Question

An astronaut on the moon drops a tool from the door of the landing ship. The quadratic function f(x)=-2x^2+10 models the height of the tool, in meters, after x seconds. How long does it take the tool to hit the surface of the moon? Round your answer to the nearest tenth.

Answer 1

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 $f(x)=-2x^2+10$ 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 $f(x)=0$ and solve for x as:

$-2x^2+10=0$

$-2x^2+10-10=0-10$

$-2x^2=-10$

Divide both sides by negative 2:

$\frac{-2x^2}{-2}=\frac{-10}{-2}$

$x^2=5$

Now, we will take square root of both sides:

$\sqrt{x^2}=\pm\sqrt{5}$

$x=\pm 2.236067$

$x\approx 2.2$

Since time cannot be negative therefore, it will take 2.2 seconds for the tool to hit the surface of the moon.