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Use square roots, reciprocal and square tables to evaluate to 4 significant figures the expression; (0.06458)^(1/2) + (2/(0.4327))3

Mathematics

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2 parts
14

56.89\text{56.89}

15

98.98\text{98.98}

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10 steps

Part 14· 5 steps

Tumia jedwali za namba tete (reciprocals) na namba za ujazo (cubes) kutathmini usemi ufuatao kwa tarakimu muhimu nne.

3(0.375)3−2981.7\frac{3}{(0.375)^3} - \frac{2}{981.7}
  1. Tafuta (0.375)3(0.375)^3.

    Kutoka jedwali la namba za ujazo, 3.753=52.7343753.75^3 = 52.734375.
    Hivyo, (0.375)3=(3.75×10−1)3=52.734375×10−3=0.052734(0.375)^3 = (3.75 \times 10^{-1})^3 = 52.734375 \times 10^{-3} = 0.052734. (Tunatumia tarakimu muhimu 5 kwa usahihi wa kati)

  2. Tafuta 3(0.375)3\frac{3}{(0.375)^3}.

    Hii ni sawa na 3×10.0527343 \times \frac{1}{0.052734}.
    Kutoka jedwali la namba tete, 10.052734≈18.9636\frac{1}{0.052734} \approx 18.9636.
    Hivyo, 3×18.9636=56.89083 \times 18.9636 = 56.8908.

  3. Tafuta 2981.7\frac{2}{981.7}.

    Hii ni sawa na 2×1981.72 \times \frac{1}{981.7}.
    Kutoka jedwali la namba tete, 1981.7≈0.00101864\frac{1}{981.7} \approx 0.00101864.
    Hivyo, 2×0.00101864=0.002037282 \times 0.00101864 = 0.00203728.

  4. Toa matokeo.

    56.8908−0.00203728=56.8887627256.8908 - 0.00203728 = 56.88876272.

  5. Zungusha jibu kwa tarakimu muhimu nne.

    56.88876272≈56.8956.88876272 \approx \boxed{\text{56.89}}

Part 15

98.98\text{98.98}

Tumia jedwali za mizizi ya mraba (square roots), namba tete (reciprocals) na namba za mraba (squares) kutathmini usemi ufuatao kwa tarakimu muhimu nne.

(0.06458)12+(20.4327)3(0.06458)^{\frac{1}{2}} + \left(\frac{2}{0.4327}\right)^3
  1. Tafuta (0.06458)12(0.06458)^{\frac{1}{2}}.

    Hii ni sawa na 0.06458\sqrt{0.06458}.
    Tunaweza kuandika 0.06458=6.458×10−2=6.458×10−1\sqrt{0.06458} = \sqrt{6.458 \times 10^{-2}} = \sqrt{6.458} \times 10^{-1}.
    Kutoka jedwali la mizizi ya mraba, 6.458≈2.54126\sqrt{6.458} \approx 2.54126.
    Hivyo, 0.06458≈2.54126×10−1=0.25413\sqrt{0.06458} \approx 2.54126 \times 10^{-1} = 0.25413. (Tunatumia tarakimu muhimu 5 kwa usahihi wa kati)

  2. Tafuta 10.4327\frac{1}{0.4327}.

    Kutoka jedwali la namba tete, 10.4327≈2.31107\frac{1}{0.4327} \approx 2.31107.

  3. Tafuta (20.4327)3\left(\frac{2}{0.4327}\right)^3.

    Kwanza, zidisha matokeo ya Hatua ya 2 kwa 2: 2×2.31107=4.622142 \times 2.31107 = 4.62214.
    Kisha, tafuta ujazo wa 4.62214.
    Kutoka jedwali la namba za ujazo, (4.62214)3≈98.728(4.62214)^3 \approx 98.728. (Tunatumia tarakimu muhimu 5 kwa usahihi wa kati)

  4. Jumlisha matokeo ya Hatua ya 1 na Hatua ya 3.

    0.25413+98.728=98.982130.25413 + 98.728 = 98.98213.

  5. Zungusha jibu kwa tarakimu muhimu nne.

    98.98213≈98.9898.98213 \approx \boxed{\text{98.98}}
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