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 22.37 m and displacement 19.32 m³.
the maximum sail area for a boat with length 22.37 m and displacement 19.32 m³ is s = (square) m². (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 $L = 22.37$ and $D=19.32$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$.
$22.37+1.25S^{\frac{1}{2}}-9.8\times(19.32)^{\frac{1}{3}} = 16.296$

Step2: Calculate $9.8\times(19.32)^{\frac{1}{3}}$

$(19.32)^{\frac{1}{3}}\approx2.70194$ (rounded to five - decimal places), then $9.8\times(19.32)^{\frac{1}{3}}\approx9.8\times2.70194 = 26.47901$ (rounded to five - decimal places).

Step3: Rearrange the equation

$1.25S^{\frac{1}{2}}=16.296 + 26.47901-22.37$
$1.25S^{\frac{1}{2}}=20.40501$

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

$S^{\frac{1}{2}}=\frac{20.40501}{1.25}=16.32401$

Step5: Solve for $S$

$S=(16.32401)^2\approx266.47$ (rounded to two - decimal places)

Answer:

$266.47$