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 21.91 m and displacement 18.92 m³.
the maximum sail area for a boat with length 21.91 m and displacement 18.92 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 $L = 21.91$ and $D=18.92$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$.
$21.91+1.25S^{\frac{1}{2}}-9.8\times18.92^{\frac{1}{3}} = 16.296$
First, calculate $18.92^{\frac{1}{3}}$.
$18.92^{\frac{1}{3}}\approx2.66677$ (rounded to five - decimal places)
Then, $9.8\times18.92^{\frac{1}{3}}\approx9.8\times2.66677 = 26.13435$
The equation becomes $21.91+1.25S^{\frac{1}{2}}-26.13435 = 16.296$.

Step2: Simplify the equation

Combine like - terms:
$1.25S^{\frac{1}{2}}=16.296+26.13435 - 21.91$
$1.25S^{\frac{1}{2}}=20.52035$

Step3: Solve for $S^{\frac{1}{2}}$

Divide both sides of the equation by 1.25:
$S^{\frac{1}{2}}=\frac{20.52035}{1.25}=16.41628$

Step4: Solve for $S$

Square both sides of the equation:
$S=(16.41628)^2\approx269.59$ (rounded to two decimal places)

Answer:

$269.59$