Answer: [tex]3.47\ seconds[/tex]
Step-by-step explanation:
Given the following function:
[tex]f(x)= -16t^2+12.5t+150[/tex]
You need to follow these steps in order to solve the exercise:
1. Substitute [tex]f(x)=0[/tex]:
[tex]0= -16t^2+12.5t+150[/tex]
2. Now you need to apply the Quadratic formula. This is:
[tex]x=t=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
In this case, you can identify that:
[tex]a=-16\\b=12.5\\c=150[/tex]
Then, you can substitute these values into the formula:
[tex]t=\frac{-12.5\±\sqrt{(12.5)^2-4(-16)(150)}}{2(-16)}[/tex]
3. Evaluating, you get:
[tex]t_1=3.47\\\\t_2=-2.69[/tex]
4. You must choose the positive value. Then:
[tex]t=3.47\ seconds[/tex]
