Respuesta :
Answer: The maximum depth that he will reach is -125 meters.
The first thing you should realize is that this is a quadratic equation and the graph will be a parabola.
We can simply the equation to:
y = (1/20)x^2 - 5x
Now, use -b/2a to find the x-value of the vertex which is 50. Then, input 50 back into the equation to get -125 for the maximum depth.
The first thing you should realize is that this is a quadratic equation and the graph will be a parabola.
We can simply the equation to:
y = (1/20)x^2 - 5x
Now, use -b/2a to find the x-value of the vertex which is 50. Then, input 50 back into the equation to get -125 for the maximum depth.
Answer:
-125 meters.
Step by step explanation:
We have been given that Guillermo is a professional deep water free diver. his altitude (in meters relative to sea level), x seconds after diving, is modeled by [tex]g(x)=\frac{1}{20}x(x-100)[/tex].
We have been given a quadratic function and the minimum value will occur at vertex.
First of all we will write it in standard quadratic form by using distribution property.
[tex]\frac{x^{2}}{20}-\frac{100x}{20}[/tex]
[tex]\frac{x^{2}}{20}-5x[/tex]
Now we will find vertex of our parabola using [tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-5)}{2(\frac{1}{20})}[/tex]
[tex]x=\frac{5}{(\frac{2}{20})}[/tex]
[tex]x=\frac{5\times20}{2}[/tex]
[tex]x=5\times10[/tex]
[tex]x=50[/tex]
Now let us substitute x=50 in our quadratic function to find lowest altitude of Guilermo.
[tex]g(50)=\frac{50^{2}}{20}-5\times 50[/tex]
[tex]g(50)=\frac{2500}{20}-250[/tex]
[tex]g(50)=125-250[/tex]
[tex]g(50)=-125[/tex]
Therefore, the lowest altitude Guilermo will reach is -125 meters.
