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Evaluate to three decimal places: 2π√(98-1)/(32-2)

Mathematics

ScanSolve AI Answer

Answer

10.968

Step-by-step solution

4 steps

  1. Evaluate the fraction inside the square root.

    98.132.2≈3.0465838509\frac{98.1}{32.2} \approx 3.0465838509

  2. Calculate the square root of the result.

    3.0465838509≈1.74544690\sqrt{3.0465838509} \approx 1.74544690

  3. Multiply by 2π2\pi.

    2π×1.74544690≈2×3.1415926535×1.74544690≈10.9679992\pi \times 1.74544690 \approx 2 \times 3.1415926535 \times 1.74544690 \approx 10.967999

  4. Round the final answer to three decimal places.

    10.967999≈10.96810.967999 \approx 10.968

    The full calculation is:

    2π98.132.22\pi\sqrt{\frac{98.1}{32.2}} =2π3.046583850931677= 2\pi\sqrt{3.046583850931677} =2π×1.745446900119311= 2\pi \times 1.745446900119311 =3.141592653589793×3.490893800238622= 3.141592653589793 \times 3.490893800238622 =10.967999099...= 10.967999099...

    Rounding to three decimal places:

    10.96810.968
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