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 21.11 m and displacement 18.23 m^{3}. the maximum sail area for a boat with length 21.11 m and displacement 18.23 m^{3} is s = square 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 $L = 21.11$ and $D=18.23$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$.
$21.11+1.25S^{\frac{1}{2}}-9.8\times(18.23)^{\frac{1}{3}} = 16.296$

Step2: Calculate $9.8\times(18.23)^{\frac{1}{3}}$

$(18.23)^{\frac{1}{3}}\approx2.63197$ (rounded to five - decimal places), then $9.8\times(18.23)^{\frac{1}{3}}\approx9.8\times2.63197 = 25.79331$ (rounded to five - decimal places).

Step3: Rearrange the equation

$21.11+1.25S^{\frac{1}{2}}-25.79331 = 16.296$
$1.25S^{\frac{1}{2}}=16.296 + 25.79331-21.11$
$1.25S^{\frac{1}{2}}=20.97931$

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

$S^{\frac{1}{2}}=\frac{20.97931}{1.25}=16.783448$

Step5: Solve for $S$

$S=(16.783448)^2\approx281.68$ (rounded to two - decimal places)

Answer:

$281.68$