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^(1/2) - 9.8d^(1/3)=16.296. find s for a boat with length 20.88 m and displacement 18.03 m^3. the maximum sail area for a boat with length 20.88 m and displacement 18.03 m^3 is s = 289.23 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 values of L and D

Substitute $L = 20.88$ and $D=18.03$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$.
$20.88 + 1.25S^{\frac{1}{2}}-9.8\times(18.03)^{\frac{1}{3}}=16.296$

Step2: Calculate $9.8\times(18.03)^{\frac{1}{3}}$

$(18.03)^{\frac{1}{3}}\approx2.62177$, then $9.8\times(18.03)^{\frac{1}{3}}\approx9.8\times2.62177 = 25.69335$

Step3: Rearrange the equation to isolate $S^{\frac{1}{2}}$

$1.25S^{\frac{1}{2}}=16.296 + 25.69335-20.88$
$1.25S^{\frac{1}{2}}=21.10935$

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

$S^{\frac{1}{2}}=\frac{21.10935}{1.25}=16.88748$

Step5: Solve for S

$S=(16.88748)^2\approx285.19$

Answer:

$285.19$