The position function of a ball dropped from the top of a $250-$meter tall building is given by $s(t)=250-4\mathrm{.}9t^2,$ where position $s$ is measured in meters and time $t$ is measured in seconds. Compute the average velocity of the ball over the given time intervals. Round your answers to eight decimal places.

Compute the average velocity of the ball over the given time intervals.

a$.5\mathrm{.}99,6$ : $$

b$.6,6\mathrm{.}01$ : $$

c$.5\mathrm{.}999,6$ : $$

d$.6,6\mathrm{.}001$ : $$

Guess the instantaneous velocity of the ball at $t=6.$