Løs 4pi^2x(15*10^9)^3/6*67*10^-11*3600*24*365

$$\frac { 4 \pi ^ { 2 } x ( 15 \times 10 ^ { 9 } ) ^ { 3 } } { 6 \cdot 67 \times 10 ^ { - 11 } \times 3600 \times 24 \times 365 }$$

Evaluer

$$\frac{1562500000000000000000000000000000000\pi ^{2}x}{14673}$$

Løsningstrinn

Eliminer 2\times 2 i både teller og nevner.

$$\frac{\pi ^{2}\times \left(15\times 10^{9}\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Regn ut 10 opphøyd i 9 og få 1000000000.

$$\frac{\pi ^{2}\times \left(15\times 1000000000\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multipliser 15 med 1000000000 for å få 15000000000.

$$\frac{\pi ^{2}\times 15000000000^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Regn ut 15000000000 opphøyd i 3 og få 3375000000000000000000000000000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multipliser 3 med 24 for å få 72.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{72\times 67\times 365\times 1800\times 10^{-11}}$$

Multipliser 72 med 67 for å få 4824.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{4824\times 365\times 1800\times 10^{-11}}$$

Multipliser 4824 med 365 for å få 1760760.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{1760760\times 1800\times 10^{-11}}$$

Multipliser 1760760 med 1800 for å få 3169368000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times 10^{-11}}$$

Regn ut 10 opphøyd i -11 og få \frac{1}{100000000000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times \frac{1}{100000000000}}$$

Multipliser 3169368000 med \frac{1}{100000000000} for å få \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{\frac{396171}{12500000}}$$

Del \pi ^{2}\times 3375000000000000000000000000000x på \frac{396171}{12500000} ved å multiplisere \pi ^{2}\times 3375000000000000000000000000000x med den resiproke verdien av \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x\times 12500000}{396171}$$

Multipliser 3375000000000000000000000000000 med 12500000 for å få 42187500000000000000000000000000000000.

$$\frac{\pi ^{2}\times 42187500000000000000000000000000000000x}{396171}$$

Del \pi ^{2}\times 42187500000000000000000000000000000000x på 396171 for å få \pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x.

$$\pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x$$

Utvid

$$\frac{1562500000000000000000000000000000000\pi ^{2}x}{14673}$$

Løsningstrinn

Eliminer 2\times 2 i både teller og nevner.

$$\frac{\pi ^{2}\times \left(15\times 10^{9}\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Regn ut 10 opphøyd i 9 og få 1000000000.

$$\frac{\pi ^{2}\times \left(15\times 1000000000\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multipliser 15 med 1000000000 for å få 15000000000.

$$\frac{\pi ^{2}\times 15000000000^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Regn ut 15000000000 opphøyd i 3 og få 3375000000000000000000000000000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multipliser 3 med 24 for å få 72.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{72\times 67\times 365\times 1800\times 10^{-11}}$$

Multipliser 72 med 67 for å få 4824.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{4824\times 365\times 1800\times 10^{-11}}$$

Multipliser 4824 med 365 for å få 1760760.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{1760760\times 1800\times 10^{-11}}$$

Multipliser 1760760 med 1800 for å få 3169368000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times 10^{-11}}$$

Regn ut 10 opphøyd i -11 og få \frac{1}{100000000000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times \frac{1}{100000000000}}$$

Multipliser 3169368000 med \frac{1}{100000000000} for å få \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{\frac{396171}{12500000}}$$

Del \pi ^{2}\times 3375000000000000000000000000000x på \frac{396171}{12500000} ved å multiplisere \pi ^{2}\times 3375000000000000000000000000000x med den resiproke verdien av \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x\times 12500000}{396171}$$

Multipliser 3375000000000000000000000000000 med 12500000 for å få 42187500000000000000000000000000000000.

$$\frac{\pi ^{2}\times 42187500000000000000000000000000000000x}{396171}$$

Del \pi ^{2}\times 42187500000000000000000000000000000000x på 396171 for å få \pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x.

$$\pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x$$