parts:
[eqn]
= \sum_{i=1}^n \sum_{j=1}^i ij + \sum_{j=1}^n \sum_{i=1}^{j-1} ij \\
= \sum_{i=1}^n \sum_{j=1}^i ij + \sum_{i=1}^n \sum_{j=1}^{i-1} ij \\
= \sum_{i=1}^n i \left( \sum_{j=1}^i j + \sum_{j=1}^{i-1} j \right) \\
= \sum_{i=1}^n i^3
[/eqn]

[Anonymous No.8493587]

>>8493578
That's what i tried to get at, thanks a lot.
I had a hard time understanding how you split them and put them back togther, that's a nice step though.

[Anonymous No.8493653]

Is a surprisingly unsurprisingly fact a unsurprising fact or a surprising fact?

[Anonymous No.8493659]

>>8493653
https://en.wikipedia.org/wiki/Unexpected_hanging_paradox

[Anonymous No.8493662]

my stupid question: How do I calculate "M" in an error bound for the Taylor's series?

|f(x) - T1(x)| <= M/2 |x-b|2

Is it just finding the largest value of f''(x) on the interval?

So I'm assuming I have to solve f'''(x)=0 and then plug that value into |f''(x)|,
but if there's no value, then I plug in both endpoints of the interval into f''(x), find the bigger one, and use that for M?

[Anonymous No.8493844]

>>8493278
From a planetary scale, we're adding a relatively small amount of carbon to the system, but we're adding just enough to disrupt the natural cycle. In some cases, we have kicked off a positive feedback loop that will not stop under any circumstances.
It probably won't kill us within the next 200 years, but at the current pace it's unlikely that humanity will survive in its current form for much longer than that.
On the upside though, I doubt we would've made it that long either way; humans really love killing other humans.

[Anonymous No.8493847]

>>8493662
If the Taylor series converges, then the value of the series at any point is exactly equal to the value of the function at that point. The error is zero.

So the difference between a Taylor polynomial (the truncation of the series to a finite number of terms) and the function is equal to the difference between the Taylor polynomial and the Taylor series, which is equal to the (infinite) sum of the terms which were discarded.

And if the series itself converges, so does any series obtained by removing some finite number of initial terms.

[Anonymous No.8493850]

I just can't do it

[Anonymous No.8493883]

This is for any sciences or engineering students in Ontario - I'm going into mech eng at a decent school in Ontario, but am playing varsity so I'll be taking a reduced courseload over five years to make work more manageable, and use up all my years of varsity eligibility. I'm wondering if Ill even be eligible to apply to a masters prpgram at a top Canadian school after I finish due to the reduced courseload. Thanks.

[Anonymous No.8494036]

>>8485521
This is gonna be a bit wibblywobbly

#1 No, or at least not with our current understanding of forces and physics. Its why we use the so called 4 fundamental forces, being strong\weak nuclear, gravity and electromagnetic to describe the interactions between matter. Its a bit wierd, because the forces still influence each other, and has to do with the distribution of energy. A sufficiently strong EM field can add apparent mass to a particle, increasing its gravitational pull (not in any significant way though).

#2 Not sure it this will answer it, but this is the discussion I've had with some people more focused on this (I'm a biochemist, not really physist). Energy is a really good way of describing the potential of "something" and how far away it is from it's entropy rest point. The energy in the big bang before expansion existed as a massive potential in the quantum foam, before expansion (with it the uneven distribution of energy density) and condensation into matter.

[Anonymous No.8494092]

I got a question about the solar spectrum. It exists out of UV, visible light and IR but why just those 3? is it just because of the temperature at the sun's surface?

[Anonymous No.8494125]

>>8493302
Thank you for the well thought out reply.
I understand that a minor isn't really that important in terms of employability, as I've been told you should minor in something that you simply want to know more about, as an interest. This is why I'm considering a math minor. I'm confident I would enjoy the classes, but I'm not sure if they would help me see my major from a different point of view, like you said, just because I don't really know at this point what level of math electrical engineering classes will delve into.

[Anonymous No.8494255]

>>8494092
It's not just those three. It covers the entire spectrum from RF to cosmic rays. It's just that the peak is roughly around the visible spectrum (or rather, the visible spectrum is around the peak of the sun's emission spectrum).

[Anonymous No.8494265]

>>8494255
Yeah, but my teacher wants me to explain why those are the peak. Is it just because the surface of the sun is 5700K?

