Equations e = 1 2πε0 qd z3 and e = 1 2πε0 p z3 are approximations of the magnitude of the electric field of an electric dipole, at points along the dipole axis. consider a point p on that axis at distance z = 4.50d from the dipole center (where d is the separation distance between the particles of the dipole). let eappr be the magnitude of the field at point p as approximated by e = 1 2πε0 qd z3 and e = 1 2πε0 p z3 (electric dipole). let eact be the actual magnitude. by how much is the ratio eappr/eact less than 1?

Ahanging spring stretches by 35.0 cm when an object of mass 450 g is hung on it at rest. in this situation, we define its position as x = 0. the object is pulled down an additional 18.0 cm and released from rest to oscillate without friction. what is its position x at a moment 84.4 s later? express your answer in cm.

Atrain is traveling at 30.0 m/s relative to the ground in still air. the frequency of the note emitted by the train whistle is 262 hz. the speed of sound in air should be taken as 344 m/s. what frequency (f approach) is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it? what frequency (f recede) is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

If you divide a speed in miles per minute by 60, you get the same speed expressed in miles