P(t)=(98-14t^1/3)dt eching

$$P ( t ) = ( 98 - 14 t ^ { 1 / 3 } ) d t$$

P uchun yechish (complex solution)

$$\left\{\begin{matrix}\\P=14\left(-\sqrt[3]{t}+7\right)d\text{, }&\text{unconditionally}\\P\in \mathrm{C}\text{, }&t=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

98-14t^{\frac{1}{3}} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=\left(98d-14t^{\frac{1}{3}}d\right)t$$

98d-14t^{\frac{1}{3}}d ga t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=98dt-14t^{\frac{1}{3}}dt$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{3} va 1 ni qo‘shib, \frac{4}{3} ni oling.

$$Pt=98dt-14t^{\frac{4}{3}}d$$

Tenglama standart shaklda.

$$tP=98dt-14dt^{\frac{4}{3}}$$

Ikki tarafini t ga bo‘ling.

$$\frac{tP}{t}=\frac{14\left(-\sqrt[3]{t}+7\right)dt}{t}$$

t ga bo'lish t ga ko'paytirishni bekor qiladi.

$$P=\frac{14\left(-\sqrt[3]{t}+7\right)dt}{t}$$

14td\left(7-\sqrt[3]{t}\right) ni t ga bo'lish.

$$P=14\left(-\sqrt[3]{t}+7\right)d$$

d uchun yechish (complex solution)

$$\left\{\begin{matrix}d=\frac{P}{14\left(-\sqrt[3]{t}+7\right)}\text{, }&t\neq 343\\d\in \mathrm{C}\text{, }&t=0\text{ or }\left(P=0\text{ and }t=343\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

98-14t^{\frac{1}{3}} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=\left(98d-14t^{\frac{1}{3}}d\right)t$$

98d-14t^{\frac{1}{3}}d ga t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=98dt-14t^{\frac{1}{3}}dt$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{3} va 1 ni qo‘shib, \frac{4}{3} ni oling.

$$Pt=98dt-14t^{\frac{4}{3}}d$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$98dt-14t^{\frac{4}{3}}d=Pt$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(98t-14t^{\frac{4}{3}}\right)d=Pt$$

Ikki tarafini 98t-14t^{\frac{4}{3}} ga bo‘ling.

$$\frac{\left(98t-14t^{\frac{4}{3}}\right)d}{98t-14t^{\frac{4}{3}}}=\frac{Pt}{98t-14t^{\frac{4}{3}}}$$

98t-14t^{\frac{4}{3}} ga bo'lish 98t-14t^{\frac{4}{3}} ga ko'paytirishni bekor qiladi.

$$d=\frac{Pt}{98t-14t^{\frac{4}{3}}}$$

Pt ni 98t-14t^{\frac{4}{3}} ga bo'lish.

$$d=\frac{P}{14\left(-\sqrt[3]{t}+7\right)}$$

P uchun yechish

$$\left\{\begin{matrix}\\P=14\left(-\sqrt[3]{t}+7\right)d\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&t=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

98-14t^{\frac{1}{3}} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=\left(98d-14t^{\frac{1}{3}}d\right)t$$

98d-14t^{\frac{1}{3}}d ga t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=98dt-14t^{\frac{1}{3}}dt$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{3} va 1 ni qo‘shib, \frac{4}{3} ni oling.

$$Pt=98dt-14t^{\frac{4}{3}}d$$

Tenglama standart shaklda.

$$tP=98dt-14dt^{\frac{4}{3}}$$

Ikki tarafini t ga bo‘ling.

$$\frac{tP}{t}=\frac{14\left(-\sqrt[3]{t}+7\right)dt}{t}$$

t ga bo'lish t ga ko'paytirishni bekor qiladi.

$$P=\frac{14\left(-\sqrt[3]{t}+7\right)dt}{t}$$

14td\left(7-\sqrt[3]{t}\right) ni t ga bo'lish.

$$P=14\left(-\sqrt[3]{t}+7\right)d$$

d uchun yechish

$$\left\{\begin{matrix}d=\frac{P}{14\left(-\sqrt[3]{t}+7\right)}\text{, }&t\neq 343\\d\in \mathrm{R}\text{, }&t=0\text{ or }\left(P=0\text{ and }t=343\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

98-14t^{\frac{1}{3}} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=\left(98d-14t^{\frac{1}{3}}d\right)t$$

98d-14t^{\frac{1}{3}}d ga t ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Pt=98dt-14t^{\frac{1}{3}}dt$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{3} va 1 ni qo‘shib, \frac{4}{3} ni oling.

$$Pt=98dt-14t^{\frac{4}{3}}d$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$98dt-14t^{\frac{4}{3}}d=Pt$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(98t-14t^{\frac{4}{3}}\right)d=Pt$$

Ikki tarafini 98t-14t^{\frac{4}{3}} ga bo‘ling.

$$\frac{\left(98t-14t^{\frac{4}{3}}\right)d}{98t-14t^{\frac{4}{3}}}=\frac{Pt}{98t-14t^{\frac{4}{3}}}$$

98t-14t^{\frac{4}{3}} ga bo'lish 98t-14t^{\frac{4}{3}} ga ko'paytirishni bekor qiladi.

$$d=\frac{Pt}{98t-14t^{\frac{4}{3}}}$$

Pt ni 98t-14t^{\frac{4}{3}} ga bo'lish.

$$d=\frac{P}{14\left(-\sqrt[3]{t}+7\right)}$$