Question

according to a certain organizations rules, the maximum sail area s for a boat with length l (in meters) and displacement d (in cubic meters) is determined by the equation given below. l + 1.25s^{\frac{1}{2}}-9.8d^{\frac{1}{3}}=16.296 find s for a boat with length 21.71 m and displacement 18.75 m^{3}. the maximum sail area for a boat with length 21.71 m and displacement 18.75 m^{3} is s = m^{2}. (round the final answer to two decimal places as needed. round all intermediate values to five decimal places as needed.)

Explanation:

Step1: Substitute given values

Substitute $L = 21.71$ and $D=18.75$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$.
$21.71+1.25S^{\frac{1}{2}}-9.8\times(18.75)^{\frac{1}{3}} = 16.296$

Step2: Calculate $D^{\frac{1}{3}}$

Calculate $(18.75)^{\frac{1}{3}}\approx2.65828$.
Then the equation becomes $21.71 + 1.25S^{\frac{1}{2}}-9.8\times2.65828=16.296$.

Step3: Simplify the left - hand side

$21.71+1.25S^{\frac{1}{2}} - 26.05114 = 16.296$.
$1.25S^{\frac{1}{2}}=16.296 + 26.05114 - 21.71$.
$1.25S^{\frac{1}{2}}=20.63714$.

Step4: Solve for $S^{\frac{1}{2}}$

$S^{\frac{1}{2}}=\frac{20.63714}{1.25}=16.50971$.

Step5: Solve for $S$

$S=(16.50971)^2\approx272.67$.

Answer:

$272.67$