Question
When set off a certain firework follows the path of the quadratic function h = -25/36x^2 + 16 2/3x, where: h = the height of the firework in feet. x = the horizontal distance it travels in feet.
To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0 = -25/36x^2 + 16 2/3x.
A: 24 feet
B: 48 feet
C: 12 feet
D: 36 feet
To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0 = -25/36x^2 + 16 2/3x.
A: 24 feet
B: 48 feet
C: 12 feet
D: 36 feet
Answers
GPT-4o mini
To determine how far the firework will travel before reaching the ground, we need to solve the equation:
\[ 0 = -\frac{25}{36}x^2 + \frac{50}{3}x \]
This can be rewritten as:
\[ 0 = -\frac{25}{36}x^2 + \frac{50}{3}x \]
To clear the fraction, we can multiply the entire equation by 36:
\[ 0 = -25x^2 + 600x \]
Now, we can rewrite the equation:
\[ 25x^2 - 600x = 0 \]
Next, we can factor out \( 25x \):
\[ 25x(x - 24) = 0 \]
This gives us two solutions:
1. \( 25x = 0 \) which results in \( x = 0 \)
2. \( x - 24 = 0 \) which results in \( x = 24 \)
Since the problem is asking for the value of \( x \) when the firework reaches the ground, we find that:
**The firework will travel 24 feet before reaching the ground.**
Thus, the correct answer is **A: 24 feet**.
\[ 0 = -\frac{25}{36}x^2 + \frac{50}{3}x \]
This can be rewritten as:
\[ 0 = -\frac{25}{36}x^2 + \frac{50}{3}x \]
To clear the fraction, we can multiply the entire equation by 36:
\[ 0 = -25x^2 + 600x \]
Now, we can rewrite the equation:
\[ 25x^2 - 600x = 0 \]
Next, we can factor out \( 25x \):
\[ 25x(x - 24) = 0 \]
This gives us two solutions:
1. \( 25x = 0 \) which results in \( x = 0 \)
2. \( x - 24 = 0 \) which results in \( x = 24 \)
Since the problem is asking for the value of \( x \) when the firework reaches the ground, we find that:
**The firework will travel 24 feet before reaching the ground.**
Thus, the correct answer is **A: 24 feet**.