Homework Help: 11th grade-Calculas

Posted by Anonymous on Sunday, April 5, 2009 at 8:54pm.

The number of hours of daylight D depends upon the latitude and the day t of the year and is given by the equation :
D(t)=12+Asin(((2pi)/(365))(t-80))

where A depends only on the latitude (and not t). for latitude 30 degress, A is about 2.3

1. When is the number of hours of daylight the greatest?
2.When is the number of hours of daylight the least?
3. When is the number of hours of daylight increasing at a rate of 2 minutes per day?
4. when is the number of hours of daylight decreasing at a rate of 2 min per day?

Can any one help me with any of these?
thanks a lot!

11th grade-Calculas - bobpursley, Sunday, April 5, 2009 at 9:05pm
Take the derivitive of D with respect to t. Set to zero, solve for the solutions. Those will be max/min day lengths. You can use the second derivitative to find out which.
for 3,4, set dD/dt equal to 2/60 and solve for t.
11th grade-Calculas - Anonymous, Sunday, April 5, 2009 at 9:37pm
wait to take the derivative, should i multiple out the stuff inside the ()?
11th grade-Calculas - Jacob, Thursday, April 23, 2009 at 10:51pm
dD/dt = A(2pi/365)*cos [(2pi/365)*(t-80)]
=0 for maximum or minimum

(2pi/365)*(t-80) = n*pi/2
when n=1 gives maximum , then (t-80) = 365/4, for minimum n = 3
and t-80 = 3*365/4

(3) = dD/dt = +2/60
(4) = dD/dt = -2/60

Answer this Question

Related Questions

calculus - The number of hours of daylight D depends upon the latitude and the ...
Math - The number of daylight hours in a day is harmonic. Suppose that in a ...
Trigonometry - The number of daylight hours in a day is harmonic. Suppose that ...
math - In Philadelphia the number of hours of daylight on day t (where t is the ...
trig - A city averages 14 hours of daylight in June, 10 in December, 12 in both ...
pre calc - Over the course of a year, the number of hours of daylight in ...
Calc..Help Please - A model for the length of daylight (in hours) in ...
Astronomy - Physics - Now, wait until the planet is at the winter solstice (12:...
Algerba - would you expect a positive, a negative, or no association between the...
homework - which locations have the greatest number of hours of daylight on june...

For Further Reading

First Name:
School Subject:
Answer: