If each pole costs sh. 3,000, find the amount of money the school will spend on the poles.

Haya master, twende na maswali haya.

24.b) If each pole costs sh. 3,000, find the amount of money the school will spend on the poles.
Swali hili haliwezi kujibiwa kwa sababu idadi ya nguzo (poles) haijatolewa katika sehemu iliyotangulia ya swali.

25. The exterior angle of a regular polygon is 20% less than the interior angle.

• a) Work out the size of each exterior angle.

  • Hatua ya 1: Fafanua pembe za ndani na nje. Acha $I$ iwe pembe ya ndani na $E$ iwe pembe ya nje. Tunajua kuwa jumla ya pembe ya ndani na pembe ya nje ni $180^\circ$.

    $$I + E = 180^\circ$$

  • Hatua ya 2: Unda mlinganyo kulingana na taarifa iliyotolewa. Pembe ya nje ni 20% chini ya pembe ya ndani, ambayo inamaanisha $E = I - 0.20I$.

    $$E = 0.8I$$

  • Hatua ya 3: Tatua kwa pembe ya ndani ($I$). Badilisha $E$ katika mlinganyo wa kwanza:

    $$I + 0.8I = 180^\circ$$ $$1.8I = 180^\circ$$ $$I = \frac{180^\circ}{1.8}$$ $$I = 100^\circ$$

  • Hatua ya 4: Tatua kwa pembe ya nje ($E$). Tumia $E = 180^\circ - I$:

    $$E = 180^\circ - 100^\circ$$ $$E = 80^\circ$$

    Ukubwa wa kila pembe ya nje ni: $\boxed{\textbf{80}^\circ}$

• b) Calculate the sum of the interior angles.

  • Hatua ya 1: Tafuta idadi ya pande ($n$) za poligoni. Kwa poligoni ya kawaida, pembe ya nje $E = \frac{360^\circ}{n}$.

    $$80^\circ = \frac{360^\circ}{n}$$ $$n = \frac{360^\circ}{80^\circ}$$ $$n = 4.5$$

  • Hatua ya 2: Kokotoa jumla ya pembe za ndani. Jumla ya pembe za ndani za poligoni hutolewa na fomula $(n-2) \times 180^\circ$.

    $$\text{Jumla ya pembe za ndani} = (4.5 - 2) \times 180^\circ$$ $$\text{Jumla ya pembe za ndani} = 2.5 \times 180^\circ$$ $$\text{Jumla ya pembe za ndani} = 450^\circ$$

    Jumla ya pembe za ndani ni: $\boxed{\textbf{450}^\circ}$

26. A motorist travelled at a speed of 60km/h to cover a journey from Mbale to Kotido in 4 hours. On his way back to Mbale, he reduced the speed by 50% due to heavy rainfall. Calculate the average speed for the whole journey.

• Hatua ya 1: Kokotoa umbali kutoka Mbale hadi Kotido. Umbali = Kasi $\times$ Muda

  $$\text{Umbali (Mbale to Kotido)} = 60 \text{ km/h} \times 4 \text{ h} = 240 \text{ km}$$

• Hatua ya 2: Kokotoa kasi ya kurudi. Kasi ilipunguzwa kwa 50%.

  $$\text{Kasi ya kurudi} = 60 \text{ km/h} - (0.50 \times 60 \text{ km/h})$$ $$\text{Kasi ya kurudi} = 60 \text{ km/h} - 30 \text{ km/h} = 30 \text{ km/h}$$

• Hatua ya 3: Kokotoa muda wa kurudi. Umbali wa kurudi ni sawa na umbali wa kwenda, yaani 240 km.

  $$\text{Muda wa kurudi} = \frac{\text{Umbali}}{\text{Kasi}} = \frac{240 \text{ km}}{30 \text{ km/h}} = 8 \text{ h}$$

• Hatua ya 4: Kokotoa jumla ya umbali uliosafiri.

  $$\text{Jumla ya umbali} = \text{Umbali wa kwenda} + \text{Umbali wa kurudi}$$ $$\text{Jumla ya umbali} = 240 \text{ km} + 240 \text{ km} = 480 \text{ km}$$

• Hatua ya 5: Kokotoa jumla ya muda wa safari.

  $$\text{Jumla ya muda} = \text{Muda wa kwenda} + \text{Muda wa kurudi}$$ $$\text{Jumla ya muda} = 4 \text{ h} + 8 \text{ h} = 12 \text{ h}$$

• Hatua ya 6: Kokotoa kasi ya wastani kwa safari nzima. Kasi ya wastani = $\frac{\text{Jumla ya umbali}}{\text{Jumla ya muda}}$

  $$\text{Kasi ya wastani} = \frac{480 \text{ km}}{12 \text{ h}} = 40 \text{ km/h}$$

  Kasi ya wastani kwa safari nzima ni: $\boxed{\textbf{40 km/h}}$