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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Haya, twende tukasuluhishe swali hili hatua kwa hatua. a) Eneo halisi la kipande cha ardhi katika km^2 Step 1: Badilisha kiwango cha ramani kutoka cm hadi km. Kiwango cha ramani ni 1:250,000, ambayo inamaanisha 1 \, cm kwenye ramani inawakilisha 250,000 \, cm ardhini. Tunajua kuwa 100 \, cm = 1 \, m na 1000 \, m = 1 \, km. Hivyo, 250,000 \, cm = (250,000)/(100) \, m = 2,500 \, m. Na 2,500 \, m = (2,500)/(1000) \, km = 2.5 \, km. Kwa hiyo, 1 \, cm kwenye ramani inawakilisha 2.5 \, km ardhini. Step 2: Kokotoa eneo halisi. Kwa eneo, tunapiga mraba kiwango cha urefu. 1 \, cm^2 kwenye ramani inawakilisha (2.5 \, km)^2 ardhini. (2.5 \, km)^2 = 6.25 \, km^2. Eneo kwenye ramani ni 4 \, cm^2. Eneo halisi = Eneo kwenye ramani × (Kiwango cha eneo) Eneo halisi = 4 \, cm^2 × 6.25 \, (km^2)/(cm^2) = 25 \, km^2. Eneo halisi la kipande cha ardhi ni 25 km^2. b) Muda ambao matrekta yatatumia kulima ekari 10 Step 1: Tafuta kiwango cha kulima kwa kila trekta. Trekta A hulima ekari 1 kwa dakika 45. Kiwango cha A (R_A) = 1 \, ekari45 \, dakika. Trekta B hulima ekari 1 kwa dakika 20. Kiwango cha B (R_B) = 1 \, ekari20 \, dakika. Step 2: Tafuta kiwango cha kulima cha matrekta yote mawili yakifanya kazi pamoja. Kiwango cha pamoja (R_jumla) = R_A + R_B R_jumla = (1)/(45) + (1)/(20) \, ekari/dakika Ili kujumlisha sehemu hizi, tunatafuta kigawo cha kawaida kidogo (LCM) cha 45 na 20, ambacho ni 180. R_jumla = (1 × 4)/(45 × 4) + (1 × 9)/(20 × 9) = (4)/(180) + (9)/(180) = (13)/(180) \, ekari/dakika Step 3: Kokotoa muda unaohitajika kulima ekari 10. Muda = Jumla ya ardhiKiwango cha pamoja Muda = 10 \, ekari(13)/(180) \, ekari/dakika = 10 × (180)/(13) \, dakika = (1800)/(13) \, dakika Step 4: Badilisha muda kuwa masaa na dakika. (1800)/(13) \, dakika ≈ 138.46 \, dakika 138 dakika ni sawa na 2 masaa na 18 dakika (138 = 2 × 60 + 18). Sehemu iliyobaki ya dakika ni 0.46 × 60 ≈ 28 sekunde. Muda ambao matrekta yatatumia kulima ekari 10 ni takriban 2 masaa, 18 dakika na 28 sekunde. c) Tafuta bajeti yote ya kulima Step 1: Eleza michango kama sehemu ya bajeti yote. Acha bajeti yote iwe B. Mchango wa Clergy = (2)/(5) B. Mchango wa MP = (1)/(4) B. Step 2: Kokotoa sehemu ya bajeti iliyobaki baada ya michango ya Clergy na MP. Jumla ya michango ya Clergy na MP = (2)/(5) B + (1)/(4) B = ((8)/(20) + (5)/(20)) B = (13)/(20) B. Sehemu iliyobaki = B - (13)/(20) B = (7)/(20) B. Step 3: Kokotoa mchango wa wanachama wa kikundi. Wanachama wa kikundi huchangia nusu ya sehemu iliyobaki. Mchango wa wanachama wa kikundi = (1)/(2) × (7)/(20) B = (7)/(40) B. Step 4: Kokotoa jumla ya mchango wa wanachama wa kikundi kwa pesa. Kila mwanachama 1 kati ya 48 alichangia UGX 50,000. Jumla ya mchango wa wanachama wa kikundi = 48 × 50,000 \, UGX = 2,400,000 \, UGX. Step 5: Linganisha mchango wa wanachama wa kikundi na sehemu yake ya bajeti ili kupata bajeti yote. (7)/(40) B = 2,400,000 \, UGX B = 2,400,000 × (40)/(7) \, UGX B = (96,000,000)/(7) \, UGX B ≈ 13,714,285.71 \, UGX Tunazungusha hadi shilingi iliyo karibu zaidi. Bajeti yote ya kulima ni takriban UGX 13,714,286. Tuma swali linalofuata 📸