Use mathematical tables to find the reciprocal of 0.0247, hence evaluate [3]3.0250.0247, correct to 2 decimal places.

Hapa kuna hatua za kutatua swali la 2: Sehemu (a): Kuamua kuratibu za T Tunatumia fomula ya sehemu kwa mgawanyiko wa ndani. Kuratibu za P ni (x_1, y_1) = (1, -2). Kuratibu za Q ni (x_2, y_2) = (4, 10). Uwiano ni m:n = 2:1. Step 1: Tumia fomula ya sehemu kupata kuratibu za T. T_x = (nx_1 + mx_2)/(m+n) = (1(1) + 2(4))/(2+1) = (1 + 8)/(3) = (9)/(3) = 3 T_y = (ny_1 + my_2)/(m+n) = (1(-2) + 2(10))/(2+1) = (-2 + 20)/(3) = (18)/(3) = 6 Kuratibu za T ni (3, 6). Sehemu (b) (i): Tafuta mteremko wa mstari ulio wima kwa PQ Step 2: Tafuta mteremko wa mstari PQ. m_PQ = (y_2 - y_1)/(x_2 - x_1) = (10 - (-2))/(4 - 1) = (10 + 2)/(3) = (12)/(3) = 4 Step 3: Tafuta mteremko wa mstari ulio wima kwa PQ. Mteremko wa mstari ulio wima ni hasi ya kinyume cha mteremko wa mstari wa asili. m_ = -(1)/(m_PQ) = -(1)/(4) Mteremko wa mstari ulio wima kwa PQ ni -(1)/(4). Sehemu (b) (ii): Kuamua mlinganyo wa mstari ulio wima kwa PQ na kupitia T Step 4: Tumia mteremko m_ na kuratibu za T (3, 6) kupata mlinganyo wa mstari. Tunatumia fomula ya pointi-mteremko: y - y_1 = m(x - x_1). y - 6 = -(1)/(4)(x - 3) Panua pande zote mbili kwa 4: 4(y - 6) = -(x - 3) 4y - 24 = -x + 3 Panga upya mlinganyo: x + 4y - 24 - 3 = 0 x + 4y - 27 = 0 Mlinganyo wa mstari ni x + 4y - 27 = 0. Sehemu (iii): Kokotoa umbali TR Step 5: Tafuta kuratibu za R ambapo mstari unakutana na mhimili wa y. Kwenye mhimili wa y, x = 0. Badilisha x=0 kwenye mlinganyo wa mstari x + 4y - 27 = 0. 0 + 4y - 27 = 0 4y = 27 y = (27)/(4) = 6.75 Kuratibu za R ni (0, 6.75). Step 6: Kokotoa umbali kati ya T (3, 6) na R (0, 6.75) kwa kutumia fomula ya umbali. D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) D = sqrt((0 - 3)^2 + (6.75 - 6)^2) D = sqrt((-3)^2 + (0.75)^2) D = sqrt(9 + 0.5625) D = sqrt(9.5625) D ≈ 3.092329 Umbali TR, kwa tarakimu tatu muhimu, ni 3.09. Tuma swali linalofuata 📸