Acable that weighs 8 lb/ft is used to lift 900 lb of coal up a mine shaft 600 ft deep. find the work done. show how to approximate the required work by a riemann sum. (let x be the distance in feet below the top of the shaft. enter xi* as xi.)

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz.

5g of ammonium nitrate was dissolved in 60g of water in an insulated container. the temperature at the start of the reaction was 23.0°c and at the end it was 19.0°c. calculate the energy absorbed by the reaction.

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)