solve Definition and 7 Threads

I have this expression, $$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r}$$. Now I want to solve this equation for ##r## perturbatively. This will give the expression $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \pi P q^2-1\right)}{8 \left(\pi ^2 T^3\right)}+.......$$. I was reading...

Hello there, I am trying to solve the Following equation for r, $$2 a Q^4+5 r^4 \left(3 c (\omega +1) r^{1-3 \omega }-2 r (r-3 M)-4 Q^2\right)=0$$ Clearly this is unsolvable. But if we substitute a=0 and c=0 we get one of the solution, ##r=\frac{1}{2} \left(\sqrt{9 M^2-8 Q^2}+3 M\right)##. Can I...

I was going through an article. I have the following functions, $$f(\text{r})\text{=}-\frac{2 M r^2}{g^3+r^3}+\frac{8}{3} \pi P r^2+1$$ $$\text{v}(\text{r})\text{=}\frac{f(r)}{r^2}$$ Now I want to solve v'[r]=0 for r. Clearly This cannot be solved analytically. But there they solved it...

Wolfram gave the solution and a hint: i want to understand the hands on approach steps... In my approach (following Wolfram's equation) i have, ##(x-3)^2(2+12(x-3)+(x-3)^2=-25## ##(x-3)^2((x+3)^2-33)=-25## ##(x-3)\sqrt{((x+3)^2-33)}=-5i## ...

I saw this link; is the approach here correct...

DofA = D0 + 1/2at^2 DofB = vt DofA = DofB, but how do I solve this and get the time when A and B hit?

I really do not understand what they are asking here...wording here in english is a bit confusing to me...but from similar examples, i made use of the approach below (which i still do not understand) hence my post. ##\dfrac{30π}{60 ×180} = \dfrac{0.0254}{d}## ##d = \dfrac{274.32}{30π}## ##d=...