Question

the end of a hose was resting on the ground, pointing up an angle. sal measured the path of the water coming out of the hose and found that it could be modeled using the equation $f(x) = -0.3x^2 + 2x$, where $f(x)$ is the height of the path of the water above the ground, in feet, and $x$ is the horizontal distance of the path of the water from the end of the hose, in feet. when the water was 4 feet from the end of the hose, what was its height above the ground? \bigcirc 3.2 feet \bigcirc 4.8 feet \bigcirc 5.6 feet \bigcirc 6.8 feet

Explanation:

Step1: Identify the value of x

We know that x is the horizontal distance from the end of the hose, and here x = 4 feet.

Step2: Substitute x into the function

We substitute x = 4 into the function \( f(x)= - 0.3x^{2}+2x \).
First, calculate \( x^{2} \) when x = 4: \( 4^{2}=16 \)
Then, calculate \( -0.3x^{2} \): \( - 0.3\times16=-4.8 \)
Next, calculate \( 2x \): \( 2\times4 = 8 \)
Now, add these two results together: \( f(4)=-4.8 + 8=3.2 \)? Wait, no, wait, let's recalculate. Wait, \( -0.3\times16=-4.8 \), and \( 2\times4 = 8 \), so \( -4.8+8 = 3.2 \)? But wait, that seems low. Wait, no, maybe I made a mistake. Wait, no, let's do it again. \( f(x)=-0.3x^{2}+2x \), x = 4. So \( -0.3(4)^2+24=-0.316 + 8=-4.8+8 = 3.2 \). Wait, but the options have 3.2 as an option. Wait, but let me check again. Wait, maybe I misread the equation. The equation is \( f(x)=-0.3x^{2}+2x \). So when x = 4, \( -0.3(16)+8=-4.8 + 8 = 3.2 \). So the height is 3.2 feet.

Answer:

3.2 feet