Aperson walks 4.0 kilometers north, then 4.0 kilometers west. his displacement is closest to

Use the Pythagoras for the magnitude and the tan^-1 x = -1 for the angle

displacement = 4^2 + 4^2 = 32 = 4 sqrt(2) =  5.65 km

angle is 135 degrees.

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.