The temperature T in #""^oC# of a particular city during a 24 hour period can be modelled by #T = 10 + 8 sin 12 pi t# where t is the time in hours, with t = 0 corresponding to midday. Find the rate at which the temperature is changing at 4pm.?

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Answer 1 · 2018-05-23T11:19:26

#96^@C//hour#

#T=10+8sin12pit#

When it is #1200# time, #t=0#.

When it is #1600# time, #t=4#.

#(dT)/dt=96cos12pit#

When #t=4#,

#(dT)/dt=96cos48pi#
#color(white)((dT)/dt)=96#