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Melissa and Robbie are flying remote control gliders. The altitude of Melissa's glider, [tex]h(s)[/tex], in feet, is modeled by this function, where [tex]s[/tex] is time, in seconds, after launch:

[tex]
h(s) = 0.4(s^3 - 11s^2 + 31s - 1)
[/tex]

The altitude of Robbie's glider is modeled by function [tex]r[/tex], where [tex]s[/tex] is time, in seconds, after launch.

Which glider reaches the greater maximum altitude in the first 6 seconds after launch?

A. Both gliders reach the same altitude on the given interval.
B. Melissa's glider
C. Neither glider reaches a maximum altitude on the given interval.
D. Robbie's glider



Answer :

GinnyAnswer
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

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