In einstein's theory of special relativity the mass of an object moving with velocity v is m = m0 1 − v2/c2 where m0 is the mass of the object when at rest and c is the speed of light. the kinetic energy of the object is the difference between its total energy and its energy at rest: k = mc2 − m0c2. (a) show that when v is very small compared with c, this expression for k agrees with classical newtonian physics: k = 1 2 m0v2. (b) use taylor's inequality to estimate the difference in these expressions for k when |v| ≤ 50 m/s.

Researchers determine that the biodiversity in a woodland region is declining. they identify two major threats to the region's biodiversity, a method to address each threat, and the expected outcome of each method. this information is shown in the table. a) reforestation would not benefit many species because most forest species live on the ground. b) reforestation would take the longest time to be effective because trees take several years to grow. c) biological augmentation would benefit only a few species because is is typically not very effective. d) biological augmentation would take less time to ve effective because it targets the majority of prey species.