Suppose you wanted to "pull an Einstein," and create a static universe  in which the gravitational attraction of matter is exactly balanced by the gravitational repulsion of dark energy with equation-of-state parameter − 1/ 3 < wq < − 1 and energy density εq.

What is the necessary matter density (εm) required to produce a static universe, expressed in terms of εq and wq?

Will the curvature of this static universe be negative or positive?

What will be its radius of curvature, expressed in terms of εq and wq?

Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s