According to a certain​ organization's 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.
Upper L plus 1.25 Upper S Superscript one half Baseline minus 9.8 Upper D Superscript one third Baseline equals 16.296
Find S for a boat with length 20.52 m and displacement 17.72 mcubed.

The equation given is:

\[
L + 1.25 \cdot \sqrt{S} - 9.8 \cdot D^{\frac{1}{3}} = 16.296
\]

You need to find \( S \) when the length \( L = 20.52 \, \text{m} \) and the displacement \( D = 17.72 \, \text{m}^3 \).

Let's substitute the known values of \( L \) and \( D \) into the equation and solve for \( S \).

\[
20.52 + 1.25 \cdot \sqrt{S} - 9.8 \cdot (17.72)^{\frac{1}{3}} = 16.296
\]

First, calculate \( 9.8 \cdot (17.72)^{\frac{1}{3}} \), and then solve for \( S \). I'll handle the calculations step by step.The sail area \( S \) for the boat with a length of 20.52 meters and a displacement of 17.72 cubic meters is approximately \( 291.05 \, \text{m}^2 \).

Would you like more details on the steps, or do you have any questions?

Here are some related questions to expand your understanding:
1. How does the displacement \( D \) affect the sail area in the equation?
2. What happens to the sail area \( S \) if the length of the boat is increased?
3. Can you solve for \( L \) if the sail area \( S \) and displacement \( D \) are known?
4. How would the formula change if a different coefficient is used for \( S^{1/2} \)?
5. What is the physical meaning of the cube root of displacement \( D \)?

**Tip:** When solving for variables under a square root, it's important to isolate the square root term before squaring both sides to avoid errors.

According to a certain organization's 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 + 1.25 * sqrt(S) - 9.8 * D^(1/3) = 16.296. Find S for a boat with length 20.52 m and displacement 17.72 m³.

Find the sail area of a boat using the equation L + 1.25 * sqrt(S) - 9.8 * D^(1/3) = 16.296, given a boat length of 20.52 m and a displacement of 17.72 m³. This problem involves algebraic manipulation and solving radical equations, suitable for high school students.

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