Question 1029901: In Africa, the time for sunrise any day during the year can be shown as the formula:
t=-1.4sin[2pi/365 (d-75)] + 7
where t is the time in hours after midnight
and d is the number of the day in the year (forget leap year)
d=1 is Jan. 1st
a) What are the earliest and latest sunrise times (in Hr:Min format) during 1 year?
b) The servents birthday is on March 15th. Determine time (in Hr:min format) the sun rose on the day of the servents birthday.
c) Determine on which days (month/day) of the year the sun rose at 7:30 am?
2. The depth d of the water in a harbour, measured in meteres, t hours after midnight, can be approximated by the function d(t)=5cos(pi/12 t) + 11,
where 0 less than or equal - t- less than or equal 24
A ship, which requires a minimum depth of 8 meters to leave the harbour is docked at midnight. During which time interval within 24 hours can the ship not leave the dock?
Please explain in detail the steps to answering the questions thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In Africa, the time for sunrise any day during the year can be shown as the formula:t = -1.4sin[2pi/365(d-75)] + 7 where t is the time in hours after midnight and d is the number of the day in the year (forget leap year)
d=1 is Jan. 1st
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a) What are the earliest and latest sunrise times (in Hr:Min format) during 1 year?
earliest time is when t = 164 = 5:36 AM
latest is when t = 1 at 8:36AM
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b) The servants birthday is on March 15th. Determine time (in Hr:min format) the sun rose on the day of the servants birthday.
Mar 15 is day number 75 when t = 6.96 ; time = 6:58 AM
c) Determine on which days (month/day) of the year the sun rose at 7:30 am?
day 62 and day 272
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2. The depth d of the water in a harbour, measured in meteres, t hours after midnight, can be approximated by the function d(t)=5cos(pi/12 t) + 11,
where 0 less than or equal - t- less than or equal 24
A ship, which requires a minimum depth of 8 meters to leave the harbour is docked at midnight. During which time interval within 24 hours can the ship not leave the dock?
Ans:: 8:42AM till 15:36AM
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Cheers,
Stan H.
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