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. How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.
• 4.30 m
• 160.56 m
• 160.23 m
• 13.94 m
I know it is 160 but can't find which one --.56 or .23
I get 160.56
just use the quadratic formula.
x = (-9.6 ±√(9.6^2 + 4(.06)(5.4)))/-.12
= (-9.6 ±√93.456)/-.12
= (-9.6 ±9.667)/-.12
= .067/-.12 or 19.267/.12
= -0.558 or 160.56
If you had plugged in bobpursley's data, you'd have seen that f(160.56) = 0.005, pretty close to zero.
Easy question. Put this in your google search window:
-.06*(160.23)^2 + 9.6*160.23)+5.4 =
does it equal zero? Verify by trying this:
-.06*(160.56)^2 + 9.6*160.56)+5.4 =
That did not help with the choices of .56 or .23
Any more help will be appreciated.
Well, well, well, it seems like this rocket is really taking off! And you're right, the rocket will land approximately 160 meters away from its starting point. But which one is it, 160.56 or 160.23? Let me tell you a little secret: rockets are great at aiming for whole numbers! So, forget about those little decimals and go with a nice and tidy 160 meters horizontally from the starting point. No need to complicate things, right? Just remember, rockets have a blast when they land in whole numbers!
To find the horizontal distance at which the rocket will land, we need to determine the value of x when y equals zero. This is because when the rocket lands, its height above the ground will be zero.
The equation given is y = –0.06x² + 9.6x + 5.4. To find the horizontal distance when y equals zero, we can set the equation equal to zero and solve for x.
0 = –0.06x² + 9.6x + 5.4
To solve this quadratic equation, we can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / 2a
In our case, a = -0.06, b = 9.6, and c = 5.4. Plugging these values into the quadratic formula, we can calculate the values of x.
x = (-9.6 ± √(9.6² - 4(-0.06)(5.4))) / (2(-0.06))
Simplifying further, we get:
x = (-9.6 ± √(92.16 + 1.3)) / (-0.12)
x = (-9.6 ± √93.46) / (-0.12)
Now we can calculate the two possible values of x:
x = (-9.6 + √93.46) / (-0.12) ≈ -1.4
x = (-9.6 - √93.46) / (-0.12) ≈ 160.23
Therefore, the rocket will land approximately 160.23 meters horizontally from its starting point.
Based on the provided options, the correct answer is: 160.23 m.