σt^2=(1/p)*(σp^2+(1/s)*(σs^2+(1/a)*(σa^2)))
Solve for σp
You asked:
Given \(σ \cdot {t}^{2} = \frac{1}{p} \cdot \left(σ \cdot {p}^{2} + \frac{1}{s} \cdot \left(σ \cdot {s}^{2} + \frac{1}{a} \cdot σ \cdot {a}^{2}\right)\right)\) evaluate the expression \(σ p\).
MathBot Answer:
\[p σ = - \frac{a σ}{p s} + t^{2} σ - \frac{s σ}{p}\]
$$\begin{aligned}t^{2} σ &= \frac{p^{2} σ + \frac{a σ + s^{2} σ}{s}}{p}\\t^{2} σ &= \frac{a σ}{p s} + p σ + \frac{s σ}{p}\\p σ&=- \frac{a σ}{p s} + t^{2} σ - \frac{s σ}{p}\end{aligned}$$