A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.06x² + 9.6x + 5.4, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.%0A%0AHow far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.

Question

A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.06x² + 9.6x + 5.4, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.%0A%0AHow far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.

Answer 1

To find how far horizontally from its starting point the rocket will land, we need to find the x-intercept of the equation. This represents the point where the rocket lands on the ground (y = 0).

So, we set y = 0 in the equation y = -0.06x^2 + 9.6x + 5.4 and solve for x:

0 = -0.06x^2 + 9.6x + 5.4

Solving this quadratic equation, we get two solutions:

x = 7.43 or x = 102.57

Since the rocket is launched from a roof into a large field, we are only interested in the positive solution. Therefore, the rocket will land approximately 102.57 meters horizontally from its starting point.

Rounded to the nearest hundredth, the rocket will land approximately 102.57 meters horizontally from its starting point.

Answer 2

the answers are either

4.30
160.56
161.12
13.94

Answer 3

To find how far horizontally from its starting point the rocket will land, we need to find the x-intercept of the equation y = -0.06x² + 9.6x + 5.4. This represents the point where the rocket lands on the ground (y = 0).

Setting y = 0 in the equation and solving for x:

0 = -0.06x² + 9.6x + 5.4

0 = -0.06x² + 9.6x + 5.4

Multiplying the equation by 100 to clear decimals:

0 = -6x² + 960x + 540

Rearranging the equation:

6x² - 960x - 540 = 0

Dividing the equation by 6 to simplify:

x² - 160x - 90 = 0

Now, we can solve for x using the quadratic formula:

x = [ -(-160) ± √((-160)² - 4(1)(-90)] / 2(1)
x = [ 160 ± √(25600 + 360) ] / 2
x = [ 160 ± √25960 ] / 2
x = [ 160 ± 161.12 ] / 2
x = (160 + 161.12) / 2 or x = (160 - 161.12) / 2
x = 321.12 / 2 or x = -1.12 / 2
x = 160.56 or x = -0.56

Since the rocket is launched in a large field, the solution of x = 160.56 is the correct answer.

Therefore, the rocket will land approximately 160.56 meters horizontally from its starting point. So, the correct answer is 160.56.