The force required to compress a non-standard spring as a function of displacement from equilibrium  x  is given by the equation  f(x)  =  ax2  -  bx, where  a  =  45  n/m2,  b  =  8  n/m, and the positive  x  direction is in the compression direction of the spring. write a general equation in terms of given variables for the work required to compress thai spring from equilibrium to any point xp.

Matt is driving down 7th street. he drives 150 meters in 18 sec. assuming he doesn’t slow down or speed up, what is his speed?

The number of passengers who arrive at the platform of a subway station for the 10 am train is a random variable with a mean of 120 and a variance of 16. find the lower bound of the probability that there will be between 100 and 140 passengers (round off to second decimal place).

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants