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Evaluate the terms in the numerator.

Mathematics

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3 parts
d

4.8130\text{4.8130}

e

2.9256\text{2.9256}

f

157.3200\text{157.3200}

Step-by-step solution

12 steps

Here are the solutions to the problems.

Part d· 3 steps

  1. Evaluate the terms in the numerator.

    (1.789)4≈10.239601(1.789)^4 \approx 10.239601 (12.19)2≈148.5961(12.19)^2 \approx 148.5961

  2. Multiply the terms in the numerator.

    10.239601×148.5961≈1521.800910.239601 \times 148.5961 \approx 1521.8009

  3. Divide the numerator by the denominator.

    1521.8009316.2≈4.812969\frac{1521.8009}{316.2} \approx 4.812969

    Rounding to four decimal places:

    4.8130\boxed{\text{4.8130}}

Part e

2.9256\text{2.9256}

  1. Evaluate the square root and cube root in the numerator.

    151.8≈12.319172\sqrt{151.8} \approx 12.319172 73.853≈4.196963\sqrt[3]{73.85} \approx 4.196963

  2. Add the terms in the numerator.

    12.319172+4.196963=16.51613512.319172 + 4.196963 = 16.516135

  3. Evaluate the term in the denominator.

    2.3762≈5.6453762.376^2 \approx 5.645376

  4. Divide the numerator by the denominator.

    16.5161355.645376≈2.92560\frac{16.516135}{5.645376} \approx 2.92560

    Rounding to four decimal places:

    2.9256\boxed{\text{2.9256}}

Part f

157.3200\text{157.3200}

  1. Evaluate the terms in the numerator.

    (9.683)3≈906.9080(9.683)^3 \approx 906.9080 89.74≈9.473120\sqrt{89.74} \approx 9.473120

  2. Add the terms in the numerator.

    906.9080+9.473120=916.38112906.9080 + 9.473120 = 916.38112

  3. Evaluate the term inside the cube root in the denominator.

    (0.9437)2≈0.89057969(0.9437)^2 \approx 0.89057969 198.5−0.89057969=197.60942031198.5 - 0.89057969 = 197.60942031

  4. Evaluate the cube root in the denominator.

    197.609420313≈5.824809\sqrt[3]{197.60942031} \approx 5.824809

  5. Divide the numerator by the denominator.

    916.381125.824809≈157.3200\frac{916.38112}{5.824809} \approx 157.3200

    Rounding to four decimal places:

    157.3200\boxed{\text{157.3200}}
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