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}}=16.286
find s for a boat with length 21.45 m and displacement 18.52 m³.
the maximum sail area for a boat with length 21.45 m and displacement 18.52 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 $L = 21.45$ and $D=18.52$ into the equation $L + 1.25S^{\frac{1}{2}}-9.8D^{\frac{1}{3}}=16.286$.
$21.45 + 1.25S^{\frac{1}{2}}-9.8\times(18.52)^{\frac{1}{3}}=16.286$

Step2: Calculate $9.8\times(18.52)^{\frac{1}{3}}$

$(18.52)^{\frac{1}{3}}\approx2.64677$ (rounded to five - decimal places), then $9.8\times(18.52)^{\frac{1}{3}}\approx9.8\times2.64677 = 25.93835$ (rounded to five - decimal places).
The equation becomes $21.45 + 1.25S^{\frac{1}{2}}-25.93835 = 16.286$.

Step3: Simplify the left - hand side

$1.25S^{\frac{1}{2}}+(21.45 - 25.93835)=16.286$.
$1.25S^{\frac{1}{2}}-4.48835 = 16.286$.

Step4: Isolate the term with $S$

$1.25S^{\frac{1}{2}}=16.286 + 4.48835$.
$1.25S^{\frac{1}{2}}=20.77435$.

Step5: Solve for $S^{\frac{1}{2}}$

$S^{\frac{1}{2}}=\frac{20.77435}{1.25}=16.61948$.

Step6: Solve for $S$

$S=(16.61948)^2\approx276.22$ (rounded to two decimal places).

Answer:

$276.22$