Ineed with this.
a quarterback takes the ball from the line of scrimmage, runs backward for 10.0 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. at this point, he throws a 50.0-yard forward pass straight down the field. what is the magnitude of the football’s resultant displacement?

with steps.

The magnitude of the football's resultant displacement is 42.72 yards.

The given parameters;

initial displacement backwards = 10 yardsfinal displacement forward = 50 yardsvertical displacement = 15 yards

The resultant horizontal displacement, x = 50 yards - 10 yards = 40 yards

The resultant vertical displacement, y = 15 yards

The magnitude of the football's resultant displacement is calculated by applying Pythagoras theorem as shown below;

R² = y² + x²

R² = 40² + 15²

R² = 1,825

R = √1,825

R = 42.72 yards

Thus, the magnitude of the football's resultant displacement is 42.72 yards.

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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.