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${\displaystyle v(t)=v_{f}+(v_{i}-v_{f})e^{-t/RC}}$

${\displaystyle e^{-t/RC}={\frac {v(t)-v_{f}}{v_{i}-v_{f}}}}$

${\displaystyle -t/RC=\ln {\bigg (}{\frac {v(t)-v_{f}}{v_{i}-v_{f}}}{\bigg )}}$

${\displaystyle t=-RC\cdot \ln {\bigg (}{\frac {v(t)-v_{f}}{v_{i}-v_{f}}}{\bigg )}}$

${\displaystyle t=RC\cdot \ln {\Bigg (}{\frac {0-{\frac {10}{3}}}{0-{\frac {5}{3}}}}{\Bigg )}}$

${\displaystyle t=RC\cdot \ln {\bigg (}{\frac {v_{f}-v_{i}}{v_{f}-v(t)}}{\bigg )}}$

${\displaystyle t=RC\cdot \ln {\Bigg (}{\frac {5-{\frac {5}{3}}}{5-{\frac {10}{3}}}}{\Bigg )}}$

${\displaystyle t=RC\cdot \ln {\Bigg (}{\frac {10/3}{5/3}}{\Bigg )}}$

${\displaystyle f={\frac {1}{(R+2R')(C)\cdot \ln 2}}}$

${\displaystyle f={\frac {1}{R'C\cdot \ln 2+(R+R')\cdot \ln 2}}}$

${\displaystyle \oint _{s}\mathbf {E} \cdot \mathrm {d} \mathbf {A} ={\frac {Q_{enc}}{\varepsilon _{0}}}}$

${\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n+k)!}}}$

In electromagnetism, electric flux ${\displaystyle (\Phi _{E})}$ is defined as the dot product of an electric field ${\displaystyle (\mathbf {E} )}$ and the vector area ${\displaystyle (\mathbf {A} )}$ of a surface it passes through.

${\displaystyle \Phi _{E}=\mathbf {E} \cdot \mathbf {A} }$

In less formal terms, electric flux can be understood to represent the "amount of electric field" generated by a charge arrangement. If the electric field is not constant across a surface, the formula is better written as

${\displaystyle \Phi _{E}=\iint _{s}\mathbf {E} \cdot \mathrm {d} \mathbf {A} }$

where ${\displaystyle s}$ represents a closed surface and ${\displaystyle \Phi _{E}}$ represents the net electric flux flowing through it. ${\displaystyle \Phi _{E}}$ is directly proportional to the net charge enclosed by the surface ${\displaystyle (Q_{enc})}$. This can be seen through Gauss' Law:

${\displaystyle \oint _{s}\mathbf {E} \cdot \mathrm {d} \mathbf {A} ={\frac {Q_{enc}}{\varepsilon _{0}}}}$

where ${\displaystyle \varepsilon _{0}}$ represents the electric constant ${\displaystyle (\sim 8.85\times 10^{-12}\ {\text{F}}/{\text{m}})}$.

The SI unit for electric flux is the Volt metre (Vm).

${\displaystyle {\text{V}}\cdot {\text{m}}={\frac {{\text{N}}\cdot {\text{m}}^{2}}{\text{C}}}={\frac {{\text{kg}}\cdot {\text{m}}^{3}}{{\text{s}}^{3}\cdot {\text{A}}}}}$

${\displaystyle -\pi \int \limits _{4}^{8}{\big (}x-4{\big )}^{2}\ \mathrm {d} x}$

${\displaystyle -\pi \int \limits _{4}^{8}{\big (}x^{2}-8x+16{\big )}\ \mathrm {d} x}$

${\displaystyle -\pi {\bigg [}{\frac {1}{3}}x^{3}-4x^{2}+16x{\bigg ]}_{4}^{8}}$

${\displaystyle -\pi {\bigg [}{\bigg (}{\frac {1}{3}}(8)^{3}-4(8)^{2}+16(8){\bigg )}-{\bigg (}{\frac {1}{3}}(4)^{3}-4(4)^{2}+16(4){\bigg )}{\bigg ]}}$

${\displaystyle -\pi {\bigg (}{\frac {128}{3}}-{\frac {64}{3}}{\bigg )}}$

${\displaystyle -{\frac {64\pi }{3}}}$

${\displaystyle -\pi \int \limits _{4}^{8}{\big (}x-4{\big )}^{2}\ \mathrm {d} x}$

${\displaystyle -\pi \int \limits _{u(4)}^{u(8)}u^{2}\ \mathrm {d} u}$

${\displaystyle -\pi {\bigg [}{\frac {1}{3}}u^{3}{\bigg ]}_{0}^{4}}$

${\displaystyle -{\frac {\pi }{3}}{\Big (}4^{3}-0^{3}{\Big )}}$

${\displaystyle -{\frac {64\pi }{3}}}$

${\displaystyle {\frac {\sin x+x^{2}+{\frac {5}{x}}}{{\sqrt {x+1}}-\ln(x^{2})}}\cdot 2x^{3}}$

(sin(x) + x^2 + 5/x)/(sqrt(x+1)-ln(x^2))

${\displaystyle ((a)+(b)*(c))/(d)*(e)}$

${\displaystyle {\frac {a+b\times c}{d}}\times e}$

2 + (5(3 + a))