User:Vincent525

$$\min \left\{\dfrac{k}{\sin{kt}}\left(-\dfrac{2}{3}t^3-50\right)\right\}$$

$$k \geq \dfrac{3}{20}\pi$$

$$\dfrac{4}{3}t^3+\dfrac{2a}{k}\sin{kt}+100 \ge 0$$

$$a\cdot\dfrac{\sin{kt}}{k} \ge -\dfrac{2}{3}t^3-50 $$

$$f(t) = \dfrac{k}{\sin{kt}}\left(-\dfrac{2}{3}t^3-50\right)$$

$$\tan{kt} = \dfrac{t}{3} + \dfrac{25}{t^2}$$

$$F = k_\mathrm{e} \frac{q_1q_2}{r^2} = \left(8.99\times10^9\,\mathrm{N\cdot m^2\cdot C^{-2}}\right)\cdot\dfrac{Q}{\left(2\times10^{-2}\,\mathrm{m}\right)^2}$$