Hot air is less dense than cool air, so hot air will rise above cool air. Increasing the air temperature inside a
hot air balloon makes it lighter than the surrounding air, so the balloon can lift up. The density of hot air is
about 0.25 kg/mº less than that of cool air, which means a cubic meter of hot air can lift about 0.25 kg.
What is the minimum volume of hot air needed to lift a hot air balloon carrying 500 kg?

Peter measures the angles in a triangle. he finds that the angles are 95, 10 and 75. is he correct? explain your answer

The graph represents f(x)=[x]+3. what is f(-2.2)?

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0