Question

the aspect ratio is used when calculating the aerodynamic efficiency of the wing of a plane. for a standard wing area, the function $a(s)=\frac{s^{2}}{36}$ 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 solution to the nearest tenth if necessary.

$y = \frac{s^{2}}{36}$ and $y = 5.7$; $s = 14.3$ feet

$y = 5.7s^{2}$ and $y = 36$; $s = 2.5$ feet

$y = 36s^{2}-5.7$ and $y = 0$; $s = 0.4$ feet

$y=\frac{s^{2}}{36}+5.7$ and $y = 0$; $s = 5.5$ feet

Explanation:

Step1: Set up the equation

We know that the aspect - ratio function is $A(s)=\frac{s^{2}}{36}$, and the aspect ratio $A(s) = 5.7$. So we set $y=\frac{s^{2}}{36}$ and $y = 5.7$. Then we have the equation $\frac{s^{2}}{36}=5.7$.

Step2: Solve for $s$

Multiply both sides of the equation $\frac{s^{2}}{36}=5.7$ by 36 to get $s^{2}=5.7\times36$. Then $s^{2}=205.2$. Take the square - root of both sides: $s=\pm\sqrt{205.2}$. Since the wingspan $s$ (a length) cannot be negative, we take the positive value. $s=\sqrt{205.2}\approx14.3$ feet.

Answer:

$y=\frac{s^{2}}{36}$ and $y = 5.7$; $s = 14.3$ feet