Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is approximated by the equation below. p(x) = 29.92e−0.2x (x ≥ 0) If the barometric pressure as measured by a hot-air balloonist is 20.5 in. of mercury, what is the balloonist's altitude?

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.