A delivery company model fuel consumption using the rule F = (64 a7 b9) / (8a3 b3). a) Simplify using index laws.

Kwa kuwa siwezi kufanya kipimo halisi, siwezi kukupa thamani kamili ya pembe BAC.

9. Muuzaji analipwa kamisheni ya 8% kwa bidhaa zinazouzwa zaidi ya sh. 20,000. Katika mwezi mmoja, aliuza bidhaa zenye thamani ya 64,000 na mapato yake yote yalikuwa Ksh. 23120. Je, mshahara wake wa msingi ulikuwa kiasi gani?

Thamani ya bidhaa zinazostahiki kamisheni = Thamani ya bidhaa zilizouzwa - Kizingiti cha kamisheni

$$= \text{Ksh. } 64,000 - \text{Ksh. } 20,000$$ $$= \text{Ksh. } 44,000$$

Kamisheni = 8% ya Ksh. 44,000

$$= 0.08 \times 44,000$$ $$= \text{Ksh. } 3,520$$

Mshahara wa msingi = Mapato yote - Kamisheni

$$= \text{Ksh. } 23,120 - \text{Ksh. } 3,520$$ $$= \text{Ksh. } 19,600$$

Mshahara wake wa msingi ulikuwa:

$$\boxed{\text{Ksh. } 19,600}$$

10. Kampuni ya usafirishaji inatumia mfumo wa matumizi ya mafuta kwa kutumia kanuni ifuatayo:

$$F = \frac{64 a^7 b^9}{8 a^3 b^3}$$

a) Rahisisha kwa kutumia sheria za viashiria.

$$F = 8a^4b^6$$

Kanuni iliyorahisishwa ni:

$$\boxed{8a^4b^6}$$