This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Swali la 9: A line PQ = 12.5cm. By using another line, divide PQ into nine equal parts. Huu ni mchoro wa kijiometri. Hapa kuna hatua za kugawa mstari PQ katika sehemu tisa sawa: 1. Chora mstari PQ wenye urefu wa 12.5 cm. 2. Kutoka nukta P, chora mstari mwingine (ray) PR kwa pembe kali (acute angle) na mstari PQ. 3. Kutumia rula na dira (compass), weka alama tisa kwenye mstari PR, kuanzia P, kwa umbali sawa. Kwa mfano, unaweza kuweka alama kila 1 cm au umbali mwingine wowote unaofaa. Ziite P_1, P_2, P_3, , P_9. 4. Unganisha nukta ya mwisho ya alama kwenye PR (P_9) na nukta Q. Hivyo utapata mstari P_9Q. 5. Kutoka kila nukta nyingine (P_1, P_2, , P_8) kwenye mstari PR, chora mistari sambamba na P_9Q. Mistari hii itakata mstari PQ katika nukta nane. 6. Nukta hizi nane, pamoja na P na Q, zitagawa mstari PQ katika sehemu tisa sawa. Swali la 10: The sum of the interior angles of a polygon is 1980^. Find the number of sides the polygon has. Step 1: Tumia fomula ya jumla ya pembe za ndani za poligoni. Jumla ya pembe za ndani za poligoni yenye pande n inatolewa na fomula: S = (n-2) × 180^ Step 2: Badilisha thamani ya jumla ya pembe za ndani (S) kwenye fomula. Tunapewa S = 1980^. 1980^ = (n-2) × 180^ Step 3: Tatua kwa n. Gawanya pande zote mbili kwa 180^: (1980)/(180) = n-2 11 = n-2 Ongeza 2 kwa pande zote mbili: n = 11 + 2 n = 13 Idadi ya pande za poligoni ni 13. Swali la 11: The diagram below is a sketch of a rice field (not drawn to scale), use it to generate a surveyor's field book. (All measurements are in metres) Hapa chini ni kitabu cha shamba cha mpimaji (surveyor's field book) kulingana na mchoro uliotolewa. Mstari wa msingi (baseline) ni XY, na vipimo vyote viko katika mita. | Chainage (m) | Offset Left (m) | Offset Right (m) | Remarks | | :----------- | :-------------- | :--------------- | :------ | | 150 (Y) | 50 (E) | | To E | | 120 | 30 (D) | | To D | | 80 | 20 (C) | | To C | | 40 | 20 (B) | | To B | | 0 (X) | 30 (A) | | To A | Tuma swali linalofuata 📸