Determining temperatures A meteorologist determines that the temperature T (in °F) for a c...

Determining temperatures A meteorologist determines that the temperature T (in °F) for a certain 24-hour period in winter was given by the formula  for 0 ≤ t ≤ 24, where t is time in hours and t =0 corresponds to 6 A.M.

(a) When was T > 0, and when was T < 0?

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(b) Sketch the graph of T.

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(c) Show that the temperature was 32°F sometime between 12 noon and 1 P.M. (Hint: Use the intermediate value theorem.)