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A eq for the length of daylight (hrs) in NY on the tth day of the year is L(t)=12+2.8...

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sllysmith | Student, Undergraduate | (Level 2) eNoter

Posted March 6, 2012 at 6:57 AM via web

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A eq for the length of daylight (hrs) in NY on the tth day of the year is

L(t)=12+2.8 sin[2pi/365(t-80)]  ...in brackets[2 times pi over 365(t-80)]

Use this model to compare how the number of hours of daylight is increasing in NY on May 21 and June 15. (Assume there are 365 days in a year. Round your answers to four decimal places.)

may 21 L(t)=___

june 15 L(t)=___

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted March 6, 2012 at 7:59 PM (Answer #1)

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You should determine how many days passed by till May 21. Since the problem provides the information that there are 365 day in year, hence you need to consider only 28 days in February.

You need to add the number of days of each month to the 21 days of May month such that:

`t = 31+28+31+30+21`

t = 141 days

Substituting 141 for t in equation L(t) such that:

`L(141) = 12+2.8 sin[(2pi)/(365(141-80))]`

`L(141) = 12+2.8 sin((2pi)/22265)`

`L(141) = 12+2.8*5.6440`

`L(141) = 12.0015`

You should determine how many days passed by till June 15.

`t = 31 + 28 + 31 + 30 + 31 + 15`

`t = 166`

Substituting 166 for t in equation L(t) such that:

`L(166) = 12+2.8 sin[(2pi)/(365(166-80))]`

`L(166) = 12+2.8 sin((2pi)/31390)`

`L(166) = 12.0011`

Hence, evaluating the lengths of daylight in NYon May 21 and June 15 yields `L(141) = 12.0015 ` (May 21) and `L(166) = 12.0011` (June 15).

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