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
a) Ili kujua kama dereva atakamatwa, tunahitaji kuangalia kasi yake. Polisi huwakamata madereva wanaosafiri kwa kasi zaidi ya 80 km/hr. Kasi ya sehemu ya kwanza ya safari: 60 km/hr. Kasi ya sehemu ya pili ya safari: 80 km/hr. Kwa kuwa hakuna kasi iliyo zaidi ya 80 km/hr (60 km/hr 80 km/hr na 80 km/hr 80 km/hr), dereva hatakamatwa. Dereva hatakamatwa. b) Tunatumia fomula ya umbali wa kusimama d = (s^2)/(200) + (s)/(10). Kupata umbali wa kusimama kwa s = 46 km/hr: Step 1: Badilisha s = 46 kwenye fomula. d = (46^2)/(200) + (46)/(10) Step 2: Kokotoa 46^2. d = (2116)/(200) + (46)/(10) Step 3: Gawanya na kurahisisha. d = 10.58 + 4.6 Step 4: Jumlisha. d = 15.18 m Umbali wa kusimama kwa 46 km/hr ni 15.18 m. Kupata umbali wa kusimama kwa s = 85 km/hr: Step 1: Badilisha s = 85 kwenye fomula. d = (85^2)/(200) + (85)/(10) Step 2: Kokotoa 85^2. d = (7225)/(200) + (85)/(10) Step 3: Gawanya na kurahisisha. d = 36.125 + 8.5 Step 4: Jumlisha. d = 44.625 m Umbali wa kusimama kwa 85 km/hr ni 44.625 m. Kupata kasi wakati umbali wa kusimama ni 35 m: Step 1: Badilisha d = 35 kwenye fomula. 35 = (s^2)/(200) + (s)/(10) Step 2: Zidisha pande zote mbili kwa 200 ili kuondoa vigawe. 35 × 200 = s^2 + (s)/(10) × 200 7000 = s^2 + 20s Step 3: Panga upya kuwa mlinganyo wa quadratic. s^2 + 20s - 7000 = 0 Step 4: Tumia fomula ya quadratic s = -b ± sqrt(b^2 - 4ac)2a, ambapo a=1, b=20, c=-7000. s = -20 ± sqrt(20^2 - 4(1)(-7000))2(1) s = -20 ± sqrt(400 + 28000)2 s = -20 ± sqrt(28400)2 Step 5: Kokotoa mzizi wa mraba. sqrt(28400) ≈ 168.5229 Step 6: Kokotoa maadili ya s. s_1 = (-20 + 168.5229)/(2) = (148.5229)/(2) ≈ 74.26145 s_2 = (-20 - 168.5229)/(2) = (-188.5229)/(2) ≈ -94.26145 Step 7: Chagua thamani chanya kwa sababu kasi haiwezi kuwa hasi. s ≈ 74.26 km/hr Kasi ambayo gari linasafiri ikiwa umbali wake wa kusimama ni 35 m ni 74.26 km/hr. Tuma swali linalofuata 📸