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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Swali la 15: Kizuizi cha mbao chenye vipimo vya 24cm kwa 48cm kwa 60cm kinakatwa kuwa idadi ndogo zaidi ya cubes zinazopatikana. Step 1: Tafuta urefu wa upande wa cube kubwa zaidi. Ili kupata idadi ndogo zaidi ya cubes, kila cube lazima iwe kubwa iwezekanavyo. Hii inamaanisha urefu wa upande wa cube lazima uwe kigawanyo kikubwa zaidi cha kawaida (GCD) cha vipimo vya kizuizi cha mbao. Vipimo ni 24 cm, 48 cm, na 60 cm. Tunatafuta GCD(24, 48, 60). Vigawanyo vya 24: 1, 2, 3, 4, 6, 8, 12, 24 Vigawanyo vya 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Vigawanyo vya 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Kigawanyo kikubwa zaidi cha kawaida ni 12. Kwa hivyo, urefu wa upande wa kila cube, s, ni 12 cm. Step 2: Kokotoa idadi ya cubes kwa kila mwelekeo. Idadi ya cubes kando ya urefu = 60 cm12 cm = 5 Idadi ya cubes kando ya upana = 48 cm12 cm = 4 Idadi ya cubes kando ya urefu = 24 cm12 cm = 2 Step 3: Kokotoa jumla ya idadi ya cubes. Jumla ya idadi ya cubes = (Idadi ya urefu) × (Idadi ya upana) × (Idadi ya urefu) Jumla ya idadi ya cubes = 5 × 4 × 2 = 40. 40 cubes Swali la 16: Kutokana na a = -2, b = -1 na c = 3, tathmini: (2(a + c)^2 - (a - b))/(3(a + b)) Step 1: Badilisha thamani za a, b, c kwenye usemi. (2((-2) + 3)^2 - ((-2) - (-1)))/(3((-2) + (-1))) Step 2: Rahisisha nambari (numerator). Kwanza, hesabu ndani ya mabano: a + c = -2 + 3 = 1 a - b = -2 - (-1) = -2 + 1 = -1 Sasa, badilisha hizi kwenye nambari: 2(1)^2 - (-1) 2(1) - (-1) 2 + 1 = 3 Kwa hivyo, nambari ni 3. Step 3: Rahisisha denomineta (denominator). Kwanza, hesabu ndani ya mabano: a + b = -2 + (-1) = -2 - 1 = -3 Sasa, badilisha hii kwenye denomineta: 3(-3) = -9 Kwa hivyo, denomineta ni -9. Step 4: Gawanya nambari kwa denomineta. (3)/(-9) = -(1)/(3) -(1)/(3) Kumbuka: Swali (b) "Determine his average speed" halina muktadha wa kutosha katika picha hii ili kutatuliwa. Drop the next question.