Worksheet 6.1 - Integral As Net Change - Calculus Maximus Page 3
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9Calculus Maximus
WS 6.1: Integral as Net Change
Free Response. Show all integral set ups and include units when appropriate.
6. The temperature outside a house during a 24-hour period is given by
t
F t
80 10cos
, 0
t
24
12
Where
F t is measured in degrees Fahrenheit and t is measured in hours.
t
t
(a) Find the average temperature, to the nearest degree Fahrenheit, between
6
and
14
.
(b) An air conditioner cooled the house whenever the outside temperature was at or above 78 degrees
Fahrenheit. For what values of t was the air conditioner cooling the house?
(c) The cost of cooling the house accumulates at the rate of $0.05 per hour for each degree the outside
temperature exceeds 78 degrees Fahrenheit. What was the total cost, to the nearest cent, to cool the
house for this 24-hour period?
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