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3 Skryf 5880 as ' \( n \) produk van priemfaktore. 4erdeel R180 in de verhouding 1:6:2 ' \( n \) Motoris lê ' \( n \) afstand van 60 km af teen ' \( n \) spoed van \( 100 \mathrm{~km} / \mathrm{h} \). Hoe ver sal hy ry in dleselfde tyd indien hy teen \( 80 \mathrm{~km} / \mathrm{h} \) ry. Die verhouding van hokkle seuns tot hokkie dogters is \( 3: 8 \) by ' \( n \) sportsdag. Indlen daar 40 dogters was, hoeveel leerders was daar in totaal?

Ask by Reed Huang. in South Africa
Mar 11,2025

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1. \( 5880 = 2^3 \times 3 \times 5 \times 7^2 \) 2. R20, R120, R40 3. 48 km 4. 55 learners in total.

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The Deep Dive

Om 5880 as 'n produk van priemfaktore te skryf, begin ons deur dit te deel. Dit is 2 × 2 × 2 × 3 × 5 × 7. Dus, 5880 = \(2^3 \times 3^1 \times 5^1 \times 7^1\). Dit is soos die pragtige legkaart van priemfaktore wat saamkom om die eindresultaat te vorm! Vir die verdeling van R180 in die verhouding 1:6:2, moet ons eers die totale verhouding bereken: 1 + 6 + 2 = 9. Daarna deel ons die totale bedrag deur die totale verhouding: R180 / 9 = R20. Dus, die dele is R20 (1 deel), R120 (6 dele), en R40 (2 dele). 'n Lekker, gelyke verdeling vir almal! Om te bepaal hoe ver die motoris sal ry teen \(80 \mathrm{~km} / \mathrm{h}\) nadat hy 60 km teen \(100 \mathrm{~km} / \mathrm{h}\) gery het, bereken eers die tyd: 60 km / 100 km/h = 0.6 uur. As hy teen 80 km/h ry, sou hy in dieselfde tyd \(0.6 \times 80 = 48 \mathrm{~km}\) ry. So, meer waardevolle kilometers! Laastens, in die verhouding van hokkie seuns tot dogters (3:8), en met 40 dogters, beteken dat die seuns \( (3/8) \times 40 = 15\) seuns is. Totaal leerders: 40 + 15 = 55. 'n Hokkie festyn van gelukkige spelers!

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