# calculus

A model for the length of daylight (in hours) in Philadelphia on the tth day of the year is
L(t) = 12 + 2.8 sin 2π/365(t − 80)

.
Use this model to compare how the number of hours of daylight is increasing in Philadelphia on April 21 and June 5. (Assume there are 365 days in a year. Round your answers to four decimal places.)
April 21 L'(t) =

June 5 L'(t) =

1. 👍 0
2. 👎 0
3. 👁 196
1. I took the first derivative and plug in April 21 = 111, and June 5 = 156 in t. got 0.0482 but its not correct

1. 👍 0
2. 👎 0
2. Assuming April 21 ----> 111
L(111) = 12 + 2.8 sin 2π/365(111 − 80)
= 12 + 2.8 sin 2π/365(31)
= 13.424...

But whatever setting, you should have known that 0.0482 was wrong
since sin(anything) lies between -1 and +1
then 2.8 sin 2π/365(t − 80)
must lie between -2.8 and 2.8
and when 12 is added to that, the only answers possible are those between 9.2 and 14.8

1. 👍 0
2. 👎 0
👨‍🏫
Reiny

## Similar Questions

1. ### Calculus Help

A model for the length of daylight (in hours) in Philadelphia on the tth day of the year is L(t) = 12 + 2.8 sin[(2π/365)(t − 80)]. Use this model to compare how the number of hours of daylight is increasing in Philadelphia on

2. ### trig

A city averages 14 hours of daylight in June, 10 in December, 12 in both March and September. Assume that the number of hours of daylight varies sinusoidally over a period of one year. Write an expression for n, the number of

3. ### finite math

Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model-A hibachi requires 3 lb of cast iron and 6 min of labor. To produce each model-B hibachi requires 4 lb of cast iron

4. ### The Graphical Method

A manufacturer produces two models of mountain bikes. Model A requires 5 hours of assembly time and 2 hours of painting time, and Model B requires 4 hours of assembly time and 3 hours of painting time. The maximum total weekly

1. ### Math

Brian was training to run a marathon. During the three day period before the race he decided he would train for 11 hours. If he trained for 2 3/5 hours first day and 2 9/10 second day, how many hours would he need to train third

2. ### math

The Wellbuilt Company produces two types of wood chippers, Deluxe and Economy. The Deluxe model requires 3 hours to assemble and ½ hour to paint, and the Economy model requires 2 hours to assemble and 1 hour to paint. The maximum

3. ### HISTORY

What impact did the Industrial Revolution have on Philadelphia? A. Philadelphia's population shrank, which increased the need for farmers. B. There was increased agricultural production around Philadelphia, justifying slavery. C.

4. ### Math

Soundex produces x Model A radios and y Model B radios. Model A requires 15 min of work on Assembly Line I and 10 min of work on Assembly Line II. Model B requires 10 min of work on Assembly Line I and 12 min of work on Assembly

1. ### science

The diagram shows when Summer is occurring in the Northern Hemisphere. At which position will the day with the shortest amount of daylight hours occur for the Northern Hemipshere? Diagram : A B sun D C I think D

2. ### Math

Ramundus is making a xylophone. So far, he has bars that are 1 3/4 feet 1 7/12 feet and 1 2/3 feet long. What is the length of the longest bar 3/4? Alana practiced dancing for 11/4 hours on Monday 19/8 hours on Wednesday and 2 3/5

3. ### Math:)

The data in the table represents the average number of daylight ours each month in Springfield in 2015, rounded to the nearest quarter-hour. Jan~9.5 hrs Feb~10.5 hrs Mar~12 hrs Apr~13.25 hrs May~14.5 hrs Jun~15 hrs Jul~14.75 hrs

4. ### Math- Trigonometry

The flowering of many commercially grown plants in greenhouses depends on the duration of natural darkness and daylight. Short-day plants, such as chrysanthemums, need 12 or more hours of darkness before they will start to bloom.