Write the Word or Phrase That Best Completes Each Statement $$\mathrm { d } = \mathrm { D } \tan \left[ \frac { \pi } { 2 } \left( 1 - \frac { 2 \mathrm { M } } { \mathrm { S } } \right) \right]$$

Short Answer

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The ground movement of an earthquake near a fault line is modeled by the equation
$$\mathrm { d } = \mathrm { D } \tan \left[ \frac { \pi } { 2 } \left( 1 - \frac { 2 \mathrm { M } } { \mathrm { S } } \right) \right]$$
where $\mathrm { M }$ is the horizontal movement (in meters) at a distance $\mathrm { d }$ (in kilometers) from the earthquake, $\mathrm { D }$ is the dep in kilometers) below the surface of the center of the earthquake, and $\mathrm { S }$ is the total horizontal displacement (also in meters) at the fault line. What is the horizontal movement 5 kilometers from an earthquake centered 3 kilometers the surface with a total horizontal displacement of 4 meters? Round the answer to the nearest $0.01$ meter.