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

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

I-evaluate

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

Mga Hakbang ng Solution

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang -6 at -6 para makuha ang -12.

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

I-multiply ang c at c para makuha ang c^{2}.

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

Kalkulahin ang 10 sa power ng -12 at kunin ang \frac{1}{1000000000000}.

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

I-multiply ang 5 at \frac{1}{1000000000000} para makuha ang \frac{1}{200000000000}.

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

I-multiply ang \frac{1}{200000000000} at 9 para makuha ang \frac{9}{200000000000}.

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

I-multiply ang 4 at 1.0006 para makuha ang 4.0024.

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

I-multiply ang 4.0024 at 8.854 para makuha ang 35.4372496.

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

Kalkulahin ang 10 sa power ng -12 at kunin ang \frac{1}{1000000000000}.

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

I-multiply ang 35.4372496 at \frac{1}{1000000000000} para makuha ang \frac{22148281}{625000000000000000}.

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

I-multiply ang \frac{22148281}{625000000000000000} at 1.5 para makuha ang \frac{66444843}{1250000000000000000}.

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

I-multiply ang \frac{66444843}{1250000000000000000} sa \frac{c^{2}}{Nm^{2}} sa pamamagitan ng pag-multiply ng numerator sa numerator at denominator sa denominator.

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

Ipakita ang \frac{66444843c^{2}}{1250000000000000000Nm^{2}}m bilang isang single fraction.

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

I-cancel out ang m sa parehong numerator at denominator.

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

Ipakita ang \frac{66444843c^{2}}{1250000000000000000Nm}\pi bilang isang single fraction.

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

I-divide ang \frac{9}{200000000000}c^{2} gamit ang \frac{66444843c^{2}\pi }{1250000000000000000Nm} sa pamamagitan ng pagmu-multiply sa \frac{9}{200000000000}c^{2} gamit ang reciprocal ng \frac{66444843c^{2}\pi }{1250000000000000000Nm}.

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

I-cancel out ang c^{2} sa parehong numerator at denominator.

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

I-multiply ang \frac{9}{200000000000} at 1250000000000000000 para makuha ang 56250000.

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

I-cancel out ang 3 sa parehong numerator at denominator.

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

I-differentiate ang w.r.t. N

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