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Perform the following calculations: a) -81 + 0.79, b) 31 + (-16). Simplify: 2.1) 34, 2.2) 1.23, 2.3) 2.31.75. Calculate: 3.1) (62.4)1.3 - 173/85 + fourth_root(898)

Mathematics

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Answers

6 parts
a
-80.21
b
15
2.1
81
2.2
1.728
2.3
4.4170
3.1
247.9319

Step-by-step solution

11 steps

1. Do the following with the aid of a calculator

Part a· 1 step

  1. Add the numbers.

    −81+0.79=−80.21-81 + 0.79 = -80.21

    The result is:

    −80.21\boxed{-80.21}

Part b15

  1. Simplify the expression.

    Adding a negative number is equivalent to subtracting.

    31+(−16)=31−1631 + (-16) = 31 - 16
  2. Perform the subtraction.

    31−16=1531 - 16 = 15

    The result is:

    15\boxed{15}

    2. Simplify

Part 2.181

  1. Calculate 3 raised to the power of 4.

    34=3×3×3×33^4 = 3 \times 3 \times 3 \times 3
  2. Perform the multiplication.

    3×3=93 \times 3 = 9 9×3=279 \times 3 = 27 27×3=8127 \times 3 = 81

    The simplified value is:

    81\boxed{81}

Part 2.21.728

  1. Calculate 1.2 raised to the power of 3.

    1.23=1.2×1.2×1.21.2^3 = 1.2 \times 1.2 \times 1.2
  2. Perform the multiplication.

    1.2×1.2=1.441.2 \times 1.2 = 1.44 1.44×1.2=1.7281.44 \times 1.2 = 1.728

    The simplified value is:

    1.728\boxed{1.728}

Part 2.34.4170

  1. Calculate 2.3 raised to the power of 1.75.

    2.31.752.3^{1.75}

    Using a calculator:

    2.31.75≈4.41702.3^{1.75} \approx 4.4170

    The simplified value (rounded to four decimal places) is:

    4.4170\boxed{4.4170}

    3. Use the calculator to calculate

Part 3.1247.9319

  1. Calculate each term separately.

    First term: (62.4)1.3(62.4)^{1.3}

    (62.4)1.3≈251.3852(62.4)^{1.3} \approx 251.3852

    Second term: 17385\frac{173}{85}

    17385≈2.0353\frac{173}{85} \approx 2.0353

    Third term: 8984\sqrt[4]{898}

    8984=8981/4=8980.25≈5.4886\sqrt[4]{898} = 898^{1/4} = 898^{0.25} \approx 5.4886
  2. Substitute these values back into the expression.

    (62.4)1.3+17385−8984≈251.3852+2.0353−5.4886(62.4)^{1.3} + \frac{173}{85} - \sqrt[4]{898} \approx 251.3852 + 2.0353 - 5.4886
  3. Perform the addition and subtraction.

    251.3852+2.0353=253.4205251.3852 + 2.0353 = 253.4205 253.4205−5.4886=247.9319253.4205 - 5.4886 = 247.9319

    The final calculated value (rounded to four decimal places) is:

    247.9319\boxed{247.9319}
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