Simplify completely Water flows from a pipe at the rate of 250 li full of water measuring 3.2m by 2.5m by 2m tank completely.

Nambari ni $2x^2 + x - 3$. Tunaweza kuifactor kwa kutafuta namba mbili zinazozidisha $2 \times -3 = -6$ na kujumlisha 1. Namba hizo ni 3 na $-2$.

$$2x^2 + x - 3 = 2x^2 + 3x - 2x - 3$$ $$= x(2x + 3) - 1(2x + 3)$$ $$= (2x + 3)(x - 1)$$

Denominator ni $4x^2 - 9$. Hii ni tofauti ya miraba, $a^2 - b^2 = (a - b)(a + b)$.
Hapa, $a = 2x$ na $b = 3$.

$$4x^2 - 9 = (2x)^2 - 3^2 = (2x - 3)(2x + 3)$$

Sasa tunaweza kuandika upya sehemu na kufuta vigezo vinavyofanana.

$$\frac{(2x + 3)(x - 1)}{(2x - 3)(2x + 3)}$$

Futa $(2x + 3)$ kutoka juu na chini:

$$= \frac{x - 1}{2x - 3}$$

Jibu: $\boxed{\frac{x - 1}{2x - 3}}$

2. Maji hutiririka kutoka kwenye bomba kwa kiwango cha lita 250 kwa dakika kuingia kwenye tanki lililojaa maji lenye vipimo vya 3.2m kwa 2.5m kwa 2m. Hesabu muda unaochukua kujaza tanki kabisa.

Vipimo vya tanki ni urefu ($L$) = 3.2 m, upana ($W$) = 2.5 m, na kina ($H$) = 2 m.
Ujazo ($V$) wa tanki ni:

$$V = L \times W \times H$$ $$V = 3.2 \text{ m} \times 2.5 \text{ m} \times 2 \text{ m}$$ $$V = 16 \text{ m}^3$$

Tunajua kuwa $1 \text{ m}^3 = 1000 \text{ lita}$.

$$V = 16 \text{ m}^3 \times 1000 \text{ lita/m}^3$$ $$V = 16000 \text{ lita}$$

Kiwango cha mtiririko wa maji ni lita 250 kwa dakika.
Muda ($T$) = Ujazo wa tanki / Kiwango cha mtiririko

$$T = \frac{16000 \text{ lita}}{250 \text{ lita/dakika}}$$ $$T = 64 \text{ dakika}$$

Jibu: $\boxed{\text{64 dakika}}$