A golf ball is hit from the top of a tee. The quadratic equation
𝑦 = −5𝑥2 + 20𝑥 + 0.05 describes its height, 𝑦, in metres as time, 𝑥, in seconds
passes. Determine how long the ball is in the air
Use the quadratic formula.
The quadratic formula is:
𝑥 = (-𝑏 ± sqrt(𝑏^2 - 4𝑎𝑐)) / (2𝑎)
where 𝑎 = -5, 𝑏 = 20 and 𝑐 = 0.05
Plugging these values into the formula, we get:
𝑥 = (-20 ± sqrt(20^2 - 4(-5)(0.05))) / (2(-5))
Simplifying:
𝑥 = (-20 ± sqrt(404)) / (-10)
The two solutions are:
𝑥 ≈ 0.259 seconds and 𝑥 ≈ 3.841 seconds
Since the ball will hit the ground after some time, the only valid solution is:
𝑥 ≈ 3.841 seconds
Therefore, the ball is in the air for approximately 3.841 seconds.
Again , the bot seems to fall apart when it comes to arithmetic
I get x = (20 ± √401)/10 = appr -.0025 or 4.0025
I wonder if the bot can find the mistake, I can see it.
I will let the bot adjust its wrong answer to the correct one.
I apologize for my mistaken answer and any confusion it may have caused. You are correct, the correct solutions are approximately -0.0025 or 4.0025 seconds. Thank you for bringing this to my attention.
no bot!
those are the solutions for y =0.
What is the answer to the actual question??
I am sure "hala aly", the poster of this problem, has already figured it out
I'm sorry for misunderstanding your question earlier. To determine the time the ball is in the air, we need to find the time at which the ball hits the ground, which is when the height becomes 0. So, we need to solve the quadratic equation:
- 5𝑥^2 + 20𝑥 + 0.05 = 0
Using the quadratic formula, we get:
𝑥 = (-20 ± √(20^2 - 4(-5)(0.05))) / (2(-5))
= (-20 ± √(401)) / (-10)
≈ 0.0025 or 4.0025 (rounded to four decimal places)
Since the negative value is not meaningful in this context, the time the ball is in the air is approximately 4.0025 seconds.
Just noticed that this same question shows up in the right column under
"Related Questions" 3 times, and each time the bot got it wrong.
It was corrected once by oobleck once, but the other two slipped by
without anybody else looking at it.