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Ili kujua ni lini mikono itakutana tena juu ya dial, tunahitaji kutafuta Kima cha Chini cha Shirika (LCM) cha muda wa kila mkono.

Mathematics

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Answer

24 sekunde\text{24 sekunde}

Step-by-step solution

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Kuna nambari inayokosekana katika Swali la (3). Inasema "mkono mmoja huzunguka kila sekunde 8, na mkono mwingine huzunguka kila sekunde." Nambari ya sekunde kwa mkono wa pili haipo.

Nitachukulia kuwa mkono wa pili huzunguka kila sekunde 6.

  1. Ili kujua ni lini mikono itakutana tena juu ya dial, tunahitaji kutafuta Kima cha Chini cha Shirika (LCM) cha muda wa kila mkono.

    Muda wa mkono wa kwanza ni sekunde 8.
    Muda wa mkono wa pili (kwa kudhani) ni sekunde 6.

  2. Tafuta nambari tasa za kila nambari.

    Kwa 8:

    8=2×4=2×2×2=238 = 2 \times 4 = 2 \times 2 \times 2 = 2^3

    Kwa 6:

    6=2×3=21×316 = 2 \times 3 = 2^1 \times 3^1
  3. Ili kupata LCM, chukua kila nambari tasa inayopatikana katika factorization zote na uichukue kwa nguvu yake kubwa zaidi.

    • Nambari tasa zinazoonekana ni 2 na 3.
    • Kwa nambari tasa 2: Nguvu kubwa zaidi ya 2 inayopatikana katika 8 (232^3) na 6 (212^1) ni 232^3.
    • Kwa nambari tasa 3: Nguvu kubwa zaidi ya 3 inayopatikana katika 8 (hakuna 313^1) na 6 (313^1) ni 313^1.
  4. Zidisha nambari tasa hizi (zilizochukuliwa kwa nguvu zao kubwa zaidi) pamoja ili kupata LCM.

    LCM(8,6)=23×31\text{LCM}(8, 6) = 2^3 \times 3^1 =8×3= 8 \times 3 =24= 24

    Mikono itakutana tena juu ya dial baada ya 24 sekunde\text{24 sekunde}.

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