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)?
Answers
Answer:
8
Step-by-step explanation:
The number of months that having average high temperature above freezing (32 F) is approximately for 3 months.
What is a function?A function is defined as a relation between a set of inputs having one output each. It is a set of permissible outputs with the property that each input is related to exactly one output.
For the given situation,
The function is [tex]t=21.55 cos(\frac{\pi }{6}(m-7) )+43.75[/tex]
The temperature for months are calculated using the function t.
Here m = 1 refers January,
m = 2 refers February and so on.
Now substitute m = 1 for January,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(1-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-6) )+43.75[/tex]
⇒ [tex]t=22.2[/tex]
For February m = 2,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(2-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-5) )+43.75[/tex]
⇒ [tex]t=25.08[/tex]
For march m = 3,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(3-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-4) )+43.75[/tex]
⇒ [tex]t=32.9[/tex]
For April m = 4,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(4-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-3) )+43.75[/tex]
⇒ [tex]t=43.75[/tex]
For May m = 5,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(5-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-2) )+43.75[/tex]
⇒ [tex]t=54.525[/tex]
For June m = 6,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(6-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-1) )+43.75[/tex]
⇒ [tex]t=62.41[/tex]
For July m = 7,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(7-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(0) )+43.75[/tex]
⇒ [tex]t=65.3[/tex]
For August m = 8,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(8-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(1) )+43.75[/tex]
⇒ [tex]t=62.41[/tex]
For September m = 9,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(9-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(2) )+43.75[/tex]
⇒ [tex]t=54.525[/tex]
For October m = 10,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(10-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(3) )+43.75[/tex]
⇒ [tex]t=43.75[/tex]
For November m = 11,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(11-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(4) )+43.75[/tex]
⇒ [tex]t=32.975[/tex]
For December m = 12,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(12-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(5) )+43.75[/tex]
⇒ [tex]t=25.087[/tex]
Thus from the above temperatures of each month, the temperature for three months are less than 32°F.
Hence we can conclude that the number of months that having average high temperature above freezing (32 F) is approximately for 3 months.
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