One of the very useful series that show up in physics is the riemann zeta function 1 1 i ()5 4 32 where z > 1 (as you know, it does not converge for r 1). these series show up often in + +. (1) statistical mechanics, for example. show that u-1 du roo c)t(e (2) where the gamma function r() for r> 0 is given by r(z) jo (3) the integral in eq.(2) is related so-called bose-einstein integrals.

During physical science, ms. greene challenged her students to produce an energy transformation. james and jill wrapped a 4-inch nail with a coil of fifty turns of wire. they connected one end of the coil to one terminal of a knife switch. they connected the other terminal of the knife switch to the battery. finally, they connected the end of the coil to the other terminal of the battery. james held the tip of a 1-inch nail near the flat end of the 4-inch nail. jill closed the knife switch quickly and then opened it. the 1-inch nail was pulled toward the 4-inch nail. what is the best explanation of why the nail moved? a) electrical energy was converted to mechanical energy in the 1-inch nail. b) the 4-inch nail became an electromagnet and the magnetic force attracted the 1-inch nail. c) the electric current in the 4-inch nail was converted to mechanical energy in the 1-inch nail. d) the 4-inch nail had a positive charge and the 1-inch nail had a negative charge. opposites attracted.

An alligator swims to the left with a constant velocity of 5 \,\dfrac{\text{m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction. when the alligator sees a bird straight ahead, the alligator speeds up with a constant acceleration of 3 \,\dfrac{\text {m}}{\text s^2}3 s 2 m ? 3, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction leftward until it reaches a final velocity of 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction leftward. how many seconds does it take the alligator to speed up from 5 \,\dfrac{\text {m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction to 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction?

Ameter stick is pivoted at the 0.50-m line. a 3.0-kg object is hung from the 0.15-m line. where should a 5.0-kg object be hung to achieve equilibrium (the meter stick oriented horizontal and motionless)?