Issolvi 3(9.81)=6.67(10^-11)(m/r^2)-(w^2)r

$$3 ( 9.81 ) = 6.67 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r$$

Solvi għal m

$$m=\frac{100000000000r^{2}\left(100rw^{2}+2943\right)}{667}$$

$$r\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'r^{2}.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}rr^{2}$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 1 u 2 biex tikseb 3.

$$3\times 9.81r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Immultiplika 3 u 9.81 biex tikseb 29.43.

$$29.43r^{2}=6.67\times 10^{-11}m-w^{2}r^{3}$$

Ikkalkula 10 bil-power ta' -11 u tikseb \frac{1}{100000000000}.

$$29.43r^{2}=6.67\times \frac{1}{100000000000}m-w^{2}r^{3}$$

Immultiplika 6.67 u \frac{1}{100000000000} biex tikseb \frac{667}{10000000000000}.

$$29.43r^{2}=\frac{667}{10000000000000}m-w^{2}r^{3}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{667}{10000000000000}m-w^{2}r^{3}=29.43r^{2}$$

Żid w^{2}r^{3} maż-żewġ naħat.

$$\frac{667}{10000000000000}m=29.43r^{2}+w^{2}r^{3}$$

L-ekwazzjoni hija f'forma standard.

$$\frac{667}{10000000000000}m=w^{2}r^{3}+\frac{2943r^{2}}{100}$$

Iddividi ż-żewġ naħat tal-ekwazzjoni b'\frac{667}{10000000000000}, li hija l-istess bħal multiplikazzjoni taż-żewġ naħat bir-reċiproku tal-frazzjoni.

$$\frac{\frac{667}{10000000000000}m}{\frac{667}{10000000000000}}=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Meta tiddividi b'\frac{667}{10000000000000} titneħħa l-multiplikazzjoni b'\frac{667}{10000000000000}.

$$m=\frac{r^{2}\left(rw^{2}+29.43\right)}{\frac{667}{10000000000000}}$$

Iddividi r^{2}\left(29.43+w^{2}r\right) b'\frac{667}{10000000000000} billi timmultiplika r^{2}\left(29.43+w^{2}r\right) bir-reċiproku ta' \frac{667}{10000000000000}.

$$m=\frac{10000000000000r^{2}\left(rw^{2}+29.43\right)}{667}$$