Tape recorders contain strips of thin plastic tape, which are covered in a layer of very fine iron dust. The iron dust reacts to a changing magnetic field and slightly rearranges itself on the tape, thereby recording the pattern generated by the changing magnetic field.

Aperson walks first at a constant speed of 4.89 m/s along a straight line from point a to point b and then back along the line from b to a at a constant speed of 2.95 m/s. what is the average speed over the entire trip?

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j

A60-gram sample of radioactive isotope is measured after two half-lives have passed. what pair of percentages describe the sample after two-half lives? a.) 50% unchanged and 50% stable b.) 25% unchanged and 75% stable c.) 12.5% unchanged and 87.5% stable d.) 75% unchanged and 25% stable