Answer:
The domain of the function is the interval [0,2.23]
see the explanation
Step-by-step explanation:
Let
t ----> the time in seconds
h(t) ----> the height of the laptop in units
we have
[tex]h(t)=-16t^{2}+28t+17[/tex]
we know that
When the laptop hits the ground, the value of h(t) is equal to zero
so
For h(t)=0
[tex]-16t^{2}+28t+17=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]-16t^{2}+28t+17=0[/tex]
so
[tex]a=-16\\b=28\\c=17[/tex]
substitute in the formula
[tex]x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}[/tex]
[tex]x=\frac{-28(+/-)\sqrt{1,872}} {-32}[/tex]
[tex]x=\frac{-28(+/-)12\sqrt{13}} {-32}[/tex]
[tex]x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477[/tex]
[tex]x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477[/tex] ---> is not a solution
[tex]x_2=\frac{-28(-)12\sqrt{13}} {-32}[/tex]
[tex]x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec[/tex]
therefore
The domain of the function is the interval [0,2.23]
All real numbers greater than or equal to 0 seconds and less than or equal to 2.23 seconds
[tex]0\ sec \leq x \leq 2.23\ sec[/tex]
