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Solve for s in the equation sqrt(P) = rsqrt(1 − as2)

Mathematics

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Answer

s=±r2−Par2s = \pm\sqrt{\frac{r^2 - P}{ar^2}}

Step-by-step solution

5 steps

  1. Square both sides of the equation to eliminate the square roots.

    Given the formula:

    P=r1−as2\sqrt{P} = r\sqrt{1 - as^2}

    Square both sides:

    (P)2=(r1−as2)2(\sqrt{P})^2 = (r\sqrt{1 - as^2})^2 P=r2(1−as2)P = r^2(1 - as^2)

  2. Expand the right side of the equation.

    P=r2−ar2s2P = r^2 - ar^2s^2

  3. Rearrange the equation to isolate the term containing s2s^2.

    Move r2r^2 to the left side:

    P−r2=−ar2s2P - r^2 = -ar^2s^2

  4. Isolate s2s^2 by dividing both sides by −ar2-ar^2.

    P−r2−ar2=s2\frac{P - r^2}{-ar^2} = s^2

    To make the denominator positive, multiply the numerator and denominator by −1-1:

    s2=−(P−r2)−(−ar2)s^2 = \frac{-(P - r^2)}{-(-ar^2)} s2=r2−Par2s^2 = \frac{r^2 - P}{ar^2}

  5. Take the square root of both sides to solve for ss.

    s=±r2−Par2s = \pm\sqrt{\frac{r^2 - P}{ar^2}}
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