/sci/ - Science & Math

Reminder that homework threads are against the rules.

>>11394139
>2x(-x^2-1)cos^4(-x^2+1)
Yep. That's what I got. So what does that expression represent? It represents the slope of F(x). [eqn] \frac{\text{d}F}{\text{d}x}\Bigg|_{x=1/2}=2(1/2)\big(-(1/2)^2-1\big)\cos^4\big(-(1/2)^2+1\big)=(-5/4)\big(\cos(3/4)\big)^4 [/eqn]
which is definitely a negative number. So F(x) is decreasing at x=1/2.
>>11394277
Khan Academy.

>>11394139
>2x(-x^2-1)cos^4(-x^2+1)
Yep. That's what I got. So what does that expression represent? It represents the slope of F(x). [eqn] \frac{\text{d}F}{\text{d}x}\Bigg|_{x=1/2}=2(1/2)\big(-(1/2)^2-1\big)\cos^4\big(-(1/2)^2+1\big)=(-5/4)\big(\cos(3/4)\big)^4 [/eqn]
which is definitely a negative number. So F(x) is decreasing at x=1/2.

I've got 2 differentials equations that models the motion of a spring-mass-damper system.
[eqn] m_2\ddot{x}_2+c_2\dot{x}_2+k_2x_2-c_2\dot{x}_1+k_2x_1=f(t)\\m_1\ddot{x}_1+(c_1+c_2)\dot{x}_1+(k_1+k_2)x_1-c_2\dot{x}_2-k_2x_2=0 [/eqn]
where all the Cs and Ks and Ms are constants and f(t) is an arbitrary forcing function of time.

Q: is there any good way to simplify this system other than writing down the transfer function?

>>11117505
>>11117586
>>11117600
lol

https://archive.is/20181112031503/https://www.actualized.org/articles/a-rant-against-morality
>reality should have pedophiles
>Yes, I actually like defending pedophiles
>I claim that it is a graver sin than pedophilia (which, BTW, was legitimately practiced in many cultures).

>>11117916
>t. donates many hundreds of shekels to new-age pedophiles

>>11117832
based greg poster

Did you know that is is guaranteed that at least one other human on planet earth has the same number of hairs on their body as you do?

>>11062868
Because E=mc^2 is only valid for objects with no momentum.
For a photon, [math]|\mathbf{p}|=\frac{h}{\lambda}[/math] where h is planck's constant and lambda is wavelength. this is the de Broglie relation. From Einstein we know
[eqn]E^2=p^2c^2+m_0^2c^4[/eqn]
But, the rest mass of a photon is zero so
[eqn]E=\frac{hc}{\lambda}[/eqn]
which is a very commonly used and cited formula for the energy of a photon.

>>10798367
Photons do not have mass, you are correct. In classical mechanics, momentum is merely the product of mass and velocity. In special relativity, however, there is a famous relation between the square of energy and the square of momentum:
[eqn]E^2=p^2c^2+m_0^2c^4[/eqn]
since the rest mass of a photon is zero and since [math]E=\hbar\omega[/math] for a photon,
[eqn]\hbar\omega=\frac{hc}{\lambda}=|\mathbf{p}|c[/eqn]
so
[eqn]|\mathbf{p}|=\frac{h}{\lambda}[/eqn]
where p is momentum, h is Planck's constant, lambda is wavelength. This is de Broglie's equation.

>>10742444
waste of trips. it's not my fault you're an underage, pathetic sadboi. /sci/ is a free market board.

>Ever since the neolithic revolution we have started working agricuck fake jobs that don't do anything in this world. An agricuck cuck doesn't hunt food or do anything substantial neither do most people working at the grain mill or brewer or so. The academy is shit too. Human bodies are also breaking down in the presence of farming. And modern apothecary has allowed unfit people to survive this far. In the prehistoric ages all a person had to do was work for an honest living in a REAL JOB and had a wife and family. This agricultural world is a nightmare and academia only does basic philosophy not applied. What we do has no real world connection

imagine being such a cynical sadboi you cant into jazz
https://www.youtube.com/watch?v=OPTjfKTnuCc
https://www.youtube.com/watch?v=JB2X5dfeTA4
>>10671447
based
https://www.youtube.com/watch?v=9cqRxo1V_OM
>>10671484
>I mostly listen to video game soundtracks because I am autism.
that made me feel very sad for you

https://www.youtube.com/watch?v=zprYyWMcUGY
https://www.youtube.com/watch?v=Pv8IM_-Bam0

>>10641085
based and liberty pilled