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.
ScanSolve AI Answer
Tutatumia radius ya Dunia R = 6370 km na kwamba 1 nautical mile (nm) = 1.852 km. 1) Kokotoa umbali kati ya pointi P(40^ N, 15^ W) na Q(40^ N, 160^ W). Pointi zote mbili ziko kwenye latitudo moja ( = 40^ N). Tofauti ya longitudo () itakuwa: = 160^ - 15^ = 145^ Fomula ya umbali kando ya latitudo ni: D = ()/(360^) × 2 R a) Katika km: Step 1: Badilisha maadili kwenye fomula. D = (145^)/(360^) × 2 (6370 km) (40^) Step 2: Kokotoa. D = 0.402777... × 2 (6370 km) × 0.766044... D ≈ 12340.83 km D ≈ 12341 km b) Katika nm: Step 3: Badilisha umbali kutoka km kwenda nm. D_nm = D_km1.852 km/nm D_nm = 12340.83 km1.852 km/nm D_nm ≈ 6663.51 nm D_nm ≈ 6664 nm 2) Tafuta mzingo wa latitudo 70^ S. Latitudo ni = 70^. Fomula ya mzingo wa latitudo ni: C = 2 R a) Katika km: Step 1: Badilisha maadili kwenye fomula. C = 2 (6370 km) (70^) Step 2: Kokotoa. C = 2 (6370 km) × 0.342020... C ≈ 13680.84 km C ≈ 13681 km b) Katika nm: Step 3: Badilisha mzingo kutoka km kwenda nm. C_nm = C_km1.852 km/nm C_nm = 13680.84 km1.852 km/nm C_nm ≈ 7387.06 nm C_nm ≈ 7387 nm 3) Tafuta mzingo wa Tropiki ya Kansa (23(1)/(2)^ N). Latitudo ni = 23.5^. Fomula ya mzingo wa latitudo ni: C = 2 R a) Katika km: Step 1: Badilisha maadili kwenye fomula. C = 2 (6370 km) (23.5^) Step 2: Kokotoa. C = 2 (6370 km) × 0.917063... C ≈ 36706.70 km C ≈ 36707 km b) Katika nm: Step 3: Badilisha mzingo kutoka km kwenda nm. C_nm = C_km1.852 km/nm C_nm = 36706.70 km1.852 km/nm C_nm ≈ 19819.06 nm C_nm ≈ 19819 nm 4) Tafuta urefu wa sambamba kupitia (1^ S, 37^ E). Hii inamaanisha mzingo kamili wa latitudo 1^ S. Latitudo ni = 1^. Fomula ya mzingo wa latitudo ni: C = 2 R a) Katika km: Step 1: Badilisha maadili kwenye fomula. C = 2 (6370 km) (1^) Step 2: Kokotoa. C = 2 (6370 km) × 0.999847... C ≈ 40023.80 km C ≈ 40024 km b) Katika nm: Step 3: Badilisha mzingo kutoka km kwenda nm. C_nm = C_km1.852 km/nm C_nm = 40023.80 km1.852 km/nm C_nm ≈ 21611.12 nm C_nm ≈ 21611 nm Tuma swali linalofuata 📸