A hot-air balloon is 120 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 30 mi/hr (44 ft/s). if the balloon rises vertically at a rate of 8 ft/s, what is the rate of change of the distance between the motorcycle and the balloon 9 seconds later?

Aboy with a mass 25 kg climbs into a small tree. he sits on a branch that is 2.o m above to the ground. what is his gravitational potential energy above the ground?

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Ineed this now one scientist feels that the changes in global climatic patterns may be good for the health of the biosphere. another scientist feels that sharp changes in climatic patterns could result in the extinction of the biosphere. which of these is the most likely reason the two scientists gave conflicting opinions on the impact of changes in the global climatic pattern? they do not have enough knowledge on the topic. they did not discuss the issue among themselves. they believe conflicting opinion strengthens science. they study different areas of science and have different scientific focuses.