4/3pir^3=h/3{left(175r/1right)}^3pi eching

$$\frac{ 4 }{ 3 } \pi { r }^{ 3 } = \frac{ h }{ 3 } { \left( \frac{ 175r }{ 1 } \right) }^{ 3 } \pi$$

h uchun yechish

$$\left\{\begin{matrix}\\h=\frac{4}{5359375}\approx 0,000000746\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&r=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\pi ni ikki tarafidan bekor qilish.

$$\frac{4}{3}r^{3}=\frac{h}{3}\times \left(\frac{175r}{1}\right)^{3}$$

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

$$4r^{3}=h\times \left(\frac{175r}{1}\right)^{3}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$4r^{3}=h\times \left(175r\right)^{3}$$

\left(175r\right)^{3} ni kengaytirish.

$$4r^{3}=h\times 175^{3}r^{3}$$

3 daraja ko‘rsatkichini 175 ga hisoblang va 5359375 ni qiymatni oling.

$$4r^{3}=h\times 5359375r^{3}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$h\times 5359375r^{3}=4r^{3}$$

Tenglama standart shaklda.

$$5359375r^{3}h=4r^{3}$$

Ikki tarafini 5359375r^{3} ga bo‘ling.

$$\frac{5359375r^{3}h}{5359375r^{3}}=\frac{4r^{3}}{5359375r^{3}}$$

5359375r^{3} ga bo'lish 5359375r^{3} ga ko'paytirishni bekor qiladi.

$$h=\frac{4r^{3}}{5359375r^{3}}$$

4r^{3} ni 5359375r^{3} ga bo'lish.

$$h=\frac{4}{5359375}$$

r uchun yechish

$$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&h=\frac{4}{5359375}\end{matrix}\right,$$