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 21.68 m and displacement 18.72 m^3. the maximum sail area for a boat with length 21.68 m and displacement 18.72 m^3 is s = 288.0 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 $L = 21.68$ and $D=18.72$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$.
$21.68+1.25S^{\frac{1}{2}}-9.8\times18.72^{\frac{1}{3}} = 16.296$

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

Calculate $18.72^{\frac{1}{3}}\approx2.65698$.
$21.68+1.25S^{\frac{1}{2}}-9.8\times2.65698 = 16.296$

Step3: Simplify the equation

$21.68+1.25S^{\frac{1}{2}} - 26.0384 = 16.296$.
$1.25S^{\frac{1}{2}}=16.296 + 26.0384-21.68$.
$1.25S^{\frac{1}{2}}=20.6544$.

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

$S^{\frac{1}{2}}=\frac{20.6544}{1.25}=16.52352$.

Step5: Solve for $S$

$S=(16.52352)^2\approx288.00$.

Answer:

$288.00$