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 l + 1.25s^{\frac{1}{2}}-9.8d^{\frac{1}{3}} = 16.296. find s for a boat with length 21.08 m and displacement 18.20 m^{3}. the maximum sail area for a boat with length 21.08 m and displacement 18.20 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: Rearrange the given formula for S

Given $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.296$. First, isolate the term with S:
$1.25S^{\frac{1}{2}}=16.296 + 9.8D^{\frac{1}{3}}-L$.

Step2: Substitute the values of L and D

We have $L = 21.08$ m and $D = 18.20$ m³.
$D^{\frac{1}{3}}=18.20^{\frac{1}{3}}\approx2.63077$.
$9.8D^{\frac{1}{3}}=9.8\times2.63077 = 25.78155$.
$16.296+9.8D^{\frac{1}{3}}-L=16.296 + 25.78155-21.08=21.00755$.
So, $1.25S^{\frac{1}{2}}=21.00755$.

Step3: Solve for S

First, find $S^{\frac{1}{2}}$:
$S^{\frac{1}{2}}=\frac{21.00755}{1.25}=16.80604$.
Then square both sides to get S:
$S=(16.80604)^2\approx282.44$.

Answer:

$282.44$