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 ufumbuzi wa swali la 17 na 18: Swali la 17: Hatua ya 1: Andika mlinganyo wa uwiano. P inatofautiana moja kwa moja na mraba wa Q na kinyume na R. P = k (Q^2)/(R) Hatua ya 2: Tafuta thamani ya kigezo k kwa kutumia thamani zilizopewa (P=2, Q=4, R=6). 2 = k (4^2)/(6) 2 = k (16)/(6) 2 = k (8)/(3) k = (2 × 3)/(8) = (6)/(8) = (3)/(4) Hatua ya 3: Andika mlinganyo kamili wa P. P = (3)/(4) (Q^2)/(R) Hatua ya 4: Tafuta P wakati Q = 8 na R = 4. P = (3)/(4) (8^2)/(4) P = (3)/(4) (64)/(4) P = (3)/(4) × 16 P = 3 × 4 P = 12 Thamani ya P ni 12. Tuma swali linalofuata 📸 Swali la 18: Hatua ya 1: Andika mlinganyo wa uwiano wa sehemu. B inatofautiana kwa sehemu na mraba wa M na kwa sehemu na kinyume cha N. B = k_1 M^2 + k_2 (1)/(N) Hatua ya 2: Tumia seti ya kwanza ya thamani (M=2, N=(1)/(2), B=96) kuunda mlinganyo. 96 = k_1 (2)^2 + k_2 (1)/(1)2 96 = 4k_1 + 2k_2 (Mlinganyo 1) Hatua ya 3: Tumia seti ya pili ya thamani (M=3, N=2, B=46) kuunda mlinganyo mwingine. 46 = k_1 (3)^2 + k_2 (1)/(2) 46 = 9k_1 + (1)/(2)k_2 (Mlinganyo 2) Hatua ya 4: Tatua mfumo wa milinganyo kwa k_1 na k_2. Kutoka Mlinganyo 1, gawanya kwa 2: 48 = 2k_1 + k_2 k_2 = 48 - 2k_1 Badilisha k_2 kwenye Mlinganyo 2: 46 = 9k_1 + (1)/(2)(48 - 2k_1) 46 = 9k_1 + 24 - k_1 46 - 24 = 8k_1 22 = 8k_1 k_1 = (22)/(8) = (11)/(4) Sasa tafuta k_2: k_2 = 48 - 2((11)/(4)) = 48 - (11)/(2) = (96 - 11)/(2) = (85)/(2) Hatua ya 5: Andika usemi wa B kwa kutumia M na N. B = (11)/(4) M^2 + (85)/(2N) Usemi wa B kwa kutumia M na N ni B = (11)/(4) M^2 + (85)/(2N). 3 done, 2 left today. You're making progress.