Q:

Jack was so frustrated with his slow laptop that he threw it out of his second story window. The height, h, of the laptop at time t seconds can be given by the equation h(t)= -16t^2 + 28t + 17. Assuming the laptop hits the ground below, find the domain of the function.

Accepted Solution

A:
Answer:The domain of the function is the interval [0,2.23]see the explanationStep-by-step explanation:Lett ----> the time in secondsh(t) ----> the height of the laptop in unitswe have[tex]h(t)=-16t^{2}+28t+17[/tex]we know thatWhen the laptop hits the ground, the value of h(t) is equal to zerosoFor h(t)=0[tex]-16t^{2}+28t+17=0[/tex]Solve the quadratic equationThe 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] Β ---> 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] thereforeThe 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]