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 lako: 3. Pata eneo la uso wa tufe kubwa zaidi. Step 1: Eleza uhusiano kati ya ujazo na eneo la uso kwa vitu vinavyofanana. Kwa vitu viwili vinavyofanana, uwiano wa ujazo wao ni sawa na mchemraba wa uwiano wa vipimo vyao vya mstari, na uwiano wa eneo la uso wao ni sawa na mraba wa uwiano wa vipimo vyao vya mstari. Hii inamaanisha: (A_1)/(A_2) = ((V_1)/(V_2))^2/3 Ambapo A_1, A_2 ni maeneo ya uso na V_1, V_2 ni ujazo. Step 2: Badilisha ujazo uliotolewa ili kupata uwiano wa ujazo. Ujazo wa tufe kubwa (V_L) ni 4752 cm^3. Ujazo wa tufe ndogo (V_S) ni 1408 cm^3. Uwiano wa ujazo ni: (V_L)/(V_S) = (4752)/(1408) Kurahisisha uwiano huu: (4752)/(1408) = (27 × 176)/(8 × 176) = (27)/(8) Step 3: Kokotoa uwiano wa eneo la uso kwa kutumia uwiano wa ujazo. Tunatumia formula kutoka Hatua ya 1: (A_L)/(A_S) = ((V_L)/(V_S))^2/3 (A_L)/(A_S) = ((27)/(8))^2/3 Kwanza, tafuta mzizi wa tatu wa uwiano, kisha mraba matokeo: ((27)/(8))^1/3 = [3]27[3]8 = (3)/(2) Kisha, mraba matokeo: ((3)/(2))^2 = (3^2)/(2^2) = (9)/(4) Hivyo, uwiano wa eneo la uso ni (A_L)/(A_S) = (9)/(4). Step 4: Tumia eneo la uso wa tufe ndogo kupata eneo la uso wa tufe kubwa. Eneo la uso wa tufe ndogo (A_S) ni 352 cm^2. (A_L)/(352 cm)^2 = (9)/(4) A_L = 352 cm^2 × (9)/(4) A_L = (352 ÷ 4) × 9 A_L = 88 × 9 A_L = 792 cm^2 Eneo la uso wa tufe kubwa ni 792 cm^2. That's 2 down. 3 left today — send the next one.