Question

Natalie found a tennis ball outside a tennis court. She picked up the ball and threw it over the 12-foot fence into the court. The height of the ball, h, and time t seconds is given by the equations h(t) = -16t^2 + 18t +5. Will she make it iver the fence?

Answer 1

Answer:

Natalie cannot make it over the fence.

Step-by-step explanation:

After reading the statement, we must demostrate if the following inequation is possible, that is:

$-16\cdot t^{2}+18\cdot t+5 \ge 12$

After some algebraic handling we find this equivalent expression:

$16\cdot t^{2}-18\cdot t +7\le 0$ (1)

The polynomial is factorized by the Quadratic Formula:

$\left(t-0.563-i\,0.348)\cdot (t-0.563+i\,0.348)\le 0$

Since all roots are complex, we conclude that Natalie cannot make it over the fence.