3(981)=667(10^-11)(m/r^2)-(w^2)r eching

$$3 ( 981 ) = 667 ( 10 ^ { - 11 } ) ( \frac { m } { r ^ { 2 } } ) - ( w ^ { 2 } ) r$$

m uchun yechish

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

$$r\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini r^{2} ga ko'paytirish.

$$3\times 981r^{2}=667\times 10^{-11}m-w^{2}rr^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$3\times 981r^{2}=667\times 10^{-11}m-w^{2}r^{3}$$

2943 hosil qilish uchun 3 va 981 ni ko'paytirish.

$$2943r^{2}=667\times 10^{-11}m-w^{2}r^{3}$$

-11 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{100000000000} ni qiymatni oling.

$$2943r^{2}=667\times \frac{1}{100000000000}m-w^{2}r^{3}$$

\frac{667}{100000000000} hosil qilish uchun 667 va \frac{1}{100000000000} ni ko'paytirish.

$$2943r^{2}=\frac{667}{100000000000}m-w^{2}r^{3}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\frac{667}{100000000000}m-w^{2}r^{3}=2943r^{2}$$

w^{2}r^{3} ni ikki tarafga qo’shing.

$$\frac{667}{100000000000}m=2943r^{2}+w^{2}r^{3}$$

Tenglamaning ikki tarafini \frac{667}{100000000000} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

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

\frac{667}{100000000000} ga bo'lish \frac{667}{100000000000} ga ko'paytirishni bekor qiladi.

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

\left(2943+w^{2}r\right)r^{2} ni \frac{667}{100000000000} ga bo'lish \left(2943+w^{2}r\right)r^{2} ga k'paytirish \frac{667}{100000000000} ga qaytarish.

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