156k views
4 votes
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.

1 Answer

4 votes

Answer:

2.2 seconds.

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:


(-2x^2)/(-2)=(-10)/(-2)


x^2=5

Now, we will take square root of both sides:


√(x^2)=\pm√(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.

User Rohith R
by
6.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.