The aspect ratio is used when calculating the aerodynamic efficiency of the wing of a plane. For a standard wing area, the function [tex]A(s)=\frac{s^2}{36}[/tex] can be used to find the aspect ratio depending on the wingspan in feet.

If one glider has an aspect ratio of 5.7, which system of equations and solution can be used to represent the wingspan of the glider? Round the solution to the nearest tenth if necessary.

A. [tex]y=\frac{s^2}{36}[/tex] and [tex]y=5.7[/tex]; [tex]s=14.3[/tex] feet
B. [tex]y=5.7 s^2[/tex] and [tex]y=36[/tex]; [tex]s=2.5[/tex] feet
C. [tex]y=36 s^2-5.7[/tex] and [tex]y=0[/tex]; [tex]s=0.4[/tex] feet
D. [tex]y=\frac{s^2}{36}+5.7[/tex] and [tex]y=0[/tex]; [tex]s=5.5[/tex] feet



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]