Answer:
Guillermo reach his lowest altitude 50 sec after diving and the lowest altitude is -125 m
Step-by-step explanation:
Let
x -----> the time in seconds
y ----> altitude in meters
we have
[tex]g(x)=\frac{1}{20}x(x-100)[/tex]
[tex]g(x)=\frac{1}{20}x^{2}-5x[/tex]
This is a vertical parabola open upward
The vertex is a minimum
To find out the lowest altitude, find the vertex
Complete the square
Factor the leading coefficient
[tex]g(x)=\frac{1}{20}(x^{2}-100x)[/tex]
[tex]g(x)+125=\frac{1}{20}(x^{2}-100x+2,500)[/tex]
Rewrite as perfect square
[tex]g(x)+125=\frac{1}{20}(x-50)^{2}[/tex]
[tex]g(x)=\frac{1}{20}(x-50)^{2}-125[/tex]
The vertex is the point (50,-125)
therefore
Guillermo reach his lowest altitude 50 sec after diving and the lowest altitude is -125 m (below the sea level)
