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.
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Sawa blessed, twende kazi. 8. Kiasi P ni sehemu isiyobadilika na sehemu inatofautiana kinyume na mraba wa t. Tunapewa kuwa P = k_1 + (k_2)/(t^2), ambapo k_1 na k_2 ni vigezo. Step 1: Tumia taarifa uliyopewa kuunda milinganyo miwili. Tunajua P=6 wakati t=6: 6 = k_1 + (k_2)/(6^2) 6 = k_1 + (k_2)/(36) (Mlinganyo 1) Tunajua P=18 wakati t=3: 18 = k_1 + (k_2)/(3^2) 18 = k_1 + (k_2)/(9) (Mlinganyo 2) Step 2: Tatua milinganyo miwili kwa k_1 na k_2. Toa Mlinganyo 1 kutoka Mlinganyo 2: (18 - 6) = (k_1 + (k_2)/(9)) - (k_1 + (k_2)/(36)) 12 = (k_2)/(9) - (k_2)/(36) Pata kigawo cha kawaida (LCM) cha 9 na 36, ambacho ni 36: 12 = (4k_2 - k_2)/(36) 12 = (3k_2)/(36) 12 = (k_2)/(12) Kisha, k_2 = 12 × 12 = 144. Badilisha thamani ya k_2 katika Mlinganyo 1: 6 = k_1 + (144)/(36) 6 = k_1 + 4 k_1 = 6 - 4 k_1 = 2 Kwa hiyo, uhusiano kati ya P na t ni P = 2 + (144)/(t^2). Step 3: Tafuta t wakati P=11. Badilisha P=11 katika mlinganyo: 11 = 2 + (144)/(t^2) 11 - 2 = (144)/(t^2) 9 = (144)/(t^2) t^2 = (144)/(9) t^2 = 16 t = ±sqrt(16) Kwa kuwa t kwa kawaida ni thamani chanya katika muktadha huu: t = 4 t = 4 9. Kokotoa thamani kamili ya 0.23 - 0.14. Step 1: Fanya hesabu ya kutoa. 0.23 - 0.14 = 0.09 0.09 That's 2 down. 3 left today — send the next one.