[Anonymous No.8494274]

>>8494265
yes
https://en.wikipedia.org/wiki/Color_temperature#The_Sun

[Anonymous No.8494283]

I can't remember all the stupid ways to simply functions and how to recognize them, could/should I learn the Ruffin rule so that even if is hard and takes longer at least I have a 1 method for all?

(A specific good source for math knowledge? Not that there aren't any in my language).

[Anonymous No.8494287]

>>8494274
that's what I told my teacher, lol. Maybe he didn't get what I was saying. Thanks a lot buddy!

[Anonymous No.8494395]

why is coal a solid and petroleum liquid?

[Anonymous No.8494432]

If the alpha angle in the formula for transforming rectangular coordinates into polar ones gives me arctg of something i dont know, is there a way to write the polar coordinates or do i just leave it like this

z=|z|(cos(arctg(something))+ isin(arctg(something)))

[Anonymous No.8494451]

>>8494125
Not him but I say go for it if it interests you. The more math you know, the more you will be able to do in any STEM field. I personally would argue the most important benefits of studying math come from the way in which it teaches you to think and reason. You very may well get this from studying engineering and physics too, Idk.

[Anonymous No.8494528]

Im reading my uni physics textbook on waves. Why are they so fucking uninteresting? Can someone propose me brief lectures to understand all the basic concepts?

[Anonymous No.8494549]

Prove that 5^32 - 2^32 is divisible by 609. Any help?

[Anonymous No.8494578]

>>8494549
(5^32-2^32)=(5^16+2^16)*(5^16-2^16)
(5^16-2^16)=(5^8-2^8)*(5^8+2^8)
(5^8-2^8)=(5^4-2^4)*(5^4+2^4)
(5^4-2^4)=625-16=609

[Anonymous No.8494588]

>>8494578
Thank you.

[Anonymous No.8494626]

I've got one for biofags/medfags that I would really appreciate help with.

So the question says that mackerel are very active fish who swim freely in the surface waters of the sea. Plaice, who are of a similar mass, are very inactive and spend their time moving slowly along the sea bed. It asks what you would expect of the relative positions of the oxygen dissociation curves of these two fish.

Now, the syllabus textbook provided detail on the structure and role of haemoglobin, how different species have different forms of haeomoglobin, and it also describes why oxygen dissociation curves take the shape that they do. Furthermore, it describes the effects of CO2 concentration on the affinity of haemoglobin for oxygen and how oxygen is loaded, transported, and unloaded, and provides an example of how lugworms and llamas live in environments with a lower partial pressure of oxygen and therefore require haemoglobin with a higher affinity for oxygen and subsequently have oxygen dissociation curves shifted to the left of humans.

Now, from that information, why should I assume that a more active fish would have an oxygen dissociation curve to the right of the less active fish? Their justification for the relative positions of the curve is that the more active fish requires haemoglobin with a lower affinity for oxygen so that it is more readily unloads oxygen to the rapidly respiring cells. Fair enough. But having a higher affinity for oxygen also increases the percentage saturation with oxygen of haemoglobin at any given partial pressure. This would allow haemoglobin to more readily and rapidly bind with oxygen and carry it to the tissues with the highest concentration of surrounding CO2 without losing it prematurely in the blood or at the gas-exchange system due to the generally higher levels of CO2 (relative to Plaice) which result from increased respiration.

[Anonymous No.8494943]

I'm falling to understand this argument to say Intermediate Value Theorem fails in Q.
Suppose we change Q to R, and define for the x^2 = 2(either to be -1 or 1). What is my c such that f(c) = 0?

[Anonymous No.8494949]

>>8494943
>Suppose we change Q to R, and define for the x^2 = 2(either to be -1 or 1)
no longer continuous (at the boundary points +-sqrt(2), which is why it works over Q)

[Anonymous No.8494964]

>>8494949
Oh, that explains why I was failing to find this c. Thanks anon.

[Anonymous No.8495218]

I am mounting a DC electric stepper motor on an aluminium (or possibly steel). Accuracy of the stepper motor is paramount. It will have an optical encoder.

Do I have to shield the motor in any way? Like put a rubber/non-conductive plate between the motor and the block?
Do I have to shield it from general environmental interference?

[Anonymous No.8495224]

How do I apply Ruffini's rule to the breakdown of polynomials of the second degree?

Yes I know that is used for those of the third and higher, but I am trying to learn just 1 even if long method.

[Anonymous No.8495285]

>>8495224
Similar to this question, how do you apply ruffini's rule you got a polynomial of the second/third degree in the dividend?

[Anonymous No.8495314]

How do I solve this? I just need some tips, not necesarily the complete answer. Thanks.

[Anonymous No.8495357]

>>8495314
Did I messed up?