Question

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.

Answer 1

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

$h(t)=-16t^{2}+28t+17$

we know that

When the laptop hits the ground, the value of h(t) is equal to zero

so

For h(t)=0

$-16t^{2}+28t+17=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+28t+17=0$

so

$a=-16\\b=28\\c=17$

substitute in the formula

$x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}$

$x=\frac{-28(+/-)\sqrt{1,872}} {-32}$

$x=\frac{-28(+/-)12\sqrt{13}} {-32}$

$x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477$

$x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477$  ---> is not a solution

$x_2=\frac{-28(-)12\sqrt{13}} {-32}$

$x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec$

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

$0\ sec \leq x \leq 2.23\ sec$