solutions Definition and 9 Threads

Let's denote ##\sqrt[3] r =t##. The three expressions above can be written as $$x_1=2t \cos \frac {\phi} 3, x_2=t (-\cos \frac {\phi} 3 -\sin \frac {\phi} 3), x_3=t (-\cos \frac {\phi} 3 +\sin \frac {\phi} 3)$$ The Vieta's formulae for the given equation are $$x_1+x_2+x_3=0$$ $$x_1 x_2+ x_2 x_3...

I'm currently revisiting Susskind's GR series, with the intent on hosting a weekly group "watch and work" "party" at the uni I work at. The free lectures are great and I'm glad to have them. However, I think they could be supplemented with some problems and solutions, particularly ones that...

I am a retired Tech who needs find better solutions for my everyday projects (my oldest book = CRC Handbook of Chemistry and Physics 52nd edition) . Presently - understanding heat transfer , water vapour mobility , air movement due to Temp and relative humidity. Too many variables , need help.

For a linear nth order differential equation with constant coefficients, the general solution can be expressed as a linear combination of n linearly independent solutions. Fine... By finding n linearly independent solutions, we are essentially covering all the necessary components to form the...

Added solutions. Check if there is a correct solution.

Hello, can anyone advise about specified differences between ph meters for solutions, cream and oil.

All simple harmonic motion must satisfy $$\frac{d^2s}{dt^2}=-k^2s$$ for a positive value k. The most well known solution is the sinusoidal one $$ s=Acos/sin(\omega t + \delta)$$ A is amplitude, ##\omega##is related to frequency and ##\delta## is phase displacement. My lecturer said that there...

Solutions are also attached as a file

For this, I am trying to find solutions, however, I think I am getting a strange result that I am not too sure how to intercept. I first multiply the first equation by 2 to get ##2x_1 - 8x_3 = 4## and then I add it to the second equation below to get ##0 = 1##. I think this means that there...