Answer :
To solve this problem, follow these steps:
1. Understand the System of Equations:
To find the wingspan [tex]\( s \)[/tex] of the glider given that the aspect ratio [tex]\( A(s) \)[/tex] is 5.7, we need to set up the appropriate system of equations.
2. Given Function:
The function for the aspect ratio [tex]\( A(s) \)[/tex] is:
[tex]\[ A(s) = \frac{s^2}{36} \][/tex]
3. Set the Aspect Ratio Equal to 5.7:
According to the problem, the aspect ratio is given as 5.7. Thus, we set up the equation:
[tex]\[ \frac{s^2}{36} = 5.7 \][/tex]
4. Solve for [tex]\( s \)[/tex]:
To find the wingspan [tex]\( s \)[/tex], solve the equation:
[tex]\[ s^2 = 5.7 \times 36 \][/tex]
[tex]\[ s^2 = 205.2 \][/tex]
[tex]\[ s = \sqrt{205.2} \][/tex]
[tex]\[ s \approx 14.3 \text{ feet} \][/tex]
Here, we have rounded the solution to the nearest tenth.
5. Verify the System of Equations:
The correct system of equations which matches the calculation is:
[tex]\[ y = \frac{s^2}{36} \quad \text{and} \quad y = 5.7 \][/tex]
This corresponds to solving for [tex]\( s \)[/tex] when [tex]\( y = 5.7 \)[/tex]:
[tex]\[ y = 5.7 \quad \Rightarrow \quad s = 14.3 \text{ feet} \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{y = \frac{s^2}{36} \text{ and } y = 5.7; s = 14.3 \text{ feet}} \][/tex]
1. Understand the System of Equations:
To find the wingspan [tex]\( s \)[/tex] of the glider given that the aspect ratio [tex]\( A(s) \)[/tex] is 5.7, we need to set up the appropriate system of equations.
2. Given Function:
The function for the aspect ratio [tex]\( A(s) \)[/tex] is:
[tex]\[ A(s) = \frac{s^2}{36} \][/tex]
3. Set the Aspect Ratio Equal to 5.7:
According to the problem, the aspect ratio is given as 5.7. Thus, we set up the equation:
[tex]\[ \frac{s^2}{36} = 5.7 \][/tex]
4. Solve for [tex]\( s \)[/tex]:
To find the wingspan [tex]\( s \)[/tex], solve the equation:
[tex]\[ s^2 = 5.7 \times 36 \][/tex]
[tex]\[ s^2 = 205.2 \][/tex]
[tex]\[ s = \sqrt{205.2} \][/tex]
[tex]\[ s \approx 14.3 \text{ feet} \][/tex]
Here, we have rounded the solution to the nearest tenth.
5. Verify the System of Equations:
The correct system of equations which matches the calculation is:
[tex]\[ y = \frac{s^2}{36} \quad \text{and} \quad y = 5.7 \][/tex]
This corresponds to solving for [tex]\( s \)[/tex] when [tex]\( y = 5.7 \)[/tex]:
[tex]\[ y = 5.7 \quad \Rightarrow \quad s = 14.3 \text{ feet} \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{y = \frac{s^2}{36} \text{ and } y = 5.7; s = 14.3 \text{ feet}} \][/tex]
