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Evaluate the value of x in 81^x+1 + 33x = 246

Mathematics

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Huu hapa ni ufumbuzi wa swali la 10:

a) Kokotoa thamani kamili ya R.

  1. Kokotoa thamani ya kigawanyo.

    0.003146−0.003130=0.0000160.003146 - 0.003130 = 0.000016
  2. Kokotoa thamani kamili ya R.

    R=10.000016R = \frac{1}{0.000016} R=116×10−6R = \frac{1}{16 \times 10^{-6}} R=10616R = \frac{10^6}{16} R=1,000,00016R = \frac{1,000,000}{16} R=62500R = 62500

    a) 62500\boxed{\text{62500}}

    b) Thamani ya kukadiria ya R inaweza kupatikana kwa kurekebisha kila desimali katika kigawanyo hadi sehemu 5 za desimali. Kokotoa:

    i) Thamani ya kukadiria

  3. Rekebisha kila desimali katika kigawanyo hadi sehemu 5 za desimali.

    0.003146 hadi sehemu 5 za desimali ni 0.00315 (kwa sababu tarakimu ya 6 ni 6, tunazungusha juu tarakimu ya 5).
    0.003130 hadi sehemu 5 za desimali ni 0.00313 (kwa sababu tarakimu ya 6 ni 0, tunaiacha tarakimu ya 5 kama ilivyo).

  4. Kokotoa kigawanyo kilichokadiriwa.

    0.00315−0.00313=0.000020.00315 - 0.00313 = 0.00002
  5. Kokotoa thamani ya kukadiria ya R.

    Rkadiriwa=10.00002R_{\text{kadiriwa}} = \frac{1}{0.00002} Rkadiriwa=12×10−5R_{\text{kadiriwa}} = \frac{1}{2 \times 10^{-5}} Rkadiriwa=1052R_{\text{kadiriwa}} = \frac{10^5}{2} Rkadiriwa=100,0002R_{\text{kadiriwa}} = \frac{100,000}{2} Rkadiriwa=50000R_{\text{kadiriwa}} = 50000

    b) i) 50000\boxed{\text{50000}}

    ii) Hitilafu iliyoletwa na ukadiriaji

  6. Kokotoa hitilafu kwa kutoa thamani ya kukadiria kutoka kwa thamani kamili.

    Hitilafu=∣Thamani kamili−Thamani ya kukadiria∣\text{Hitilafu} = |\text{Thamani kamili} - \text{Thamani ya kukadiria}| Hitilafu=∣62500−50000∣\text{Hitilafu} = |62500 - 50000| Hitilafu=12500\text{Hitilafu} = 12500

    b) ii) 12500\boxed{\text{12500}}

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