Resolver frac{5*10^{-6}c*9*10^-6c}{4pi*1.0006*8.854*10^-12*c^2/Nm^2*1.5m}

$$\frac { 5 \cdot 10 ^ { - 6 } c \cdot 9 \cdot 10 ^ { - 6 } c } { 4 \pi \cdot 1.0006 \cdot 8.854 \cdot 10 ^ { - 12 } \cdot \frac { c ^ { 2 } } { N m ^ { 2 } } \cdot 1.5 m }$$

Calcular

$$\frac{18750000Nm}{22148281\pi }$$

Pasos da solución

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -6 e -6 para obter -12.

$$\frac{5\times 10^{-12}c\times 9c}{4\pi \times 1.0006\times 8.854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica c e c para obter c^{2}.

$$\frac{5\times 10^{-12}c^{2}\times 9}{4\pi \times 1.0006\times 8.854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Calcula 10 á potencia de -12 e obtén \frac{1}{1000000000000}.

$$\frac{5\times \frac{1}{1000000000000}c^{2}\times 9}{4\pi \times 1.0006\times 8.854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica 5 e \frac{1}{1000000000000} para obter \frac{1}{200000000000}.

$$\frac{\frac{1}{200000000000}c^{2}\times 9}{4\pi \times 1.0006\times 8.854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica \frac{1}{200000000000} e 9 para obter \frac{9}{200000000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{4\pi \times 1.0006\times 8.854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica 4 e 1.0006 para obter 4.0024.

$$\frac{\frac{9}{200000000000}c^{2}}{4.0024\pi \times 8.854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica 4.0024 e 8.854 para obter 35.4372496.

$$\frac{\frac{9}{200000000000}c^{2}}{35.4372496\pi \times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Calcula 10 á potencia de -12 e obtén \frac{1}{1000000000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{35.4372496\pi \times \frac{1}{1000000000000}\times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica 35.4372496 e \frac{1}{1000000000000} para obter \frac{22148281}{625000000000000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{22148281}{625000000000000000}\pi \times \frac{c^{2}}{Nm^{2}}\times 1.5m}$$

Multiplica \frac{22148281}{625000000000000000} e 1.5 para obter \frac{66444843}{1250000000000000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843}{1250000000000000000}\pi \times \frac{c^{2}}{Nm^{2}}m}$$

Multiplica \frac{66444843}{1250000000000000000} por \frac{c^{2}}{Nm^{2}} mediante a multiplicación do numerador polo numerador e do denominador polo denominador.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}}{1250000000000000000Nm^{2}}\pi m}$$

Expresa \frac{66444843c^{2}}{1250000000000000000Nm^{2}}m como unha única fracción.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}m}{1250000000000000000Nm^{2}}\pi }$$

Anula m no numerador e no denominador.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}}{1250000000000000000Nm}\pi }$$

Expresa \frac{66444843c^{2}}{1250000000000000000Nm}\pi como unha única fracción.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}\pi }{1250000000000000000Nm}}$$

Divide \frac{9}{200000000000}c^{2} entre \frac{66444843c^{2}\pi }{1250000000000000000Nm} mediante a multiplicación de \frac{9}{200000000000}c^{2} polo recíproco de \frac{66444843c^{2}\pi }{1250000000000000000Nm}.

$$\frac{\frac{9}{200000000000}c^{2}\times 1250000000000000000Nm}{66444843c^{2}\pi }$$

Anula c^{2} no numerador e no denominador.

$$\frac{\frac{9}{200000000000}\times 1250000000000000000Nm}{66444843\pi }$$

Multiplica \frac{9}{200000000000} e 1250000000000000000 para obter 56250000.

$$\frac{56250000Nm}{66444843\pi }$$

Anula 3 no numerador e no denominador.

$$\frac{18750000Nm}{22148281\pi }$$

Diferenciar w.r.t. N

$$\frac{18750000m}{22148281\pi }$$