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
Huu hapa ni utatuzi wa swali la 2: Step 1: Bainisha vigezo na uandike fomula. Tunajua umbali D = 3120 km. Acha S_B iwe kasi ya lori B (km/h). Acha S_A iwe kasi ya lori A (km/h). Acha T_B iwe muda uliotumika na lori B (masaa). Acha T_A iwe muda uliotumika na lori A (masaa). Kutoka kwa swali, tunajua: • Kasi ya lori A ni 5 km/h haraka kuliko lori B: S_A = S_B + 5. • Lori B inachukua masaa 4 zaidi kuliko lori A: T_B = T_A + 4. • Fomula ya umbali, kasi na muda ni D = S × T, ambayo inaweza kuandikwa kama T = (D)/(S). Step 2: Andika milinganyo ya muda kwa kila lori. Kwa lori A: T_A = (D)/(S_A) = (3120)/(S_B + 5) Kwa lori B: T_B = (D)/(S_B) = (3120)/(S_B) Step 3: Unda mlinganyo kwa kutumia tofauti ya muda. Badilisha milinganyo ya T_A na T_B kwenye T_B = T_A + 4: (3120)/(S_B) = (3120)/(S_B + 5) + 4 Step 4: Tatua mlinganyo wa quadratic kwa S_B. Ili kuondoa sehemu, zidisha pande zote mbili za mlinganyo kwa S_B(S_B + 5): 3120(S_B + 5) = 3120S_B + 4S_B(S_B + 5) Panua mabano: 3120S_B + 15600 = 3120S_B + 4S_B^2 + 20S_B Toa 3120S_B kutoka pande zote mbili: 15600 = 4S_B^2 + 20S_B Panga upya mlinganyo katika fomu ya quadratic aS_B^2 + bS_B + c = 0: 4S_B^2 + 20S_B - 15600 = 0 Gawanya mlinganyo mzima kwa 4 ili kurahisisha: S_B^2 + 5S_B - 3900 = 0 Step 5: Tumia fomula ya quadratic kutatua kwa S_B. Tumia fomula ya quadratic S_B = -b ± sqrt(b^2 - 4ac)2a, ambapo a=1, b=5, c=-3900: S_B = -5 ± sqrt(5^2 - 4(1)(-3900))2(1) S_B = -5 ± sqrt(25 + 15600)2 S_B = -5 ± sqrt(15625)2 Kokotoa mzizi wa mraba: sqrt(15625) = 125. S_B = (-5 ± 125)/(2) Kuna suluhisho mbili zinazowezekana: S_B1 = (-5 + 125)/(2) = (120)/(2) = 60 S_B2 = (-5 - 125)/(2) = (-130)/(2) = -65 Kwa kuwa kasi haiwezi kuwa hasi, tunachagua thamani chanya. Kasi ya lori B ni 60 km/h. That's 2 down. 3 left today — send the next one.