To determine which glider reaches the greater maximum altitude in the first 6 seconds after launch, let's analyze the given functions for the altitudes of Melissa's and Robbie's gliders.
Melissa's glider altitude is given by the function:
[tex]\[
m(s) = 0.4 (s^3 - 11s^2 + 31s - 1)
\][/tex]
Robbie's glider altitude is modeled by the function [tex]\( r(s) \)[/tex], which is given as:
[tex]\[
r(s) = 0.5(s^2 - 8s + 20)
\][/tex]
We need to find the maximum altitudes for both gliders in the interval [tex]\(0 \leq s \leq 6\)[/tex].
1. Finding the maximum altitude for Melissa's glider [tex]\( m(s) \)[/tex]:
The function [tex]\( m(s) = 0.4 (s^3 - 11s^2 + 31s - 1) \)[/tex] must be evaluated within the interval from 0 to 6.
Based on the calculations, the maximum altitude reached by Melissa's glider is approximately:
[tex]\[
\max(m(s)) = 10.018387734090215 \text{ feet}
\][/tex]
2. Finding the maximum altitude for Robbie's glider [tex]\( r(s) \)[/tex]:
The function [tex]\( r(s) = 0.5 (s^2 - 8s + 20) \)[/tex] is also evaluated within the same interval from 0 to 6.
The maximum altitude reached by Robbie's glider is:
[tex]\[
\max(r(s)) = 10.0 \text{ feet}
\][/tex]
3. Comparing the maximum altitudes:
- Maximum altitude of Melissa's glider: [tex]\(10.0184 \text{ feet}\)[/tex]
- Maximum altitude of Robbie's glider: [tex]\(10.0 \text{ feet}\)[/tex]
Since [tex]\(10.0184 \text{ feet} > 10.0 \text{ feet}\)[/tex], Melissa's glider reaches a greater maximum altitude.
Based on this analysis, the correct answer is:
B. Melissa's glider
