The function 1=21.55 cos m-7 +43.75models the average high temperature in degrees Fahrenheit each month b throughout the year in
Anchorage, Alaska, where m 1 for January and m 12 for December. Approximate y how many nmonths is the average high temperature above freezing (32 F)?
1 answer:
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Answer:
The value of x that maximizes the volume enclosed by this box is 0.46 inches
The maximum volume is 3.02 cubic inches
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The volume of the open-topped box is equal to
where
substitute
Convert to expanded form
using a graphing tool
Graph the cubic equation
Remember that
The domain for x is the interval -----> (0,1)
Because
If x>1
then
the width is negative (W=2-2x)
so
The maximum is the point (0.46,3.02)
see the attached figure
therefore
The value of x that maximizes the volume enclosed by this box is 0.46 inches
The maximum volume is 3.02 cubic inches
