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
Hapa kuna suluhisho la swali lako: Step 1: Andika uhusiano wa uwiano. P inatofautiana kwa pamoja na Q na mraba wa R. Hii inamaanisha: P = kQR^2 ambapo k ni kigezo cha uwiano. Step 2: Eleza mabadiliko katika Q na R. Tuseme maadili ya awali ni P_1, Q_1, R_1. Hivyo, P_1 = kQ_1R_1^2. Q imeongezeka kwa 10%, hivyo Q mpya (Q_2) ni: Q_2 = Q_1 + 0.10Q_1 = 1.10Q_1 R imepungua kwa 20%, hivyo R mpya (R_2) ni: R_2 = R_1 - 0.20R_1 = 0.80R_1 Step 3: Kokotoa P mpya (P_2). Badilisha Q_2 na R_2 kwenye mlinganyo wa uwiano: P_2 = kQ_2R_2^2 P_2 = k(1.10Q_1)(0.80R_1)^2 P_2 = k(1.10Q_1)(0.64R_1^2) P_2 = (1.10 × 0.64) kQ_1R_1^2 P_2 = 0.704 kQ_1R_1^2 Kwa kuwa P_1 = kQ_1R_1^2, tunaweza kubadilisha P_1 kwenye mlinganyo wa P_2: P_2 = 0.704 P_1 Step 4: Bainisha asilimia ya mabadiliko katika P. Asilimia ya mabadiliko inatolewa na fomula: Asilimia ya Mabadiliko = (P_2 - P_1)/(P_1) × 100\% Asilimia ya Mabadiliko = (0.704 P_1 - P_1)/(P_1) × 100\% Asilimia ya Mabadiliko = (0.704 - 1) × 100\% Asilimia ya Mabadiliko = -0.296 × 100\% Asilimia ya Mabadiliko = -29.6\% Asilimia hasi inaonyesha kupungua. Asilimia ya mabadiliko katika P ni: Kupungua kwa 29.6\% That's 2 down. 3 left today — send the next one.