Answer:
2.2 seconds.
Step-by-step explanation:
We have been given that an astronaut on the moon drops a tool from the door of the landing ship. The quadratic function [tex]f(x)=-2x^2+10[/tex] models the height of the tool, in meters, after x seconds.
To find the time, it will take for the tool to hit the surface of moon, we will set [tex]f(x)=0[/tex] and solve for x as:
[tex]-2x^2+10=0[/tex]
[tex]-2x^2+10-10=0-10[/tex]
[tex]-2x^2=-10[/tex]
Divide both sides by negative 2:
[tex]\frac{-2x^2}{-2}=\frac{-10}{-2}[/tex]
[tex]x^2=5[/tex]
Now, we will take square root of both sides:
[tex]\sqrt{x^2}=\pm\sqrt{5}[/tex]
[tex]x=\pm 2.236067[/tex]
[tex]x\approx 2.2[/tex]
Since time cannot be negative therefore, it will take 2.2 seconds for the tool to hit the surface of the moon.
