A swim team member performs a dive from a 14-foot high springboard. Her path is represented by the equation LaTeX: h\left(t\right)=-0.875t^2+5.25t+14h ( t ) = − 0.875 t 2 + 5.25 t + 14, where t is time in seconds and h is the height above the surface of the water. She needs to finish her flip no later than 5 feet above the surface of the water in order to prepare for the splash. What time does this happen? Round to the nearest tenth of a second.

7.4secs

Step-by-step explanation:

If the path of a swim team member is modeled by the equation

h(t) = -0.875t²+5.25t+14

where t is time in seconds and h is the height above the surface of the water

If she need to finish in no later than 5feet above the surface, the expression will become:

-0.875t²+5.25t+14≤5

-0.875t²+5.25t+14-5≤0

-0.875t²+5.25t+9≤0

Rewriting using fraction

-7/8t²+21/9t+9≤0

To get the time that this happens we will need to factorize the resulting expression above;

On factorising

Find the roots of the equation using the formulas

t = 3+3√105/7

t = 3+ 3(10.25)/7

t = 3 + (30.75)/7

t = 3 + 4.393

t = 7.393

t = 7.4secs

Hence this happens at t = 7.4secs